Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable. ======================================================================== # Uneven Growth: Automation's Impact on Income and Wealth Inequality Authors: Benjamin Moll (LSE), Lukasz Rachel (UCL), Pascual Restrepo (BU) Presented by: Benjamin Moll Venue: CAFFE — CEPR Advanced Forum in Financial Economics, 8 February 2022 Discussant: Laurent Calvet (EDHEC) Video: https://www.youtube.com/watch?v=5j97eHIJyMc&t=0s ## Talk (00:00:00 – 00:34:03) [00:00:04] A very warm welcome to everyone. And specially to our speaker for today. [00:00:10] Our speaker for today is Ben Moll from LSE. [00:00:15] And he's going to talk to us about a very important topic. [00:00:19] Uneven growth. Automation's impact on income and wealth inequality. [00:00:27] So Ben will speak for 30 minutes. Then Laurent Calvet from Edhec will discuss the paper for 30 minutes. [00:00:36] And then we'll have 15 minutes for questions. From the audience. [00:00:41] If you can turn on your videos, it'll be very nice so that we can see each other. [00:00:48] And feel that we are almost back. To a normal setup. Where we can have regular seminars. So with that Ben, the floor is all yours. [00:00:58] Excellent. Thank you. Uh. [00:01:01] Very much. Um. Really really great to be here and you know to connect with this uh. [00:01:07] Uh somewhat different group than the usual sort of macro crowd I hang out with. So I'm really keen to to uh you know looking forward to this conversation. So this is work with uh Lucas Rachel. Who was on the job market I guess last year is doing a post [00:01:21] doc at Princeton now and is going to UCL and Pascual Restrepo at uh Boston University. [00:01:28] Um. Okay. So our starting point is that. Sort of in the last 40 years in many developed countries we've seen. Uh a sort of empirical pattern that one may call sort of unevenly distributed [00:01:42] economic growth. Here's a uh graph to show you this for the United States. Um and this is the income distribution for the United States over time. So time on the x-axis. Different percentiles. Of the income distribution here and you [00:01:57] know what you obviously see is that basically the percentiles corresponding to the bottom of the distribution have basically stagnated over time, while at the top of the distribution, there has been much more growth in the [00:02:11] in the top percentiles. If you look, you know, further into the top of the distribution, say the 99th percentile, that's even more pronounced. [00:02:19] Okay. So, you know, obviously there's a question, you know, where does where does this come from? What explains this? [00:02:25] And there's a huge literature that argues that technology, so technological change, may affect wage inequality. Um and examples of this are the literature on skill-biased technological change and [00:02:39] the polarization of wages, for example. But, you know, not all income is labor income. [00:02:46] Capital income is also important in the data, particularly at the top of the distribution, where we've seen the largest increases in these incomes, as I've just shown you. [00:02:55] Um so, you know, what about capital income, and then also wealth, I guess you may wonder about. [00:03:02] Um which is ultimately what the capital income is derived from, I guess. [00:03:06] So, here's what we're going to do here in this paper. So, we're going to build a tractable framework um to study how technology determines not just the distribution of labor incomes, but more generally the distribution of total [00:03:19] incomes, including capital income and the wealth distribution, okay? And then we're going to use it to examine the distributional effects of automation technologies, meaning in particular technologies that [00:03:33] substitute labor for capital in production. So, think about robots and so on. I'll give some more concrete examples later. [00:03:42] Um Here's, I guess, our main argument in a nutshell, and that argument is that technology doesn't only affect relative wages like in the standard you [00:03:56] know labor theories but technology may also affect returns to wealth and that may then have distributional consequences. Okay? In our particular theory it's sort of going to be an analytical [00:04:09] model as I said there's a there's a very simple but also somewhat specific version of this. [00:04:14] The way it's going to work out is there's going to be one sort of common return to wealth in the in the baseline theory and then the way it's going to look is basically if you're familiar with the neoclassical [00:04:28] growth model the return to wealth is going to have the same formula as in the standard neoclassical growth model. So the the discount rate plus then something having to do with long run growth but then there's going to be an [00:04:40] additional term okay and this additional term is going to have something to do with automation. [00:04:47] More precisely there's going to be this sort of a return premium here which is going to depend on the capital share in the economy and that capital share is also as we're going to show going to be the right measure [00:05:01] that summarizes sort of how much automation there's been in this economy. [00:05:06] Okay? So you can see and so this is an increasing function so returns to wealth are going to be increasing if automation and the capital share increase. [00:05:15] This is then going to have immediately a bunch of distributional consequences of automation. So there's going to be you know first of all a a result distributional effect via wages okay not [00:05:30] just via relative wages but via the level of wages. In particular what's going to happen in this economy is that you know rather than investment increasing a lot when there's [00:05:44] automation what's instead going to happen is some of this increase in in in automation is going to show up in returns to wealth and that's going to on the flip side of it show up as stagnant wages at the [00:05:58] bottom of the wage of the income distribution. Another way of saying this is basically so this automation is going to generate some productivity gains not very small ones but they are going to be productivity gains but then the way it's [00:06:12] going to work is rather than these productivity gains accruing to workers which is what would happen in standard theories here instead these productivity gains are going to accrue at least partly to owners of capital. Okay. And I'll explain this in more detail. What's [00:06:26] going to be very important here is basically the elasticity of capital supply. So you know how much when when you have a rightward shift to the of the capital demand curve how much of that is going to show up as an increase in the [00:06:40] quantity of capital and how much of that is going to show up in an increase in the you know return to the capital. [00:06:47] Okay. Then a second effect that that's going to be there in our model and you know that effect up here that's mostly important at the bottom of the income distribution. This effect here is going to be mostly important at the top [00:07:01] of the income distribution is going to be via wealth accumulation. Okay. And essentially what's going to happen is because automation increases these returns to wealth according to this formula up here what's going to happen is that some [00:07:15] people who already have some wealth so who who own you know part of the capital that's getting more productive due to automation they're going to be able to accumulate large fortunes. This is going to come up in a very simple way in in [00:07:30] this theory so in particular both the income and wealth distributions are going to have Pareto tails like in the data and the fatness of these Pareto tails is going to be increasing uh in the capital share of the economy, okay? [00:07:44] Uh so, there's going to be be a link between factor income distribution and personal income distribution. So, when the capital share uh goes up, the personal income and wealth distribution is going to be get more dispersed. [00:07:56] Okay. So, one thing um that, you know, you're we're probably going to think in your mind is sort of, you know, I told you that when automation increases, returns to wealth uh are are going to increase. So, you may wonder, you know, [00:08:10] but what about empirical uh uh trends of for returns uh that we've observed over the the last 40 years, okay? And in particular, one one return trend that you may have in the back of your mind is [00:08:22] that, obviously, returns on safe assets uh sort of say uh government bonds um have uh been on a secular declining trend, okay? And indeed, you know, this is a this red line here uh is exactly meant to show you this, [00:08:37] However, there's also other ways of measuring sort of returns at the economy-wide level, uh uh and if you do other things or we look at other assets, I guess, um this isn't true, and you know, other assets have actually uh displayed increasing [00:08:52] trends. Here is, for example, one way macro people like to do this. This is sort of a a measure of the return to uh the overall uh capital in the US economy, and basically, what you do is you just go to the national income and [00:09:06] product accounts, and you measure uh uh sort of total uh GDP, and then you or capital income, I guess, is the more more uh the simpler way, and then you uh divide that by just a measure of the [00:09:19] capital stock. And if you do that, uh then you actually get an increasing line, okay? [00:09:24] Now, there's obviously a question and um you know, which of these uh two returns should you be looking at? Um in the baseline model, we only have uh you know, one return, so there's it's a one asset model, so you can't really talk about that in a meaningful way, but then [00:09:39] uh in a later section of the paper that I'll hopefully get to, we have a model with two assets, in particular risky asset and a safe asset, where you can then talk about in a meaningful way about this sort of diverging trend, okay? [00:09:51] Uh and then what turns out to be the right thing to look at is basically um an average return to wealth, so in particular if you have different assets, sort of you know, a weighted average of the different returns on the different assets with the way it's given by the [00:10:05] portfolio shares, okay? And it turns out that uh you know, that green line is basically closer we think to to the right thing to look at uh in the data than the than the red line there, which is just uh you know, the return on a [00:10:19] particular asset, so these safe assets. Furthermore, um you know, what matters for wealth inequality in our model, um and you could sort of see that on the formula I showed a slide ago, what matters for wealth inequality is not the [00:10:32] return to wealth, it's really the return to wealth relative to uh you know, people's discount rate and some uh uh term here that's due to the economy growing, so in particular this sort of return premium here. So, how much of a [00:10:46] gap is there, um you know, between this return to wealth uh and and this sort of baseline measure of return to wealth? [00:10:55] Why? Because that's going to determine the speed at which people are going to accumulate wealth in our model, okay? [00:11:00] And if you do that, so in particular if you try to subtract um you know, off uh uh some something that takes into account how much the economy is growing, then in fact um you know, because obviously economic growth has declined [00:11:13] over time, um you know, you can see that uh definitely these return series have been increasing over time, okay? [00:11:19] Uh so, even the safe return decline is not that large, and if you look at sort of at measures of average returns, those those have been increasing. I'll come back to this. [00:11:29] Okay. Just briefly to uh talk about uh about our contribution to the literature. So there's obviously a literature that talks about automation and inequality in particular my co-author Pasquale with Daron Acemoglu [00:11:42] has a bunch of papers. Here's a here's a bunch of other references. Again here the key contribution relative to that literature is that we talk not just about wage inequality so labor incomes but instead capital income and wealth. [00:11:56] More generally there's a there is some literature that links technological change to changes in the wealth distribution. Here's some references for that. [00:12:05] The standard mechanism in that literature is basically again that sort of technology affects relative wages and then you know because relative wages change they wage dispersion increases that affects wealth inequality. Relative to that literature we have this sort of [00:12:20] new mechanism which is that there's this effect going through returns to wealth which is absent in the existing literature. Again so technology changes returns to wealth of the distribution of returns to wealth and that affects [00:12:33] wealth inequality. Here's the plan for the talk. I'm going to show you this framework here. [00:12:41] I'll mostly focus on the steady state then where you can see lots of things and then we're going to take the model to the data. Okay. We're going to calibrate how much automation there is in some way and then try to see how much of this uneven growth is going to get [00:12:54] us. Okay. Just to already preview this this is the type of graph I'll show you coming out of our calibrated model. So essentially what I'm going to try to convince you of is that um [00:13:08] automation here is going to lead to relatively small aggregate productivity gains. Okay. But at the same time it can lead to large distributional effects. [00:13:17] Okay. So what's on this graph here again that's something that comes out of our model and we'll compare it to the data then later as well. So this is like the income percentile on the on the x axis and then it's a change in income [00:13:30] percentiles from one steady state to the next on the on the y axis. [00:13:36] Um, you know, for comparison, uh, you know, just to get you a sense of how much action you get in this model, the green line is essentially what would happen in a representative household model. [00:13:48] Uh, uh, and basically what you can see, nothing much would happen to the distribution uh, in a representative household model. [00:13:56] Okay? Um, but then the black line essentially is what happens in our model where you have these interesting channels going on and you can see that basically you get large increases in inequality, uh, in particular, driven by increases [00:14:11] in incomes at the top of the distribution. In contrast, the the uh, you know, bottom of the distribution sees largely stagnant incomes just like in the data. So again, in a representative household model basically everyone is better off. Okay? So all [00:14:26] these, you know, percentiles have income increases. In the our model, there's this very uneven growth. [00:14:33] Um, you know, at the bottom there's stagnation, at the top there's huge increases. I'll show you where this comes from. It basically comes exactly from the two channels I highlighted earlier. So at the bottom, um, basically these people only have [00:14:45] labor incomes, labor incomes stagnate. At the top, uh, these people have some wealth and some capital income and then basically when there's automation returns to wealth increase and the these guys capital income and wealth [00:14:59] increases. So basically there's sort of a double positive effect for these guys. [00:15:04] Their return to wealth increases, also their their labor incomes increases and there's a double negative effect for these guys. So they don't their labor income stagnate uh, and they also don't have any wealth so they don't benefit from these [00:15:17] increasing returns to wealth there. Okay. [00:15:22] So, um, let me show you the the model and then uh you know uh show you the the the calibration um and the taking the model to the data. Okay. So, it's a very simple stylized model um that on purpose [00:15:36] we built to keep things as tractable as possible cuz we wanted to um you know uh be able to have nice analytic results. [00:15:45] Um as a result, it's also going to make some very strong assumptions. Um we'll we'll we'll talk about these probably. [00:15:51] Um so, you know, uh people have standard uh sort of CRA utility and here in the baseline model just um accumulate uh uh in one asset. So, uh essentially the way this is going to [00:16:03] work is um Z here uh denotes your skill type and people have different wages according to their skill types. We're going to endogenize these in general equilibrium in a second. Um [00:16:16] and then um S here uh denotes basically just the time that's evolved over time and you can see so there your saving equals your your uh capital income plus your labor income minus your consumption. So, a very standard one [00:16:30] asset model. Okay. Now, this looks exactly like in a neoclassical growth model, right? So, standard model. We know that in that kind of a model, you know, not not much interesting stuff happens. In fact, um you know, if you if you had uh [00:16:45] uh you know, just this type of a setup, it would actually um uh collapse to a neoclassical growth model in which the long-run return to wealth would just be pinned down by the discount rate. Um we're going to make um an assumption to break this. Okay. [00:16:59] This assumption is going to be quite stark, um but it's going to, you know, in a very sort of tractable fashion introduce a bunch of very interesting things. Okay. Uh this assumption is going to be that when these people accumulate wealth, they're going to be [00:17:13] subject to what we call wealth dissipation shocks. Okay. So, the way this is going to work is you accumulate wealth according to this type of equation here and then at some Poisson rate P, okay? You get hit by wealth [00:17:28] dissipation shock, which basically means that your your your wealth goes from whatever it is to zero, okay? So, your wealth just kind of dissipates, disappears, okay? [00:17:38] Apart from that, you know, everything's kind of standard so people are you know, this discount at this effective discount rate and so on, okay? So, now you may ask what the hell is this type of a [00:17:51] dissipation shock, okay? We have a long discussion of this in the paper. [00:17:57] Let me give you sort of the tell you first what it does, okay? So, what it does basically is it it generates in a very simple way a non-degenerate wealth distribution, okay? A and second, an [00:18:12] upward sloping long-run supply of capital. I'll show you this later. Those are the two things we want to get out of this, okay? So, it's really a stand-in basically for lots of other mechanisms that could give you this, okay? Here's a list of them. I don't have time to go [00:18:26] through this. There's a long discussion in the paper, but just to you know, tell you about some of them. So, in particular, I think this one I like the last one here. [00:18:37] I think this is basically a reduced form for say a model with capital income risk, the rate of return risk. [00:18:44] I like in papers by you know, Benabou and Bezin for people who know this. This would give give you something that looks very similar. Here it's an extreme form of capital income risk where you know, your capital return is minus 100% basically with some probability and [00:18:59] positive otherwise. And we know that in the data Laurent has some nice work on this for example. We know that in the data there's lots of dispersion in rates of return basically and so this is a simple reduced form way of capturing this. [00:19:12] Another thing is that whenever you set P equals zero, you get back the representative agent benchmark. So, basically all the formulas I'm going to show you, what you can always do is set P equals zero and you're back in the [00:19:26] in the representative household model and you can sort of see exactly what you know, what our little trick here adds relative to that. [00:19:33] Okay. Apart from that, we basically now take this model that gives you a nice wealth distribution and we glue that together with of automation. [00:19:42] This model of automation is basically something that we have from the existing literature, in particular Pasquale's work with Daron. There's also older papers by Joseph Sera. [00:19:54] It's a task-based model, okay? Where the idea is that machines substitute for labor at the task level, okay? And then what automation is, it means automation means [00:20:05] that machines can do more tasks over time. Okay? [00:20:11] So, think about you know, the the the recruiting process, maybe. And there used to be there used to be HR workers who did all of the tasks. Now, you know, a lot more is [00:20:25] driven by software, for example. That would be the type of model. [00:20:30] Okay. Apart from that, we're going to then nest this type of model in a relatively standard sort of multi-sector economy here. We're going to have the assumption that each skill sort of produces in a different sector and then the aggregate [00:20:43] GDP is sort of a Cobb-Douglas aggregate of these different sectors. And then within these sectors again, there's this task-based model. And then basically the way this is going to work, and again the details are in the paper, [00:20:56] there's a parameter alpha that's specific to each sector Z or each skill type Z, which is what's the share of tasks that's automated. Okay? [00:21:09] Um and then basically automation is uh an increase in that alpha Z. Okay? [00:21:16] And the way this is going to work, I'll show you this in on the next slide, I think, is basically these task-based models of automation, the way they work is um in the end basically um at the sector level there's going to be [00:21:31] a reduced form production function that's just going to be a Cobb-Douglas production function, you know, like K to the alpha Z times L to the 1 minus alpha Z, and then basically an increase in alpha Z um uh is so automation is just going to be [00:21:44] an increase in alpha Z, which is just an increase in the Cobb-Douglas exponent of the economy. You can already see that's going to give some interesting things, like for example, uh uh an increase in the capital share and a decline in labor share. [00:21:56] Okay. Um So exactly. So here I've already said these things, I think. Um so you can on the production side um you know, aggregate things kind of nicely uh and you're going to end up with an [00:22:09] aggregate production function um that has uh the aggregate capital stock here and then something having to do with labor here. [00:22:18] And there's basically going to be a simple reduced form uh parameter alpha here that summarizes exactly how much um automation there has been um uh which is sort of this weighted average here of [00:22:32] these sector-specific alphas. Okay? So that obviously comes from the fact that we assume that everything sort of Cobb-Douglas here. [00:22:39] Um and then basically you can see it as a one-to-one mapping between how much automation there's been and uh what the what the capital share is in the economy. [00:22:50] In particular, the factor payments here in this economy are going to be very simple. Um so the the return the rental rate here is just a fraction alpha um um of uh uh GDP divided by capital, and you have [00:23:03] your standard sort of expressions basically like in a neoclassical growth model say for for the production side of the economy. [00:23:12] I'll show you just because it makes the math slightly easier um uh equations for the special case where depreciation is zero, okay? In which case the rental rate is going to be [00:23:26] equal to the return to wealth here. Um but you know that's not essential to the results I want to show. [00:23:33] So here comes the key thing I guess. Um so essentially you can get a closed-form solution for household's consumption and saving decisions, okay? Um you know from that um problem here two slides ago you can see that you know this has a nice solution [00:23:48] potentially. Um and in particular here is the key equation I want to focus on. [00:23:54] Um so that's an equation for wealth accumulation and you can see that um you know essentially this says savings equal to you know your standard Euler equation term here basically um the gap between the return to wealth minus the discount rate times the [00:24:08] intertemporal elasticity of substitution and then uh times uh this is what we call sort of people's effective wealth. So it's their financial wealth plus their human wealth, okay? And you can see the relevant state variable here um is is [00:24:22] going to be this effective wealth. So you know you you don't just want to take into account financial wealth, you also want to take into account human wealth, okay? [00:24:30] Now from this equation you can pretty immediately derive uh a simple equation for um you know aggregate capital accumulation so the accumulation of total wealth. So K here is just the sum of all the little [00:24:43] A's, okay? Um and in particular uh because of these wealth dissipation shocks, okay? You can see that um uh you know [00:24:55] you can derive this sort of a simple uh expression for the aggregate supply of capital that's comes from household saving in this economy. [00:25:06] And I'll show you this on the next slide. This curve here, if you look at that as a function of the interest rate or the return to wealth here, is going to be an increasing function, okay? So you have in this model a long-run capital supply curve that's increasing [00:25:20] with the interest rate as opposed to being perfectly elastic like it would be say in the neoclassical growth model. [00:25:27] So here is essentially then how you know the determination of equilibrium works in the in the capital market. [00:25:37] Okay, so this is capital on the x-axis. The interest rate or the return to capital on the y-axis. [00:25:45] You have your standard demand for capital. Demand for capital just comes from the marginal product of the firms, okay? [00:25:51] And this is this capital supply curve I just showed you, okay? [00:25:55] And the equilibrium here is the intersection of these two curves, so now let me show you basically how automation works in this economy and what happens you know with the return to wealth, okay? [00:26:08] And for comparison, it's useful to keep in mind that basically you know if instead you had the case P equals zero, so you had this kind of a representative agent model, okay? Then the long-run supply of capital in this [00:26:22] economy, okay? Would be you know, this perfectly elastic capital supply curve here at interest rate equals to discount rate, okay? And the equilibrium would be the intersection of these two points here. [00:26:37] Instead, all we're basically saying is hey, you know, maybe this assumption in the neoclassical growth model that the supply of capital is perfectly elastic is a little bit crazy and maybe we should have an upward sloping capital supply curve Uh, and and and then look [00:26:51] at the equilibrium there. So, 5 minutes then? [00:26:56] Okay. This is really the key like the you know, if you want to have the key thing that's happening in our model in one slide, this is it. Uh, so so basically now let's think about an increasing in automation, okay? [00:27:10] Again, I said automation means this alpha parameter goes up. [00:27:14] Okay. Um, what automation does here is because capital became more productive, um, it shifts this capital demand curve to the right, okay? Now, let's first think what would happen if you had a representative household model, okay? Like a [00:27:28] neoclassical growth model. Then what would happen with an increase in automation is, you know, the capital demand curve shifts to the right. Here, you'd go from this equilibrium to this equilibrium. Um, in particular, the [00:27:42] return to wealth would be unchanged, okay? Uh, still equal to row, and you'd have a huge expansion of capital in the economy. So, a big inflow, a big increase in investment, basically, okay? [00:27:55] In our model instead, uh, that doesn't happen, okay? Instead, because the capital supply curve is upward sloping, you have a much smaller increase in uh, in the amount of capital, and instead, that uh, rightward shift in the demand curve shows up in [00:28:10] the price, so the the return to capital here. [00:28:13] Once you understand this, this is really you you almost understand everything that's there in the paper, because everything else follows logically from this. You know, the fact that you know, here you're going to have this this increase in the return to wealth, okay? [00:28:26] Um, so in fact, okay, and and you can show that basically there's a yeah, so you have the simple um, equation here for the equilibrium return, where you can see that alpha shows up exactly there, and if P is equal to zero, then that effect isn't there. [00:28:41] So, um, let me Okay, now I'm running a little low on time. Let me show you uh uh two more things um and then go to the data. So, the first thing is um [00:28:54] you can now think about sort of uh when you have automation, um what's going to happen to to uh you know, the prices of productive factors um in the economy and who are these productivity gains going to accrue to. [00:29:09] And basically, the way this is going to work is um in a representative agent model where the return to wealth wouldn't move, okay? [00:29:18] You'd always have that um all the productivity So, this term here would be zero. [00:29:23] All the productivity uh gains in economy would accrue to labor, okay? And in long run, workers are always better off in a standard model, okay? [00:29:31] In our model instead, some of the productivity gains are going to accrue to owners of capital instead, um and in fact, that in fact, may be so large that labor may actually lose on average um from automation, okay? Which again, [00:29:46] seems kind of intuitive, but in a in a standard model, this effect isn't there at all, okay? [00:29:52] Now, let me briefly uh show you one more thing from the theory, which is um you know, what happens to the wealth distribution here. Essentially, in this type of a model, um we have a very simple setup where people always accumulate um according uh to this term [00:30:07] here. So, something that depends on the gap between the return to wealth and the discount rate, um and then they're hit by these dissipation shocks. This kind of uh setup where people accumulate wealth through a process like this um [00:30:21] is well known to lead to a stationary distribution that is a Pareto distribution, okay? [00:30:26] Um and essentially, all we're saying here is uh you know, let's let's you know, work that out and see what the Pareto distribution is, and you get a very simple um a characterization. In particular, you get that the distribution of wealth in this economy [00:30:39] has a a tail index, okay? And you know, there's a little bit of algebra involved in there, but it has a tail index that's exactly equal to the capital share, okay? So, whenever the capital share increases, then the fatness of the [00:30:52] Pareto distribution increases. And the mechanism for this is exactly through the return to wealth because basically people accumulate wealth as a at a faster pace. [00:31:02] Okay. Um if it's okay, let me take like uh one more uh minute. [00:31:08] Um so, you know, we have this extended model where we add another asset, in particular uh you know, a risky and a safe asset just so we can talk about this trend I showed you in the data between the diverging trend between um [00:31:23] uh risky and safe rates. Um and you know, then then So, that's useful for that, but let me skip that. And let me just show you basically um what comes out of this model once you take it to the data. [00:31:36] Um but I, you know, I I'm not going to do it justice here in in time. So, essentially what we do here um is we come up with some way of uh measuring how much automation there is at different wealth percent income percentiles. [00:31:50] Um uh and and then we feed that into our model, okay? And then we try to see um what it gives in terms of um uh changes in the overall income distribution over time, okay? So, in terms of the effect of labor incomes, [00:32:04] that's sort of we get by construction, um but then the interesting question is what happens to, you know, not just labor incomes, but capital income and wealth inequality. [00:32:14] Okay. Let me just show you uh this one graph and then sort of conclude. So, this is sort of I I guess, you know, the main graph that comes out of the model. [00:32:23] Um essentially, uh you know, look at the black line. Um The the on the x-axis here is the income percentile. Um on the y-axis is the model generated change in um [00:32:37] uh income of these different uh these different percentiles from one steady state to the next and you can see, you know, there's a big big uneven growth pattern with stagnation at the bottom and increasing incomes at the top. Where [00:32:50] does this come from? I already said it in the introduction. At the bottom, it's all due to labor income. [00:32:57] These guys don't have any assets or very few assets, so they lose from automation. At the top, these guys win from automation. Why? Because they have a lot of capital income and wealth. [00:33:08] So let me and this is something you can also kind of see in the data. Okay, let me conclude. So this was a tractable framework to think about this uneven growth that we've seen in the data. [00:33:18] We've used it to study one particular change, namely, you know, automation and you know, figured out its distributional effects. [00:33:27] Importantly, not just on wages, but also on income and wealth distributions. The the key new channel here was that technology may affect returns and that may lead to distributional effects. [00:33:39] You know, going forward, you can use this same structure cuz it's nice and tractable to also think about other types of technical change. Maybe, you know, changes in market structure. You can think about optimal taxation and so on. This is we haven't done yet. May probably a separate project, [00:33:54] but you know, with the same type of project you know, framework you can kind of do something like that. Okay, sorry for going over time. I'll stop here and thanks for listening. ## Discussion (00:34:03 – 01:02:52) [00:34:03] Thank you, Ben. So our discussant is Loic Calvez from EDHEC Business School. [00:34:13] Thank you. You see my You see my screen, right? [00:34:18] Yeah, it's perfect. Okay. [00:34:20] So thank you very much. This is a actually very interesting paper. [00:34:25] I really enjoyed reading it. I learned a lot from it. [00:34:28] So what I'll do is first I go over the model uh and then I'll uh present some suggestions for, you know, improvements, future research, and so on. [00:34:39] Okay, so the idea of the paper is that if you look at the US since 1980, right? [00:34:44] The aggregate economy has grown as a whole at a rate of 2% uh but at the same time, incomes in a lower half of the distribution have stagnated. [00:34:54] While at the top, incomes have doubled or tripled depending on the quantile you're looking at. [00:35:01] And in addition, we know that wealth inequality has strongly increased. [00:35:05] Now, what could be driving this joint set of facts? Well, automation has uh you know, has been proposed uh previously as a possible explanation. [00:35:14] There's a bunch of papers that that make this point, okay? [00:35:19] Uh so, the paper is ambitious. It's very well written. It was actually It's actually very straightforward to understand what's done even though it's a it's a technical and you know, highly sophisticated general equilibrium model. [00:35:32] Uh and what it does is that it links uh the tasks to the distribute so, the the the tasks, right? That are performed in the uh in the economy to the distribution of both income and wealth. [00:35:44] And I think that's the defining feature of this paper is that they look jointly at income and wealth. And that's a very interesting idea, okay? I've worked in a little bit in this area and I know that, you know, there's this disconnect often between the two [00:35:59] uh aspects of income and wealth and it's really good to be able to think about them jointly. [00:36:04] So, what they show is that automation generates uh what I described before, wage stagnation for low-skilled workers, income growth for high-skilled workers, and higher returns on capital. [00:36:16] And the calibrated version of the model captures key features of the data. [00:36:21] So, as I said, I'm going to go over the the the benchmark model, sort of explain its workings. Then we'll talk about the extended model and the calibration results and then I give ideas for future research. [00:36:33] So the benchmark model is an infinite horizon continuous time economy uh populated by a continuum of households that have infinite lives and I have isoelastic utility. Okay, so [00:36:47] their uh utility function is characterized by time preference rate row star and an elasticity of intertemporal substitution 1 over sigma. [00:36:58] Now each household has a skill Z and they are finitely uh many skills. [00:37:04] And everyone with skill Z receives wage WZ. [00:37:09] And LZ denotes the fraction of the population with skill Z. Okay, so that's the key segmentation of the population of workers. Okay. [00:37:21] Um now wealth accumulation is subject to dissipation shocks and that's key, arriving at a constant rate P. Okay, so household hit by such a shock immediately uh consume all its wealth. [00:37:34] So when you go from time T to time T plus DT with probability PDT, you get the dissipation shock. Okay. Um and there's an effect so the effective uh time preference rate becomes the initial [00:37:47] one plus P. Okay. Uh now the households solve this optimization problem, right? So they it's a actually what they're solving turns out to be deterministic [00:38:00] despite the existence of the dissipation rate. So they solve this problem. Okay. [00:38:04] And in fact this is one of my points I would have liked to see a little bit more discussion uh of uh you know, the interaction between P and the and the optimization problem. I saw there is some in the appendix but it would be good to provide a little bit more [00:38:16] intuition on on this. Now there is an aggregate technology, right? So, essentially there's one big farm in this economy, as far as I understand. So, there's If you work in sector Z, right? [00:38:30] Uh you produce an intermediate output YZ. [00:38:35] Okay? So, workers have these different skills, and these are like little industries, and in each industry people produce the intermediate output YZ, and then the aggregate output is uh the a Cobb-Douglas function of the [00:38:50] intermediate outputs, where the the uh share of each sector, right? The shares add up to unity. [00:38:56] Okay. So, how are the What is the technology used for uh the uh intermediate outputs? Uh so, here they use a a model automation. [00:39:06] Uh so, which which exists in the in the literature as as Ben explained in his presentation. So, there's a There is, you know, in order to produce YZ, you need to complete you know, continuum of tasks that indexed by U between 0 and 1. [00:39:21] Okay? And the intermediate output YZ is given by this equation, right? So, you integrate between 0 and 1 the log of the production of each task, right? [00:39:34] Uh and then you you take the exponential, and you get the the intermediate output YZ. Okay? So, now, how is the task you know, what is the output corresponding to a task? Well, and this is where what's key here, if [00:39:46] the task U is below some number alpha Z, right? Then you can automate it. So, you can, you know, produce YZ of U using capital. [00:39:57] If U is above alpha Z, so if you're in a task like a high-level task that's above alpha Z, then you can only use labor to produce it. Okay? [00:40:10] So, alpha Z is the uh parameter that controls how much how easy it is, how possible it is to automate a task within a sector, within sector Z. [00:40:21] Okay? Now, what is a general equilibrium? [00:40:24] Well, in general equilibrium, production the production process minimizes cost, households maximize utility, and then of course you have market clearing, so labor markets clear. So, the integral of LZU is LZ in every [00:40:39] sector, and then the aggregate capital supplied by households and used by firms is denoted by K, and you know, all these they're both equal, of course. So, this is the aggregate uh uh amount of capital that's demanded by firms. This is aggregate demand. On the [00:40:54] other side, we have aggregate supply. This is coming out of the household optimization problem. Okay? [00:41:00] Because it's all like a very nice model, you can very easily derive, you know, LZU, how much labor is allocated to a particular task, KZU, if it's a higher lower level task, how much capital you need to perform it. And then once you [00:41:14] have LZU and KZU, you can obtain the intermediate output YZ without any difficulty. Okay? [00:41:20] Uh once you have the the intermediate output, right, produced by each sector, then you can aggregate up and you get the aggregate output. [00:41:28] Okay. So, the aggregate output, as Ben explained, is a Cobb-Douglas function of the aggregate capital K. Okay? And that comes out very naturally of this of this nice technology. Okay? [00:41:41] Where alpha is the average So, alpha depends on the automation, right? Key that's key of the of each sector, right? [00:41:50] Alpha Z is the share of a sector that can be automated, and it's weighted by uh by AZ. [00:41:56] Now, the wage is also, right, is given by a standard formula. The wage in sector Z is 1 minus alpha Z. So, this is the the fraction of tasks that cannot be automated, right? [00:42:11] times Y and times a constant. Okay. So, essentially what's happening in the model is as alpha Z goes up, it means that within sector Z, right? You can automate more tasks, right? Now, there are two effects. [00:42:26] The direct effect is that the wage goes down, right? So, the share of wealth created in the sector go goes less to wage to to labor to a workers and more to capital, right? So, that's a direct [00:42:41] effect, negative effect of automation on wages. And then there is also the fact that when as you automate more, the economy more becomes more productive, output goes up. Okay? So, there is this tension between these two [00:42:54] effects that explains why in, you know, under some values of parameters and so on, you can get stagnant wages, higher higher I mean, output or growth uh in the extended version and so forth. [00:43:08] Okay? From this equation, you can derive that the aggregate wage bill is 1 minus alpha times output. Okay? [00:43:16] The factor price of capital, right? So, this is how much you get when you lend capital, but there's also depreciation, right? That's just alpha Y over K, familiar formula. Okay? [00:43:29] So, what is the demand for capital from the firms? Well, it's So, you get it from this equation, so it's KD, it's uh alpha divided by R plus delta times Y just from this equation. Okay? And then [00:43:43] what is Y? Well, you can substitute substitute out Y and replace it with uh W bar divided by 1 minus alpha. [00:43:51] Okay? So, that's what you get. So, this is the demand for capital. Okay? [00:43:57] If you normalize the demand capital by the aggregate wage bill, you get this equation. KD is alpha over 1 minus alpha times 1 over R plus delta. [00:44:06] Okay? Okay, so this is demand. What about supply? [00:44:11] Household optimality implies this familiar uh accumulation equation except for the fact that we also have the destruction, right? We have the destruction of capital at rate P due to these dissipation shocks. [00:44:25] So, in a steady state, of course, the derivative is zero, and you can express the supply of capital in this fashion. [00:44:31] So, function of rho, uh the interest rate, and so forth. What's very important for the model is that the interest rate is contained between rho and rho plus sigma P. Right? So, sigma is the inverse of the elasticity of substitution. [00:44:45] P is the probability of destruction. And that that's that's what allows the model to have an upward-sloping uh supply as opposed to a horizontal supply as is the case in a in a representative agent model or if you P is equal to zero. [00:44:59] Okay, so we've seen this graph. I think we get a Ben explained it very well. You have supply, you have demand at the steady state. [00:45:06] Um you know, this is the supply from from uh from households. This is the demand by by firms. If alpha goes up, there's an outward shift in demand. The interest rate, I mean, the rate of return of from [00:45:20] capital goes up, and the capital goes up. So, you get both higher return on wealth and higher output, okay? In in a steady state. [00:45:30] So, I think this is very clear, very elegant model. [00:45:34] And then they look at the implications for labor. So, when a sector becomes more automated, then the steady state wage falls relative to other uh sectors. And this [00:45:45] is a direct, very simple implication of of this equality here, right? So, if you take the ratio WZ over WF, and you compare two sectors, you just get essentially the ratio of the alphas, and [00:45:59] so you get the result. Uh Uh, what's a little bit more what's a little bit more, you know, takes more work at least is to show that automation can decrease the average wage if uh, P is sufficiently high. That is if so automation can, you know, [00:46:13] promotes, you would think, right? The accumulation of capital, but if capital gets destroyed sufficiently fast, overall, you know, uh, you see that automation has a negative impact on on the average wage. [00:46:27] Another, uh, the the nice nice one of the nice features of the model is that it's a very modular model, a very modular paper in the sense that they take, you know, uh, the consumption portfolio problem, [00:46:40] they take a technology with automation, and they also take uh, and, you know, they you through the distribution rate, they also get you know, results that are familiar also since Champernowne and, you know, Wald and Wold also since the '50s, we [00:46:53] know that when you have a uh, uh, a a wealth accumulation process with dissipation, and with the a strictly positive lower bound provided here by the back human capital, you know that you get Pareto tails. Okay? And so here [00:47:07] you get, you know, that wealth and income have Pareto tail with exponent here, uh, zeta, and they characterize zeta, and this is known as a set from the '50s. You have to take the ratio of the household accumulation rate to the dissipation rate. Okay? [00:47:21] Which in our case is, I mean, in the case of the paper, R star minus rho divided by sigma. That's the accumulation rate of cap- of wealth divided by the dissipation rate. [00:47:32] It's very It's actually quite straightforward to show this. [00:47:35] Uh, you can just write down the stationarity of the CDFs. I I, you know, had fun just checking the the formulas, and, you know, you get this immediately. [00:47:43] Okay? So, what this implies is that as alpha goes up, as you get more automation, right? R star, the rate of return on capital, goes up, right? The other terms are constant, right? And as [00:47:57] a result, you get uh 1 over zeta that's higher, which corresponds to thicker tails, right? The the the smaller the zeta, right? The thicker the tail, and that's exactly what you get. Okay, so this is a very [00:48:10] beautiful and elegant model, I I thought. [00:48:13] Um it's ingenious, it's pedagogical, uh it's so so that you combine like standard uh things. What I would simply I would make two remarks. First, the dissipation rate is not so common in financial economics, [00:48:26] uh but the authors provide explanations some explanations, but maybe at least from a finance perspective, more slightly more explanations might be useful. And I just also would like to mention that these are steady-state comparisons based on so-called MIT [00:48:39] shock, so like one-time unexpected increase in in automation. I guess in a in a you know, in an economy in which automation is a steady process, you know, there there might be more more going on. People might want to hedge, [00:48:53] you know, the automation risk, and so forth. Also, I think there's more that could be said. [00:48:57] Um let me talk briefly about the extended model. So, uh they have two assets, equity and and safe asset, uh plus other uh ingredients. [00:49:08] Um one thing is the stock price in the uh extended model follows a process of the form RK DT plus new uh DW. [00:49:19] And RK is the mean after-tax return per dollar of capital. [00:49:23] W is meant to capture reducing credit risk, okay? [00:49:28] Um and I'll come back to that. Uh so, investors have you know, Duffie Duffie-Epstein preferences, and limited participation, and so on. So, this is something I was not completely convinced about is the specification of the stock. [00:49:41] I'll come back to it. Then they do some calibrations. So, the calibration is based on the formula, so there is they start from the capital share in 1980, which is 30.5%. They assume that it's also, you know, in every [00:49:55] in every um sector, right? The share of uh what can be automated is also 34.5%. [00:50:04] And then they use this formula uh which you know, allows them to relate. [00:50:09] So, in it's uh in 2014 uh the share of of capital is 32.8%. [00:50:15] So, this is desired like aggregate numbers. [00:50:18] And they use they use this a formula that allows them to impute the share of automation in every sector. And what's the sector in the world? [00:50:28] They actually subdivide the population in by, you know, wage quantiles. So, by each percentile of the wage distribution is an actual sector. [00:50:38] And also uh and here what what I haven't explained that omega RZ is the share of labor income derived from routine jobs in that particular percentile. So, anyway, through this type of a formula, they're able to [00:50:51] calibrate the share of automated task in each uh sector, right? In each quantile of the wage distribution. Okay. [00:50:59] Once they've done that, they can actually, you know, look at the implications of the model. So, they see that uh you know, that you know, according to the model in most uh quantiles up to the 75th percentile [00:51:13] at least, you should expect a drop in the wage which is more or less consistent with what you'd see in the data, perhaps not at the you know, bottom very bottom, but and then above the 75th percentile, the model and the data [00:51:28] show imply an increase in in the in what in the wage. So, this is actually a very nice graph. I wonder what could be driving the discrepancy here. I was wondering if it had to do with the minimum wage or some other friction that you don't you don't capture. [00:51:42] Um then they look at the implications of the model for total income defined as a sum of capital income and labor income. [00:51:49] And what you see is that, you know, most of So, this is a hockey stick type of graph. So, you see that, you know, at the bottom and in the lower like, you know, the vast majority of the population, there's not much happening. [00:52:01] And at the top, you have a big increase in capital income. So, the the people who gain the most from automation are indeed the people at the top. Okay? And really the very top, if you look at it. [00:52:11] This is the top, you know, this is the 1% top 0.5% and so forth. [00:52:17] Um they look at different data sets. So, if you look IRS data, you don't find that capital income is so important. [00:52:24] Uh there's bits of There's an ambiguity because you they don't, you know, you have to allocate the income for S corporations and that that's a subject for debate. But the IRS data is not complete. If you use a more complete [00:52:37] data data, then you get much closer to to the findings of the author. [00:52:41] All right. So, now let me It's time for me to give you some comments. [00:52:46] Um So, as I said, one thing I didn't like felt feel very comfortable with was the definition of the stock return because my sense is that this I mean, maybe I misunderstood what you're doing, but I got the sense of the Brownian motion was [00:53:01] basically, you know, unrelated to what was happening in the production sector. [00:53:05] You just tacked on a uh a Brownian motion. [00:53:09] So, one thing I'm going to try to do in my in the second half of the discussion is like provide input from a financial economics perspective, right? Since this is a finance seminar, I will try to give you my perspective [00:53:23] um and hope that it can be useful. So, okay. So, not sure what this represents. Is it Don't think it doesn't seem to be technological risk. Maybe it's discount rate risk or I don't know. [00:53:34] So, if you focus on idiosyncratic production risk, then there is of course there's some other papers. There's a The papers I wrote with Marios Angiletos when he was at my student actually when I was at Harvard. [00:53:46] So we look at the effect of idiosyncratic production risk. Um One thing which is very important in in finance is you know when there is a risk is it priced? So you know I'm not quite sure what the answer is or is maybe it's [00:54:00] not priced because it's orthogonal to everything else. [00:54:03] Um so I just wanted to suggest that we I mean I found the logic of the extended model a bit less intuitive because I wasn't couldn't quite wrap my head around what the this equity uh uh um [00:54:18] asset represents. I just wanted to give you I mean since I have have the opportunity to give you like you know directions and so on. Uh I just wanted to mention how we tend to do things in finance. So this is just an example right not that I'm claiming [00:54:31] that's not the only paper by far. But in this example so in the paper with the Sebastian Betermier and Alvin Joe what we do is we we kind of start from the firm right? So we write that the free cash flow is [00:54:44] uh you know one minus the tax rate times the earnings before interest and taxes right? So you know we express this as a random variable right? AN plus BN. [00:54:57] So this is our shock right? This is the shock to the free cash flow. Times you know times the volatility of cash flow times the capital stock plus the tax shield. So the point is you know we introduce the shocks through [00:55:11] free cash flow or through the EBIT right? [00:55:14] Then we assume a tax shield so we we write that the debt is proportional to to the to the at most you know it can be at most BN times the capital stock and since there is a since there is a a tax advantage the debt in fact is [00:55:29] equal to BN times KN where BN is driven by collateralizability. Okay? But the point is we have introduced we have you know our shock from the you know, at the firm level then we compute the value of equity. We [00:55:43] compute the return and so now we have a stock return that's tied to the shock that hits the firm. And I think this if you did something along those lines, I think it would help us understand the role of of equity in your in the paper. [00:55:55] And you know, just to give a bit of advertisement, then we able to write in all the supply and the demand for capital of of firm n. [00:56:04] And you know, if for instance, you have a profitability shock. So for instance, you know, the automation becomes possible, the firm becomes more profitable, then we get what you also obtain, right? In the [00:56:16] sense that a shock to automation would increase the rate of return, the average rate of return on capital and would would increase also the capital stock. So some sense they are kind of [00:56:29] similar logics here. Okay, we can look at variation in supply and we can also estimate you know, the the cost of capital and the and risk in the cross-section of US firms. Okay. So just to say that this [00:56:43] would be this was one point, the definition of equity. There's another point which which caught my attention. [00:56:49] And as I already said, I really like the paper, but there are a couple of points that maybe could be improved. And one of them is your your very straightforward, you you state that the the the model's transition dynamics are too slow to generate the fast [00:57:02] changes in top inequality observed in the data. [00:57:06] Okay. So in some sense, I knew but you so some sense it means that you can only I guess look at relatively long run changes, right? [00:57:15] And you're you're very like clear about this and you said that the candidate solution is to use returns on wealth. So I wanted to mention that actually we know that this is working, right? So okay. So we you know, we know that if you want to [00:57:29] understand the the of the wealth distribution, returns are, you know, definitely a place to look. [00:57:36] Uh so, in um in the paper with Low and Backus you mentioned and Paolo Sodini, uh we consider a very simple accumulation rule in which households just earn the historical portfolio returns [00:57:50] and have homogeneous saving rates. In other words, you you know, you observe because we have this nice Swedish data set. We know people have you know how much people have at the end of the year. [00:58:00] Right? You know the portfolio that they have at the end of the year at the end of year t. [00:58:04] And if you just forgetting about saving, take a constant saving rate. If you just use the return that they earn on the assets that they had at the end of year t, you just apply the the start the the realized return between year t and year [00:58:18] t plus one, then essentially you you you can predict very well the the distribution of wealth in year t plus one. Right? So, conditional knowing the distribution of wealth at year t, the portfolios of households at year t, [00:58:33] and the realized return between t and t plus one, then you can actually capture very well the uh distribution of the top share. So, returns are extremely important. And just to illustrate this, this is what, you know, this is what the [00:58:47] the black here black line is the prediction. [00:58:50] This is the observed change over a period of time. This is the the annual change of the of the share of aggregate wealth held by the top 1%. And you can see that, you know, as you know, if you know returns, portfolio returns, [00:59:03] you can basically figure out what the uh the top share is. So, this is very powerful. And if you look at the top 0.01% of the population, similarly, if you know the returns, you can basically uh predict what the top share or figure [00:59:17] out what the top share is. Okay, so portfolio returns are very useful. [00:59:22] Uh they have also properties that could help you also that could like uh uh that might be worth incorporating in a in an extension of your work. Uh so, we know that there are wealth effects. [00:59:33] We know that the return on wealth tend to increase with wealth, so that would also help to match uh the variation in wealth inequality. This is a an effect that was um uh conjectured by Thomas Piketty, but we [00:59:47] show that it actually is there. Uh there are life cycle effects also, so wealthier, older households tend to earn higher returns, and I think that's an something important if you want to track the uh the the distribution of wealth, [01:00:00] especially at the top. There is also a paper that's I think closely related to what you do. It's a paper that has been around for a long time. Actually, I have I discussed it before the pandemic. Uh it's a paper by [01:00:13] Francisco Gomes, Thomas Jansson, and Nuchan Karabulut. Uh And essentially, what they say is that uh when there is uh increased automation, when a worker is [01:00:27] at risk of, you know, being displaced by higher higher automation, then they tend to rebalance their wealth away from stocks and more towards safe assets, okay? And so, as a result, they [01:00:40] will, you know, uh earn lower average returns. And so, that would amplify, right, the the uh inequality effects of increased automation. So, that's another channel, which I think might be [01:00:53] something you might be uh interested in. It it's not a macro model, so it doesn't These are complementary papers, but I think it's this one is worth having a look at as well. [01:01:04] Um I'm almost done. So, confounding factors, so so I mean, of course, there is a long list of theories of wealth inequality and income inequality, and I just gave a very like [01:01:17] uh uh subs- I'm just giving a subset of this uh of the list of possible explanations. There's a paper on the cost of capital to entrepreneurs. [01:01:27] There's a paper in the in the CPR workshop on pension savings in response to lower interest rates. So, there's just a long list of explanation. Changes in into the product progressivity of the tax system and on and on. [01:01:40] So, one thing that, you know, that is fair to ask is, you know, is do you think automation is a key channel? How does it compare? What is the respective role of each of these channels? I think this is not for this paper, but that's something that might [01:01:53] be interesting to to to study in a in a follow up following paper. [01:01:58] So, in conclusion, I really enjoyed this paper. It's a thought-provoking paper that uh explains I mean, it explores the impact of increased automation on both the income and the wealth side. [01:02:10] Um and I think that's a very good innovation. [01:02:14] Uh so, you know, the results are clear. Changes in the automation can account for wage stagnation in most of the population and large income and wealth gains at the top. [01:02:24] Uh I think my I guess my discussion focused on on the finance side of your model. I think a model with more finance so you maybe a better defined uh risky asset maybe with like elements [01:02:38] from returns and household finance would actually make the the model or the follow up even stronger. And of course, I look and I understand you're revising the paper. So, I look forward to a reading the next version. Thank you very much. ## Q&A (01:02:52 – 01:15:32) [01:02:52] Thank you very much, Laurent. That was a very careful and detailed discussion. Uh Ben, would you like to respond briefly before we take questions? [01:03:03] Absolutely. Yeah, thank you very much Laurent for this very thoughtful and and super interesting discussion. Um yeah, I just want to respond very briefly to three points or say something about three points. So, the first one is um [01:03:18] this point you just your your question, I guess, you know, what's that what's that DW, right? Like, what's the you know, that idiosyncratic uh uh risk? And I guess um I I already put this in the chat. So, [01:03:29] this is indeed meant to capture um idiosyncratic production risk. [01:03:35] Basically, exactly like in your work with um Marios. Um but I mean, you're correct that if that's the case, because it's a general equilibrium model, you know, strictly speaking, it should sort of we should [01:03:49] spell out, you know, where that shows up in on the production side. [01:03:53] We we basically, I mean, we we had some internal notes at some point where we spelled this out, and and we we convinced ourselves that you can sort of do it. Um uh but but then we didn't put it in the paper, which I guess makes it a little [01:04:06] hard to follow. But yeah, I the the idea is that these are kind of somehow entrepreneurs, and this is sort of idiosyncratic risk that they cannot uh uh insure, basically. And so, that's why there's a the risky asset. [01:04:18] Um the second point um just um that's not so much a response, more uh you know, an an agreement, I guess. Um it's about uh Laurence's um advertisement of this um [01:04:33] point that you know, heterogeneity in in rates of return uh is super important and can help explain a lot of things, in particular with regard to wealth inequality dynamics. So, it So, yeah, I want to I just wanted to say, you know, I'm a I'm [01:04:46] a huge fan of this literature. I I I 100% believe that's super important. And I'm a huge fan of of of your work in in in particular there. Um and so, the reason why we didn't put that in the [01:04:59] model there, uh at least in the benchmark model, is just because we wanted to have things nice and tractable. Um and so, what you'd need, right, to get it to work is you need some uh also also the extended model, you know, doesn't have enough richness [01:05:14] to to do this, even though there is an capital income risk. What you need is sort of different types, right? You know, some people always have a persistently higher return than others. [01:05:24] Um, so some people are just better investors or better entrepreneurs. Then it kind of works in terms of giving you the quantitative wealth inequality dynamics. And that was just something that, you know, was too complicated or would have made the the formulas less nice. But, you know, yeah, if you ask [01:05:38] me, how how do you how can you fix this model? That's exactly um where I would go. Um, then the final thing, I mean, more more also a point of agreement. Yeah, I think like this is on your very last slide where you said there's obviously lots of [01:05:52] other, you know, drivers of wealth inequality. Um, yeah, I mean, I think a a cool paper to write would be sort of a a horse race, um, basically of different theories. So, have have like one big theory where you put in different [01:06:06] potential drivers of wealth inequality, try to come up with some way to empirically discipline these, and then see, you know, which one explains what fraction of the aggregate increase in wealth inequality. Um, this paper is obviously not that. This paper is sort [01:06:20] of, you know, uh, focusing on one particular mechanism, trying to really come up with a clean theory of how that works, and putting some suggestive numbers on this. Um, but yeah, like a a a follow-up project would [01:06:33] be sort of to to do it properly in a in a bigger quantitative model, I think. [01:06:37] Okay, that's all I want to say, but yeah, thanks very much for for a really great discussion. [01:06:42] Very good. Thank you, Ben. So, we are ready for questions. Uh, the easiest thing will be if you unmute yourself and ask questions. So, Ulf, you can go first. [01:06:56] Yeah, I I didn't read the paper, so I probably missed exactly what's going on. I would would also like to hear a bit more about this mac How do they actually maximize these households? So, I just want to understand also from a [01:07:09] finance perspective this this displacement thing that gives you this increasing um supply. [01:07:20] Uh is it do Do I understand correctly that this essentially is just a risk premium because you have to put more of your money into savings because capital is more productive and now you risk this displacement and you risk averse with [01:07:34] this you see you require risk premium for that and therefore the expected return has to go up. [01:07:42] Um or is that uh not how you understand it? I mean, if it is, then it's kind of like fair return on the extra risk you take, I guess. I guess the related question is I don't really understand [01:07:57] it seems like it's idiosyncratic to the person. [01:08:01] They lose all this. Um but somehow it's it's IID across all these people. So, there's like which is not how it works in finance either, right? Because then you should be able to diversify away this thing and you shouldn't have that risk premium. [01:08:15] So, uh and in fact we know that risk premium have kind of gone down over time, I think. So, so those are basically the Yeah. [01:08:25] kind of things I was puzzled by. Yeah. No, I wouldn't understand it as a risk premium. Um more like it's a it's a steady state condition. So, the the way I think about it is it's it's quite mechanical. So, basically people start [01:08:39] with zero wealth. Okay? Like they start their life um or, you know, whenever they get wiped out they they start with zero wealth. You need in in a steady state you want to have some positive um um capital, okay? [01:08:54] Um the aggregate capital stock is just, you know, the the average of of you know, individuals wealth in the cross section. So, in order to have a positive capital stock, um if people get sort of wiped out every [01:09:07] now and then, it's got to be the case that peop- people essentially accumulate wealth, um you know, rather than just staying put where they are. So, they have like eight out positive whenever uh they don't hit get hit by [01:09:21] this shock. So, then basically that return to wealth um and the the amount by which it exceeds the the discount rate essentially is just enough to basically make people uh [01:09:35] accumulate um and then to balance this sort of destruction of capital. [01:09:40] You know, so so there were there was this graph, maybe let me uh show it just briefly again. Um so, oops. [01:09:47] Uh uh This this graph. So, that's the wealth accumulation process essentially for people. [01:09:59] So, you know, you're born This is effective wealth, which is financial wealth plus human wealth. [01:10:05] Um but so, you're born So, you're you start basically with zero financial wealth, which means that your effective wealth is just your human wealth. [01:10:12] Then you accumulate wealth according to this, and then you get wiped out, and then you start again with with zero wealth. [01:10:20] So, the point is in order for this to have a nice stationary equilibrium with positive capital, it's got to be that R is bigger than rho essentially. [01:10:29] Um just because, you know, you have a bunch of people who who who get hit by these idiosyncratic dissipation shocks. [01:10:36] Aggregate wealth is basically you integrate all over all these guys in the cross-section. [01:10:41] Um and so, say R is were equal to rho, um then, you know, that that line wouldn't be upward sloping, it would just be zero. And then everyone would just always stay at zero, and you wouldn't have um uh you know, a positive [01:10:54] capital supply, and you wouldn't have equilibrium in the capital market. [01:10:58] Right? So, you So, So, that's essentially I mean, it's very it's just very mechanical this I guess it wasn't obvious in the household optimization problem how that P actually entered. Like, you have to care about this risk of getting wiped out, right? [01:11:13] Right. I mean, there's So, there's different ways of of of thinking about it, which I mean, in the paper we write down a bunch of different micro foundations. So, maybe that makes it a little harder to follow because we're we're we're trying to be kind of a [01:11:28] little bit general and saying, "Well, it could be either that or that or that or that." And I guess depending on which one it is, like, you know, it it would want to make you think about it differently. So, one way of thinking about it is, for example, um [01:11:41] sort of a perpetual youth thing, um like uh like in a Blanchard-Yaari model. [01:11:47] Um so, it's essentially stochastic death. [01:11:50] Um um and so, for example, there then again there's sort of two ways of doing it. [01:11:56] One is you have some annuities where you can insure yourself against that, um uh essentially. That would be uh would give you sort of the same equations. Um um or you could also just think you cannot [01:12:10] insure against it, but, you know, when you just before you die, you know, you're going to die and you're going to eat all your wealth. I mean, all of these are kind of obviously a bit extreme assumptions to keep things tractable. Um and it you know, not [01:12:22] necessarily super clear what exactly the you know, empirical counterpoint is. I mean, I mean, I think that's fair. Um but essentially, it's Yeah, it's it's a stand-in, right? For other things that give you a [01:12:36] non-degenerate wealth distribution and uh upward-sloping capital supply, which Okay, but but it's something that they optimize over. They know it could happen and they optimize their utility subject to that shock, right? [01:12:48] 100% Yeah, okay. [01:12:49] 100% Yeah, yeah, yeah. But for example, um in a in a Blanchard Yari type setup, right? [01:12:56] Like you know, when when when you have annuities and you can ensure against that risk it basically just shows up like a higher effective discount rate and it you know, doesn't change anything else. [01:13:08] That's that's basically how this works. Yeah, but let me just finish the thought. So essentially, right? [01:13:13] There's a standard class of macro models. [01:13:16] In particular, heterogeneous agent models like Al Hayagari and so on that have all the same features of our model. In particular, they have a nice non-degenerate wealth distribution [01:13:30] and they have an upward sloping capital supply. The issue with that type of models is you can only solve them on a computer. [01:13:37] So they're you know, not not analytically tractable. So we wanted to have something essentially that functions basically like an Hayagari model but which you can solve with pencil and paper. And so that's that [01:13:50] type of model basically you know, does does the trick. And it comes at the cost of you know, yeah, there's a little bit of attention is like what exactly is this dissipation risk supposed to be? [01:14:03] Any other questions? Yes, I would like to to to ask how would this general equilibrium would be affected by a [01:14:17] decreasing cost of physical investment. You mean like the if if capital say or investment had a price and that price were declining over time. Yeah, I mean I [01:14:31] think it would work basically like in a standard um neoclassical model in terms of the aggregates. [01:14:38] Okay, so you I guess you'd get uh a more capital accumulation, I guess. What I haven't thought about is um what would happen to wealth inequality, which is I guess the the interesting [01:14:52] question. Um I don't know off the top top of my head. [01:14:56] Um Yeah, it's a good question. Um yeah, I I'd I'd I'd have to spell it I mean but it shouldn't be that hard to do basically. I mean what's nice about this this model is that you know, you have everything with pencil and paper and you can just you know, add that to the [01:15:11] equations and then do the comparative statics, right? And and essentially I pretty sure in that case you should still be able to solve everything in closed form. And uh I I but I just haven't done it basically. [01:15:23] Thank you very much, Ben. Uh I think that brings us to the end of our time.