Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable. ======================================================================== # Left Behind (Papanikolaou, MFS Summer School 2022, GE-model segment) Speaker: Dimitris Papanikolaou, lecture "Innovation and Asset Prices", Macro Finance Society virtual summer school, uploaded 2022-08-22 (this segment covers the Left Behind model; audience questions are interleaved) Discussant: None Video: https://www.youtube.com/watch?v=ZIcPKAVA57Q&t=3960s ## Talk (01:06:00 – 01:40:40) [01:06:07] all right so having uh had a view now what the partial equilibrium model delivers now let's think about more broadly what would happen in ge that's a useful exercise for at least two reasons so the first thing is [01:06:21] there are the partial equilibrium kind of understates this phenomena because assets in place as you said are basically unaffected by technology that doesn't have this idea of a replacement effect [01:06:35] um instead what you might happen in reality what when these new types of capital become more productive due to competition because firms are all competing in the same market the value of assets in place will fall [01:06:49] so g is going to give you that and the second thing that g will give you is it's actually going to endogenize the price over s for xe now what happens in ge is [01:07:01] in a world with complete markets that is there's a representative household uh that basically consumes whatever is being produced in the economy then the sign of the price of risk [01:07:14] depends on preferences so if the household has cra preferences or the is lower than the reciprocal of risk conversion then what's going to happen in that [01:07:26] model is the stf will rise if on the other hand the eis is sufficiently high higher than the reciprocal of risk conversion then households are going to view the rise in [01:07:39] future consumption as more than enough to compensate for the fact that consumption falls today and in that model the marginality will actually fall okay but to be clear this is a world in [01:07:53] which markets are complete and c has no redistributional effects whatsoever now we can contrast it in a case where [01:08:05] markets are incomplete in that the rents or the benefits from c don't accrue equally to everyone but some say jeff bezos or elon musk get much more of it than me [01:08:20] i think that's that's a world in which probably is somewhat more realistic and in that world there's a number of interesting things effect happening specifically you can actually have the stochastic discount factor to rise and [01:08:34] now of course you can ask what exactly what is this stochastic discount factor in a model within complete markets well think of it as the part of everyone's margin utility uh that's common you can actually get that to rise and it turns out you don't need a lot of [01:08:48] it you don't need a lot of ingredients there you just need basically for a small part of the population to directly benefit from these projects and then if people have some fomo [01:09:02] then they get upset that other people got rich okay so i'm going to discuss a little bit of i'm going to discuss it in the context of uh the favorite of the jv with the linear noise because it's going to build the same [01:09:15] structure like enough kind of intuitively to have investment has to go up when when the size shock hits right so consumption goes down that's always going to go up [01:09:29] so on impact what happens is investment will go up consumption will go down so in a cra world the stf rises now so [01:09:44] what happens in that model is that consumption t plus one will go up because now you have more capital sure so then depending on how you think you know if you have some type of recursive utility like they say f sensing [01:09:58] depending on how you think that about that you can get the the marginal utility of the representative diversity the rise or fall right okay so it's not just a function of current consumption i mean no because [01:10:12] it's you know it's it depends what enters your margin utility so in a world where preferences are time separable another way to say this the eas is equal to the reciprocal of risk conversion [01:10:25] then the saf will rise in a world where these two things are separate it depends on the difference between the eis and nurse coverage and what happens in that model is if the eis is very low [01:10:39] the fact that consumption falls right now makes household one to move resources into that stair into that state because they're very upset about the fact that now their consumption profile is deeply [01:10:51] upward sloping whereas if the ais is sufficiently high they don't care about it so much and then just view the future with more optimism if you want but the future looks better in which case marching until the falls that's my metaphor for that's at least [01:11:06] my understanding of what's happening in that type of model and what did you exactly mean by fomo you kind of mention it in passing but i'm going to talk a little bit about i'm going to have the household have preferences not just over its own consumption it's going to also going to allow it to [01:11:20] benchmark its utility relative to what everyone else is doing uh but uh yeah a habit but not a linear habit so your preferences are going to be you're you're going to consume [01:11:35] your your consumption basket is going to be something like this so this won't change the coefficient of relative risk conversion because everything is proportional [01:11:49] but it will make you care about what happens to your own consumption relative to what everyone else is doing now one way to think about micro founding this is we're all kind of competing for some local resources that [01:12:02] are scarce real estate land etc so alexi if you know suddenly everyone in wall street gets a massive bonus and you're renting uh that's or you're competing for schools or whatever is [01:12:16] your competing that scars that's gonna make you uh effectively consume less okay okay so the model is going to have a similar structure as before there's going to be these projects that [01:12:30] produce output uh i'm going to follow the the formulation through which it's like the original solo formulation which if the project is created at some point tau [01:12:43] it's gonna inherit the productivity that's state-of-the-art at that point in time okay that's my innovation shock the rest is relatively the same or less there are these sort of aggregate demand shocks that you know move stuff around [01:12:58] and the level of frontier technology is going to move around again so that's that's basically the model it's basically as before uh [01:13:12] a question in the chat i think i missed it before oh go for it matthew you want to ask your question um sure just while you both were talking about the uh stochastic discount factor i would just say is is one way to [01:13:26] interpret that that uh the arrival of some new innovation um makes it so that now okay well now i'll save a little bit more because uh the future consumption is going to be so much better [01:13:40] uh it's not no uh you don't want to save because of that is actually if you don't invest more output doesn't increase so it's because in these models rather than that these models the only way c affects [01:13:54] output if it's actually implemented into new capital so this would be so uh so there might be some difference so this will always happen so this will always happen and this will always happen because [01:14:07] these new investments are going to bear fruit at some point down the line so uh so this will be different than from a model where maybe you have uh you know two goods [01:14:21] two consumption goods and uh you can consume one now but then another one has to be sort of unlocked by some sort of innovation shock that's okay that that's going to be the same uh as long as that unlocking doesn't happen for free [01:14:35] but you have to give up some resources today so if it comes from if it comes if it happens for free then there's no aggregate resources being spent then it's just the endowment shock right it's just we're sitting around and now [01:14:49] suddenly there's more stuff but if you have to give up some resources today for that to happen then mechanically your consumption is going to be lower today but then you have more stuff later on so that fits into pretty much the same [01:15:03] framework so i think this idea is more general makes sense it's just what you call consumption now is some composite of these two goods um now you can say maybe the weights change [01:15:17] or something i mean you can probably you can definitely make what you said richer than this um but i think on some level you're trading off having fewer stuff now in exchange for more stuff later so i think that's a that's a robust [01:15:35] feature of the model what's not robust is how you feel about it is that what's your how would your marginal utility respond in this state of the world that i think we can debate a little bit and say well [01:15:49] it kind of depends do you value a dollar more when investment opportunities are good or less yeah i mean if there were a cancer drug for instance that's going to allow me to live 20 years longer [01:16:02] you know yeah right my uh yeah yeah so i think that that's that right but keep in mind though that this what we just said is a model through which these benefits of these new goods kind of accrue equally to everyone so i think the [01:16:16] cancer drug is a great example which is okay maybe the firm that patents the cancer drug gets very rich but there are these indirect spillovers for me which now i don't need to worry about getting cancer i mean maybe i'll [01:16:28] go bankrupt but you know still i'll live and therefore i'll save more because i'll i'll live longer perhaps or no no this is not what's happening so this is what happens at the aggregate level so if we have to [01:16:40] create spend resources to get the cancer drug going then we're going to have to right now we don't have any anything to show for it we're just giving up resources uh i think that's what you mean by [01:16:54] saving more right it's just we're we're investing more there's no saving in this model simply because the the risk-free asset is in zero net supply right for every saver there's a borrower i mean what is happening the economy as [01:17:09] a whole if you only saving more by investing more but they're really investing more to make these things uh a reality so to speak does that kind of make sense yeah i think it makes sense i think i think what what i'm uh [01:17:23] no i'll i'll think through it more but uh yeah thank you yeah i mean it's just the right language i think to think in this world i mean you can think of a saving but it's really that you're investing to make the cancer drug happen because if you don't invest then there's no cancer [01:17:37] drug yeah that's an idea for a cancer drug i think i understand the distinction you're drawing there and and why it's important um okay yeah that's the that's the that's the key part of the that this makes these sharks different which is if you don't do [01:17:51] anything about it you don't actually get anything for it so it's not mana that comes from the sky as free is you have to kind of give up something now in exchange for more stuff later so another way of what these another way [01:18:04] to think about what these types of technology sharks do is it change their rate of return of investment they changed the marginal return to investing a dollar now versus later in the language of q theory what's [01:18:18] moving around is marginal queue okay so anyway the model has a similar structure as before with some more details the details are not super important for now what i want you guys [01:18:33] to think about is the fact that this c shock is changing the profitability slash productivity of only new projects not the existing projects okay and then there's you know there's a [01:18:49] few more bells and whistles so the key part here is that a large fraction of these benefits are going to accrue to the elon musks of the world [01:19:03] not me so the way the model works is that in principle anyone can have an idea for a new project and once you have an idea for a new project is what you do is you sell the blueprint to an existing firm which implements the [01:19:18] project and you get a share error and the model is not rich enough to have real firm so if you want is you create a startup and then your startup gets acquired or if it doesn't get acquired it doesn't really matter the whole point here is that [01:19:31] an innovator gets to appropriate some fraction of the value of her idea the remainder goes to the firm that implements that project so shareholders actually get something but they don't [01:19:45] get the full amount okay so because people get rich in this model in order to keep the distribution stationary they also have to you have some type of lg structure and and then the other thing that [01:19:59] households do is they work and labor in this model is super boring there's nothing interesting happening with labor we just sit around and we supply labor and later on we're going to think about whether that makes sense or not but for now this is what's happening [01:20:13] now this model is actually very tractable that even though it's rich it actually it's not significantly harder to solve than a model with a representative agent [01:20:26] and the trick to doing so is that the cross-sectional distribution of firms and household wealth even though they're not constant they constantly evolve and respond to the shocks they actually don't matter for equilibrium [01:20:38] prices so you don't need to keep track of distributions of the state variable it's just enough to keep track of aggregate objects okay now we can talk about what the sdf is so the sdf is just a projection of [01:20:53] the individual stfs on the space of traded assets think of it as a common component of everyone's margin utility and what's going to be key here is that [01:21:06] a a key object in that scf rather a key object in marginal utility um is going to be uh look at the household's value function it's going to depend on their wealth [01:21:21] share so i'm going to consume something that's proportional to my wealth so my share of the consumption of the aggregate economy is going to be proportional to my wealth so keeping in mind that these are going [01:21:36] to be dynamics are going to be uh they're going to play a big role uh so the model has quote long-run risk in the sense that there's a permanent and transitory decomposition of uh aggregate consumption and output uh so there's a there's a sarcastic [01:21:50] trend and then the economy fluctuates around that trend uh because of uh decreasing returns to invest eventually so you know once the way the the model works is that when c improves [01:22:04] new projects become more profitable and then we slowly kind of accumulate capital stock to reach that state and then as c improves again we're going to go there anyway that's that's less interesting for what i'm going to say so this is how um [01:22:17] these are the impulse responses of some quantities the model to by improving c so a shock to c translates into higher output in the long run not right now so on impact [01:22:31] nothing happens but over time as the economy accumulates better projects output rises what's the process through which this happens well you invest more so you have to increase investment and because on [01:22:46] impact output doesn't change whereas investment rises then aggregate consumption has to fall okay so in a model of the representative agent and sierra utility that alone would lead to a rise in scf [01:23:00] but of course because consumption is higher going forward depending on how you think about the future versus the present that is how you think about the risk conversion versus aes the sign of the price surface can basically be either positive or negative uh if you look at aggregate dividends in [01:23:16] the economy they fall and the reason for that is that firms are cutting dividends to invest more because for for the whole economy investment opportunities got better so then firms are going to [01:23:30] pay out less and then invest more and here to be clear this is not really dividends this is um basically uh the difference between profits and investment so there's no this is not a model where there's a [01:23:45] clear dividend policy this is what firms could pay out if they wanted to so think of this as free cash flows to equity as opposed to uh well these are really free cash flows not uh dividends but you know [01:23:59] so that distinction is subtle but it's also important to keep that in mind that these models actually don't have any predictions about evidence unless you make an assumption about dividend policy okay so the value of labor income rises so [01:24:13] labor here is a perfect uh can work perfectly with any technology so then all the workers are happy and the sdf rises okay so now this may seem a little bit surprising [01:24:27] because you know consumption looks better going forward and by the way i've calibrated the model so that risk conversion is very high relative to eis so this is sort of the quote standard [01:24:40] calibration in literature um so then it's surprising then that the is the sdf rises even though the future looks better and let's try to understand a little bit what's happening here [01:24:54] so the first thing to realize is that individuals don't all consume the same amount because they have different wealth so an individual's consumption i can write it as some share of aggregate consumption [01:25:07] and what's important is the dynamics of this welfare so the first thing to realize is that what's happening here is there's a little bit of a duffy constantine this effect going on that if i think look at the dynamics of [01:25:18] an individual household's wealth share there's something that depends on dt which doesn't matter for us but then once the household gets an idea she's going to appropriate a fraction of [01:25:32] that idea etta and depending on how valuable that idea is that ratio which is a state variable in this economy her wealth will jump her wealth shares will jump as well [01:25:47] so basically think of this as in this model households have this idiosyncratic risk to their consumption because they're getting these new ideas [01:26:01] and the this idiosyncratic risk the size of that depends on the relative value of new projects relative to total wealth okay so another way to think of this is [01:26:18] that the volatility of consumption growth varies over time because this innovation lottery essentially reallocates wealth shares from existing households to the elon [01:26:31] musks of the world and the size of that distribution the size of that redistributive effect depends on the rate of innovation the economy there's no innovation then these new projects are not very valuable there's very little redistribution [01:26:46] happening whereas there's a lot of redistribution now this volatility of consumption becomes more important okay so then it's useful to keep then track of what's [01:27:01] happening in the cross section of households and here it's useful to draw the distinction between the average household and the median household because this illustrates what's happening which is when the shock hits nothing happens to [01:27:15] the average the average wealth share is going to be the same is one because the households are normalized to measure one but then the median falls so what this is telling you is that sorry the labels are missing for these [01:27:31] figures this is the wealth share um so what this is telling you is that now the distribution of wealth and the economy became a lot more right skewed that the elon musk of the world and jeff bezos of the world now [01:27:44] own a larger fraction of the economy as before so everything became more right skewed this is individual consumption [01:27:56] so individuals consumption still goes up but the median goes up by much less than the average which is another statement of saying that the distribution of consumption growth now became a lot more right [01:28:09] skewed that elon musk's consumption went up significantly more than mine what this is is what happens if i also [01:28:26] take into account the fact that you have relative preferences and then now you're seeing that for most of the households in fact their consumption basket which now includes the fact that not only i [01:28:39] consume my own good but i'm also worried about my relative consumption relative to the average that goes down and yet another way to say the same thing is [01:28:53] that the volatility of my stf has gone up which is a statement of the what i said before oh sorry yeah go for it uh one question [01:29:09] was whether back to the firms i guess whether you're assuming it's all equity finance yeah it's all i mean there's no debt in the model so it's i'm all doing it from the perspective of firms so [01:29:22] there's no financial friction there's no financial friction whatsoever uh yeah the good question is um just like the production-based model is instant assumption right the [01:29:36] dividend equals the revenue minus investments i think about right your model when there is a positive asset shot right you didn't actually decrease but that is the time right that is the bad time so just thinking right if you allow for [01:29:51] the like bond financing right i don't know how exactly the cause of the bond because that's where help write the firm just lose their dividend so make for more value so things like if adding raise the bond [01:30:05] finance will change maybe change the results yeah i mean maybe it depends what you assume i mean i guess i mean one has i mean obviously gonna too many things um i think just adding that mechanically [01:30:19] this will just amplify the volatility of equity so if i have to make if let's say all firms have a console bond and they have to make interest payments then that's a part of output that they need to do now what happens if they can [01:30:32] adjust that capital structure in anticipation of that i think or they need to refinance or that i mean these are all interesting questions but i don't know the answer right that's worth doing for sure [01:30:45] right i'm not messing it just like raise the price for the dividend cash flow and the price raised for the referees is it could be very different absolutely no it could be very different i think that's an interesting thing to [01:30:58] explore i don't have a uh okay as far as i know no i don't i don't think anyone has right um [01:31:13] do you have intuition here why the shock to the sdf is so permanent everything else is kind of you know even the the displacement shock um on the next i mean in these models the the okay so [01:31:28] if the shock to the sdf were not permanent then it would have to be the case that i mean it's not super permanent because the risk-free rate is moving around but risk premia in these models are in this model is pretty much constant [01:31:42] so why would the stf have a transitory component is because the the risk premium changes so it changes the rate at which the sdf uh reverts back so does it like the volatility of the sdf comes back down it comes back down but then the drift [01:31:56] doesn't the drift is more or less constant and what's the drift the drift is basically the risk-free rate yeah so there is this there's some action at risk for rate but not not that much [Music] [01:32:11] um so then you can think about what does that model imply for long-term bond prices relative to equity so there's an all paper by um uh alvarez and yerman [01:32:28] that make the point that uh for the mo for these types of for models to rationalize an equity premium of stocks over long-term bonds you need a large permanent component and that's sort of what's happening here [01:32:42] um and the reason for this is that just the wrist rate doesn't move around very much but that's a feature of the calibration just because in the data at least the the movements the risk rate at least at high frequencies are not that big i mean you'd think the increase in the [01:32:57] idiosyncratic risk that would make the risk free rate go down but not yes there's there's some of that happening but at the same time there's an offsetting effect which now we're all richer the growth rate [01:33:11] uh i think both of these elements combine to make the risk rate more stable um again the model is sort of calibrated to fit the low voltage rate so that's sort of mechanical now is that a deep feature of the model no i'm sure a different calibration could produce a [01:33:26] very volatile risk for right but that's that's that's what's happening here um so based on that you can understand now why [01:33:40] for most people in this economy this doesn't look like an amazing uh shot going forward i mean i still may end up being feeling happier uh but i'm a little bit upset about the fact that i'm definitely not consuming [01:33:54] as much as elon musk so that's that's kind of what's happening here that's why i said you needed uh there are two key ingredients here one was in complete markets so that not everyone gets the same share of rents from you innovations but also [01:34:09] you need a little bit of fomo so that i'm almost all always benchmark benchmarking my uh utility relative my my individual consumption related to the aggregate and i think there's this is not a crazy description of the world i mean there [01:34:23] are all these surveys where you know people have these self-reported measures of happiness and even though the world has grown tremendously richer over the last 50 years it's not that people report being uh significantly happier as a result and [01:34:37] again i don't i don't think i have anything to say here just that this is a feature of the model that helps you get there um this is what happens to individual firms uh and i've plotted two types of firms [01:34:51] here one is a growth firm in solid lines and the other one is a value firm in the dotted lines and what's a growth firm and a value firm in the model is a growth firm is one in which it has uh [01:35:04] very little existing projects but it's likely to receive a lot of projects going forward uh and a valley firm is the opposite the valley firm is a big firm that has a lot of existing projects but very few growth opportunities going [01:35:19] forward so for growth firms uh specific sea shock is great news uh it means higher profits going forward they invest more they cut dividends to invest but because they're going to get more [01:35:33] dividends going forward their their market values go up versus valley firms is less good news because they're being displaced because they're competing in the same market as these other firms so their dividends decline but more [01:35:50] importantly their market values decline okay so we calibrated the model to try to fit sort of the standard uh asset pricing targets so the model has a you know reasonably smooth consumption both [01:36:04] in the short run but also in the long run we try to match the volatility of the share of shareholders so they're also shareholders the model didn't talk about this this helps match quantitatively a few things [01:36:18] uh there's a sizable equity premium there is for it is low and stable and then the model generates a value factor not just a value premium but also it generates uh the failure of the kappa m to price the [01:36:33] value factor okay so actually the model is a little bit too well relative to the data so you could probably scale things down a little bit okay so i think i i walked you through the intuition what that's happening [01:36:46] uh now is there some evidence additional evidence you can use to calibrate some of these facts we also used this direct measure of innovation that i talked about earlier which is based on [01:37:00] this value of patents and look at what happens to cash flows of firms when other firms in the same industry innovate and what you see is that for value firms [01:37:15] these are firms that have low valuation ratios both the model and the data uh their cash flows declined going forward rush for growth firms again this is again what happens to other firms in the [01:37:28] same industry they have a much smaller response okay so this is an example of how you can use some direct measure of innovation in the data and then you can construct a direct model equivalent [01:37:42] because what was the value of of this approach of these patents well i could construct the value of a single idea in the model and then try to be a little bit more disciplined about [01:37:54] how i map the data to the model anyway so basically what's happening in the model is that these growth firms are less likely to be displaced simply because they keep innovating and as a result because they're less likely to be [01:38:08] displaced in a state of the world where the sdf is high they have a lower discount rate so that's basically the how does the model work [01:38:22] okay so quantitatively uh if it's the data uh or the cost of uh potentially extreme parameters so what's happening in the model is that [01:38:35] uh households are pretty risk-averse so the coefficient of risk conversion is 40 which i'm told is too high uh the other thing that's happening is that households put most of their weight in their relative consumption so these are [01:38:49] relatively extreme parameters uh and then you want to think about what what exactly is the model capturing and what's not capturing okay so let me pause here for [01:39:04] 15 seconds for questions and then i'm going to continue okay so if you think about it for more [01:39:17] than 10 seconds then you realize that what's missing from the model is many important channels and the fact that labor in the model is a great hedge for technology [01:39:31] again what the way workers feel like in the model is because their labor works with any technology vintage these guys are happy and because for most households labor income [01:39:43] is their largest source of wealth this gives households a built-in hedge against technological progress against technology or innovation even though their value of their value portfolio goes down the value of the [01:39:56] labor income goes up so now they have this amazing hedge now that's kind of an extreme assumption like it basically assumes that there's no labor market frictions whatsoever that is workers can [01:40:10] frictionally move across firms it also assumes that their labor income is fully diversifiable because what happens in the model is that workers sell claims to their labor income so [01:40:21] they take no individual risk whatsoever the model assumes there's no skill displacement that is anyone can work with any capital without any loss in productivity and there's also no automation in the [01:40:35] model like this there's there's no type of technology there's no type of capital that directly displaces labor okay so you can these are all the absence of all these channels