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Supplemental lecture: Technology diffusion and adoption — Transcript

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0:03Uh welcome back um to this uh STEG
0:07virtual course on macroeconomic
0:08development. Um the STEG is a again you
0:13guys know that know this by now but STEG
0:16is a program on structural
0:18transformation and economic growth a
0:19research program run by CR uh funded as
0:23part of the UK aid effort by the foreign
0:26commonwealth and development office
0:28United Kingdom. Uh we're very grateful
0:31for their financial support. Uh we're
0:34also grateful for uh Chris Tenetti who
0:37is not receiving much of that financial
0:39support. uh none of the lecturers are
0:40receiving much uh compensation at all.
0:42They're doing this out of the goodness
0:44of their hearts. So, we're especially
0:45appreciative of Chris today who's going
0:48to be talking about technology diffusion
0:50and giving an overview of uh models of
0:53technology diffusion. And um I also want
0:57to thank um Mandy Chen, Kirsty McNeel,
1:01and Lauren Wearing uh for uh helping
1:03with the organization and logistics of
1:05the course. Um Chris will speak for
1:08about 75 minutes. Um those of you who
1:12are in the front row, uh we ask you to
1:14mute uh while he's speaking, uh you can
1:17unmute if you have a question. Um
1:21uh we try to stick to clarifying
1:22questions during the lecture. Uh
1:25afterwards, uh bigger picture questions
1:27uh would be more appropriate. Uh for
1:29those of you who are joining as a
1:31webinar uh participant, uh you can enter
1:35enter questions into Q&A, uh Doug Gan
1:38and I will do our best to answer those.
1:40Um and those that we can't or those that
1:42are more general, we may uh leave to
1:45Chris if there's time uh at the end. So
1:49with that, let me hand over the reigns
1:51to Chris. Chris, if you want to share
1:52your screen.
1:53So thank you for having me. It's an
1:55honor to to be here part of this um this
1:57lecture series this course on macro
2:00development and um yeah my supplemental
2:03uh lecture is on technology diffusion
2:05and adoption. So here's uh what I
2:08propose um that we talk about today and
2:11I'm happy to to take questions sort of
2:13as I'm presenting in addition to the uh
2:16questions um at the end. So, I'll just
2:19quickly go over some background
2:21material, a little bit on non-rivalry
2:23and uh motivating fact. Uh and then what
2:26I'm going to spend most of my time on is
2:28exploring some theories of technology
2:30diffusion. I think uh in other lectures
2:33as part of this uh this uh series of of
2:36classes there's going to be more
2:38discussion and has been more discussion
2:40a bit on the empirics of technology
2:42diffusion and maybe a more um
2:44microeconomic uh approach to thinking
2:47about technology diffusion and adoption.
2:49And so what I wanted to do today was try
2:51to complement those lectures by uh
2:54developing some structural models of
2:56technology diffusion. And I figured I'd
2:59focus on two types of models um that are
3:03very prominent. One is a Nelson Phelps
3:06style uh model of diffusion. Um and uh
3:10just because it's what I'm most familiar
3:11with, I'll use some of the notation from
3:14a journal of economic growth uh paper
3:16that I wrote with um Benabe and Pearla.
3:20And then I'll spend some time uh
3:22discussing idea diffusion models. Um,
3:25and there's a great survey article by
3:28uh, Pakua and Bob Lucas um, that I
3:31reference here that'll give you a really
3:33nice overview of many different
3:35intricacies of the different models of
3:37diffusion. Um, what I'm going to do
3:39today is sort of walk you through um,
3:42two types of uh, these models one in
3:45discrete time and one in continuous
3:47time. Um and the idea there will be to
3:50try to help you understand um how to
3:53write down microfounded models of
3:55technology diffusion and uh we can spend
3:57a little bit of time talking about uh
3:59how to bring them to data as well. Um
4:02I'll at the end hopefully briefly
4:05discuss some models uh where I think um
4:07the frontier is of the of the research
4:10literature trying to think about
4:12innovation and the creation of new ideas
4:14uh simultaneously with thinking about
4:17idea diffusion. Um and there's some
4:19references there that I'll use to to
4:22discuss that topic. And I just want to
4:24point out and and just acknowledge
4:26upfront that I'm going to be skipping a
4:29bunch of um models that are prominent
4:31and and it's not because I think they're
4:33less good. It's in part due to these
4:35time constraints and in part due to my
4:37my lack of knowledge and expertise. And
4:39so there's some some recent papers on
4:42creative destruction um uh and how that
4:45facilitates cross-country diffusion of
4:47of knowledge and ideas and technology.
4:50There's great work on networks um that
4:53can be used especially when you have a
4:55smaller number of uh of uh agents you
4:58know people and there you're thinking
5:00about the how each person is connected
5:02to each other person is a really
5:04important thing to understand uh how
5:06that the technology flows across the the
5:09population and there are models of
5:11learning that are very closely connected
5:13to models of technology diffusion um
5:16when you take a particular stance on on
5:18what a technology is thinking about a
5:20technology as an idea. So that's sort of
5:22the the big picture of where where I'm
5:25hoping to go in today's class. And my
5:27goal is is pretty simple. I want to help
5:32uh people have an understanding sort of
5:34a broad overview of some theories of
5:37technology diffusion and sort of how the
5:39literature has evolved. And more
5:41practically I hope that the people that
5:44are listening to this lecture get an
5:46understanding of these two types of
5:48models. well enough to use them in your
5:51own research and build on them. And so
5:53this is really hopefully sort of a a
5:56class that uh helps develop tools so
5:58that you can just take these tools and
6:01and hit the ground running in your own
6:02research.
6:05So one piece of background knowledge
6:07that I just want to get on the table
6:09because it's so crucial to understanding
6:11um technology diffusion. Um, one way
6:15that economists tend to think of
6:17technology is as an idea. It's a a
6:20blueprint or a recipe. It's a way of
6:22combining some ingredients and getting
6:25some output. And so you can think about
6:28um I uh technology sort of in this broad
6:32sense. Um, it can be something as simple
6:35as oral rehydration therapy where you
6:37just simp combine some water and salt
6:40and sugar and that's a much better way
6:43of rehydrating people who are suffering
6:45from dehydration maybe from diarrhea or
6:48something like that uh than than just
6:50using water. And these are ingredients
6:53that are available to many many people.
6:56um but sometimes they're not combined in
6:59the right way in the right recipe and
7:01used when they could be used to save
7:03lives and really improve people's uh
7:05health. And so it's just that knowledge
7:07having the idea to combine these things
7:09is is the limiting factor. It's not
7:12necessarily having the ingredients. Um
7:15and so when you think of technology as
7:17an idea, non-rivalry is really an uh an
7:20obvious essential um concept to
7:22understand if you want to think about
7:24the diffusion of technology and growth
7:28ideas are non-rival. And what that means
7:30is that any specific blueprint or recipe
7:34can be used both in a factory in India
7:37and in a factory in Brazil at the same
7:39time. you know, management practices,
7:42um, you know, uh, irrigation, uh, pro,
7:45uh, practices, uh, at this that's
7:49different than a particular machine, uh,
7:52an irrigation pump or, uh, being used in
7:56a factory that's that one, you know,
7:59pump or that one machine tool can only
8:01be in India or Brazil at one given time.
8:03It can't be in both places at both
8:05times. And so this is going to motivate
8:08the need for distinct models of the
8:10distribution and the spread of ideas and
8:13technology. We have a lot of models
8:15about sort of where physical capital is
8:18produced and how it flows across space
8:21and across time. Um why don't we just
8:24relabel physical capital as as
8:26technology and and then we can just use
8:29the models off the shelf. In part it's
8:31because we think a large a large part of
8:33technological progress this improvement
8:36in productivity over time that can be
8:38seen at the aggregate level but also at
8:40the at the micro level in firms and in
8:42workers. We think it has a large a large
8:45part of that has to do with this this
8:47diffusion of this non-rival uh component
8:49of technology and the economics of
8:51non-rival goods is very different from
8:54sort of classical Adam Smith economics.
8:56This is in part what what Paul Romer won
8:58his Nobel Prize for and um I just it
9:01underlies a lot of what's going on in
9:03the models that I'm going to show you
9:04today. So I just wanted to start off by
9:06acknowledging that.
9:09The other bit of background that I
9:11wanted to bring to the table is just one
9:13sort of famous fact that motivates
9:16thinking about uh technology diffusion
9:18in the context of of rich and poor
9:21countries and countries that are growing
9:23fast versus countries that are growing
9:25slow. So this is a a chart taken from um
9:29Bob Lucas's paper in the first ever
9:31issue of uh AJ Macro um and it plots on
9:36the horizontal axis uh per capita income
9:39uh in 1960 and it's going to rank
9:42countries each dot is a country by their
9:44per capita income sometime in the past
9:471960. And on the vertical axis it has
9:49the annual growth rate uh from 1960
9:52until 2000. So after that initial uh
9:56that initial point where we're ranking
9:57them on the horizontal axis and you can
10:00see sort of uh uh highly variable growth
10:03rates amongst the countries that were
10:05initially poor. Um whereas the rich
10:07countries were growing sort of this
10:08constant pace. That's what a lot of
10:10growth economics is about. Where is this
10:12sort of 2% growth coming from?
10:15What Lucas then did is uh separated uh
10:18countries into open and market-based
10:21economies uh compared to closed
10:23economies or economies that were more
10:25centrally planned. Um and the black dots
10:29are those open countries. And he
10:31described these uh open countries as uh
10:35that that form the um this upper edge
10:38this uh of the growth triangle here. Um
10:42uh as describing the growth potential
10:44for open economies and as demonstrating
10:47the equalizing forces operating in the
10:49set of open market economies. And the
10:52basic idea was that the countries that
10:54were furthest behind were the ones that
10:57grew the fastest. And that's uh you know
10:59there's a long literature on on on
11:02growth dynamics and and convergence and
11:04things like that. But this is just one
11:06way of of seeing the simple fact that
11:09the countries that were furthest behind
11:11and open uh connected to each other in a
11:14market-based system uh were the ones
11:16that that grew fast. And so what he did
11:19in his paper and what I'm going to do
11:20over the next few slides is develop a
11:23model that's uh helps us to understand
11:27why it might be that the countries that
11:29were the furthest behind might be
11:31growing the fastest. And it has some
11:33analoges to the simple solo or
11:36neocclassical growth model where uh if a
11:39country is starting well below its
11:41steady state uh it might grow faster to
11:43its steady state than a country closer
11:45to its steady state. But there's a lot
11:47of growth accounting and development
11:49accounting that suggests a large part of
11:52this increase uh rapid growth is not
11:55just capital accumulation but it's a it
11:57seems to show up in measures of
11:59productivity growth. And so we want the
12:02story that that goes beyond just the uh
12:04accumulation of capital.
12:07So that's going to that's a a very
12:09simple motivation. This this class is
12:11mostly designed to help you think about
12:13models of technology diffusion. But
12:15that's just in the back of your mind one
12:17key motivating fact for thinking about
12:20what you want the model of technology
12:22diffusion uh to deliver.
12:25And so I'm going to spend a little bit
12:26of time working through some Nelson Felt
12:28style um models of diffusion.
12:32And uh this goes all the way back to um
12:35an AER paper in 1966. And I would say um
12:40uh this is kind of like the breadandbut
12:43model of diffusion that that first comes
12:45to my mind as a macroeconomist. Um it's
12:48very simple, it's easy to work with um
12:50and and certain variations of it are
12:53very flexible for allowing uh and
12:55capturing very different patterns of
12:57technology diffusion. So what I'll do
12:59over the next couple slides is lay out
13:01the the basics of this Nelson Phelps
13:04model. I'm not going to do it in a very
13:06fully articulated version of the model.
13:08I'm just going to focus in on on the
13:09core insight. So for simplicity, let's
13:13think about the unit of observation
13:15being a country and let's just think
13:17about the population being constant. Uh
13:20this is really going to be about
13:21productivity dynamics.
13:23And there's a frontier country that has
13:26the highest level of technological
13:27advancement at any point in time. And
13:30then there are going to be follower
13:31countries. And the follower countries
13:33are going to have varying distances to
13:35the frontier. Some are going to be, you
13:37know, operating with technologies that
13:39are almost as productive as the frontier
13:41technology and some are going to be
13:43operating with technologies that are
13:44that are much further behind the
13:46frontier. And the key idea of the Nelson
13:49Phelps model is that the rate of
13:51diffusion of technology flowing from the
13:55the leader to a follower is a function
13:58of the distance between the leader and
14:01the follower.
14:03And the way this works as as you know as
14:05an economist is that the researcher
14:07specifies some differential equation
14:11that determines the rate of flow of
14:13technology from the leader to the
14:15follower.
14:17And if you just have the frontier
14:18growing at some exogenous rate, this
14:20will allow you to get some some growth
14:23uh in the long run. Um but this is
14:25really a model not focusing on the you
14:28know what might be more traditional
14:30growth economics where innovation comes
14:32from in very rich countries. It's more a
14:35model designed to focus on diffusion.
14:37Wherever this growth is coming from uh
14:39at the frontier, how does it get
14:41diffused back to countries that are that
14:44are typically poorer and and operating
14:47with less uh productive technology?
14:50And a comment I'm I'm going to point out
14:52as you'll see when we go to the math is
14:55that the thing that makes the Nelson
14:57Phelps model so tractable and simple to
15:00analyze is because it's it's framed in a
15:03way where everything is pairwise. you
15:05can just look at a follower and the
15:08leader and then you can do that follower
15:10by follower. You don't have to worry
15:12about uh sort of entire network of all
15:15the followers and how they're connected
15:17to each other and how they're connected
15:18to the leader. It's just a simple model
15:20that says there's some frontier
15:23technology and it's going to flow to
15:24followers as a function of how far the
15:26followers are below the leader.
15:29So to put that a little bit more
15:31concretely,
15:32let's think about country I who's got
15:35some fixed population LB bar of I and
15:38output in that country is just ZI times
15:42L. So Z is going to be productivity.
15:45This is going to be a model of how
15:47productivity evolves over time.
15:50And then we can think about a
15:52distribution of productivity Z across
15:54countries. But we don't really have to
15:56worry about what that distribution is
15:59because we're going to be able to focus
16:00on uh country follower pairs. And so
16:04let's just focus on a particular Z. And
16:07what's really important in this
16:09framework is the productivity frontier.
16:12And so let's call that F of T, which
16:14could be evolving over time. That's just
16:16going to be the maximum productivity
16:19that's that's in existence in the
16:21planet. So the highest productivity
16:23amongst that distribution of
16:24productivities across countries.
16:27And then the core insight of the Nelson
16:30Phelps style diffusion model is that
16:33productivity growth Z dot over Z is just
16:37going to be given by this exogenous
16:40function that we specify. And the key
16:43thing that shows up in this function is
16:45the ratio of any particular country's
16:48productivity Z to the frontier
16:51productivity F. And M is going to be a
16:55key parameter of the diffusion equation
16:57that's going to determine the properties
16:59of how quickly technologies flow from
17:01the frontier to the followers and and uh
17:05other properties that we can discuss
17:06now.
17:10So, I'm just rewriting the law of
17:12productivity right there up at the top.
17:14Um, and the Nelson Phelps model was
17:18actually a special case of this
17:20functional form that I put up here. Um,
17:22the Nelson Phelps model put that m
17:25parameter to be minus one. And so, let's
17:28just take a second. I encourage you to
17:30take a second and work through the math
17:32a little bit. Just see what happens when
17:34you put M is minus one.
17:37Right? That's going to flip the the f
17:39over the z. The frontier is bigger than
17:42than z by by definition. The frontier is
17:45the maximum z. And so this this term is
17:49going to be negative, but you have a
17:51negative one on the outside. So this is
17:53going to be a positive term. So that
17:55means there's z bar z is going to be
17:57growing over time. And when is it going
18:00to be growing faster? If it's close to
18:02the frontier or if it's further away
18:04from the frontier. Well, when m equals
18:07negative1, you get this quote unquote
18:10confined exponential diffusion. And then
18:13what that means is the further f the
18:15frontier is ahead of the productivity a
18:18particular country is using. So the
18:20bigger f is compared to z, the faster
18:24the followup country is going to grow.
18:27And then this is a the the baseline
18:30model that Bob Lucas used in that AJ
18:32macro I paper that I mentioned of how he
18:35tried to explain sort of h how we uh why
18:40um those countries that were initially
18:43below the frontier grew faster over the
18:4750 or 40-year period that he studied
18:49compared to countries that were at the
18:51frontier. And this gives you a model of
18:53of convergence. Um
18:57Hello question.
19:01Hello Phillips. Uh yeah. Um uh does this
19:05model have any relationship with the
19:07gravity model in um uh international
19:10trade?
19:12Yeah. So the the gravity model and
19:14international trade is um one of the key
19:18uh as I understand it one of the key uh
19:21properties there is is uh the importance
19:24of distance to uh bilateral trade flows.
19:28Yeah.
19:28And so here this is is has a similar
19:31idea but it's changing the concept of
19:33distance from being geographical
19:36distance okay
19:36to being distance in some sort of
19:38technology space. And so uh with
19:42physical trade um the gravity model
19:44suggests that countries that are close
19:46to each other trade a lot and maybe
19:48that's because there are physical trade
19:50costs or maybe that's because of uh
19:54similarities in demand for products or
19:56things like that. this uh model will say
19:59that that technology tends to flow
20:02quickly um actually to countries that
20:05are more dissimilar and so if you're
20:07further away you have more technology
20:10interaction going on between them. So it
20:13it's it's related but it has some some
20:15different properties and and on the next
20:18slide I think we should talk a little
20:20bit about the economic interpretation of
20:22this function and we can talk about why
20:25the gravity model might want uh you know
20:27flows to be bigger when you're close
20:30together and why this model might want
20:31flows to be uh bigger when you're
20:33further apart. That's a great question.
20:35Okay, thank you.
20:39And uh that that actually is very
20:41natural to to segue into um the next
20:45bullet point here where we can think
20:47about uh a different model which is
20:49still almost the identical framework but
20:52just with a different parameter. So
20:54let's put m equal to one instead of
20:56negative one. This gives you a different
20:59kind of differential equation that
21:01describes diffusion differently. And in
21:04fact um Benabib and Spiegel in a
21:06handbook of economic growth chapter
21:09tried to estimate uh m and found m
21:12greater than one uh was a better fit
21:15than m minus one. And the difference
21:18here in part goes back to whether you
21:21use all the countries or whether you try
21:24to separate the countries in some way as
21:27Bob Lucas did here between open and
21:29closed. Because if you use all the
21:31countries, there's some evidence that
21:34there are countries that are far behind
21:37um and are not catching up, are not
21:40growing faster. Now, this is just
21:42showing you per capita income. The
21:44theory would suggest you'd want to do it
21:46in in measures of PFP, but nonetheless,
21:49um there are me there are countries that
21:51are far behind in PFP that are not
21:54growing more rapidly than frontier
21:56countries. And so how can you try to um
21:59rationalize that? Well, strictly
22:01speaking in the model um if you put m
22:03greater than one and you get a logistic
22:05diffusion, you get the following uh
22:07result. Um when you're close to the
22:10frontier, you don't grow that fast. When
22:12you're a little bit further behind the
22:14frontier, you do grow pretty fast. But
22:17then if you get too far behind the
22:19frontier, if the distance to the
22:21frontier is too large, the follower will
22:24not be able to keep up.
22:26growth will diverge and the income ratio
22:29of the follower to the leader will go to
22:30zero. Now, that's a stark prediction
22:32from a very simple model, but this gives
22:34you the sense of uh of the model being
22:37able to capture somewhat richer dynamics
22:40than just far behind grow fast. And so
22:43what I want to do now is spend a little
22:46bit of time thinking about sort of why
22:49you might in a more structural
22:51fundamental economic sense think that it
22:55makes sense to write down models where
22:58the further behind you are, the faster
23:00you can grow. And why it might also make
23:03sense to write down models where the
23:05further behind you are, if you're too
23:08far behind, you actually can't grow that
23:10fast. If you're if you're the technology
23:13you're currently using is so dissimilar
23:16from the frontier country, there's not
23:18really a lot to gain from adopting the
23:21technologies of the frontier country.
23:24And so I put a couple on on this slide
23:26and I'm happy to spend a little time uh
23:29walking my way through them, but I'm
23:30also happy if if uh some of the
23:32panelists sort of have some thoughts of
23:34their own that aren't on the slide and
23:36we can we can discuss those as well um
23:39as I as I walk through these slides.
23:42So the first um thing I want to talk
23:45about in that classic case of the
23:47confined exponential Nelson Phelps model
23:50um there's a very strong quote benefit
23:52to backwardness um and Pino and Andreas
23:57Rodriguez Clare uh have a beautiful
23:59handbook chapter uh where they talk
24:02about this and the key concept uh
24:05there's kind of two ways of thinking
24:06about this that are quite related. one
24:09is that it's it's easier to imitate than
24:11to innovate. And so there's some
24:12frontier countries that are doing some
24:15innovation and that's slow hard work. Um
24:19but once the ideas and the technology
24:21has been discovered, it's not as hard to
24:24copy it as it is to find it in the first
24:27place. And so countries that are
24:29adopting existing technologies can grow
24:32faster while they're sort of climbing up
24:34the the rung of the technology ladder
24:37than than countries that are at the top
24:39rung that are trying to push it out and
24:41build new rungs. So that's sort of
24:43conceptually what this this uh model
24:46tends to cover. And there's also, you
24:49know, a classic uh case of thinking
24:51about skipping some costly steps along
24:53the way. you don't even need to go up
24:55the same rungs of the ladder that other
24:58countries uh went up as they went
25:00through their process of development.
25:02And you know the classic example is you
25:04know wireless cell phones uh being
25:07adopted directly um in many countries
25:10where they were able to skip the costly
25:12investment in landline infrastructure.
25:15Right? And so that that'd be an example
25:16of sort of just just jumping over some
25:20technologies uh and getting to use these
25:22these very productive technologies right
25:25away.
25:27So there might be other reasons why you
25:29might think that it's easier to to grow
25:31fast if you're further behind the
25:33frontier. Um but there's also reasons to
25:36think that being too far behind the
25:39frontier might act as a barrier to
25:41adoption.
25:42And so
25:44there's a a fun quote from a a a science
25:47fiction author um Arthur C. Clark who
25:50said any sufficiently advanced
25:52technology is indistinguishable from
25:54magic. And it it sort of captures the
25:57fact that without sufficient human
26:00capital, it might not be possible to
26:02adopt frontier technologies. there might
26:05be some process of trying to understand
26:08how to use the technology and it it just
26:11might not be so so easy to do that um if
26:14you're currently operating with
26:16technologies that are so different from
26:18the frontier technology. And so what
26:21this is that that sort of analysis led a
26:24lot of people to do is to go back to
26:26this diffusion equation and try to say
26:29maybe we should put not just your
26:31current level of productivity but maybe
26:33your your current human capital um
26:36measured by something like uh years of
26:39education of your population um compared
26:42to um as a and that should affect how
26:46quickly you're able to adopt or not
26:47adopt these technologies. Um,
26:51another way of thinking about this
26:53that's that's, you know, related but
26:55distinct, I think, is thinking about
26:57production complimentarities. And so
26:59there's classic work in a book by
27:01Hirschman. Uh, Michael Kramer had a a
27:03famous O-ring production paper and my
27:06colleague uh Chad Jones has a very nice
27:09AJ macro uh paper about this. And the
27:13idea is that production occurs, you
27:17know, in many stages. There are many
27:19tasks, many uh uh you can think of it as
27:22intermediate goods that are used
27:25eventually to produce final goods. And
27:29if you wanted to adopt one particular
27:31technology that's being used in a in a
27:35high productivity country, it might not
27:38fit with the rest of the techniques, the
27:41rest of the tasks, the rest of the
27:42production uh processes that are being
27:45used in the country. And so it's sort of
27:48like a big push story where you'd have
27:50to sort of adopt many of the
27:53technologies all at the same time. You
27:56couldn't just adopt one and then have
27:58that work well with the rest of the
28:00system. And so you know the extreme
28:03example uh is this Leontiff production
28:06but you can have less extreme examples
28:08where you have these issues.
28:11You can also think that some of the
28:13technologies that are invented in very
28:16high productivity countries might
28:18fundamentally be better fit to being
28:22used in those countries and similar
28:24countries. In which case this technology
28:28could be high productivity in one
28:30location but not high productivity in
28:32another location. So in the agricultural
28:35context, you might invent uh you know
28:37different types of seeds or irrigation
28:40patterns um that would be useful in
28:43colder climates but not so useful in
28:45warmer climates. And in that case
28:48there's nothing to be gained by a lower
28:50productivity country adopting that high
28:52productivity technology because it's not
28:54a fundamentally high productivity
28:56technology. It's a location-pecific high
28:59productivity technology.
29:02And finally, one of the last things that
29:04you know I thought of when I was putting
29:05this together was thinking about
29:07institutional barriers. Um, so Parent
29:10and Prescott and Asimov and Robinson in
29:12a series of work have thought about
29:14extractive versus inclusive institutions
29:17or institutions that support the uh
29:20adoption of technology and profitable
29:23enterprise uh of firms and institutions
29:27that uh that that harm that that prevent
29:29that. And so they might not be able to
29:33uh adopt these better technologies even
29:35if technologically it would be
29:37beneficial for them to do so.
29:40And so this is kind of all of that's
29:42embedded in you know what is M in this
29:44model and what is the ratio of the
29:47frontier to the follower that you choose
29:49to use.
29:51Can I ask something?
29:52Yeah please. So do typically like when
29:55you think about the frontier itself, do
29:57you think of this as featuring some kind
29:58of decreasing marginal returns or do you
30:01think of it as like being a constant
30:03increasing productivity or some kind of
30:04step function or Yeah,
30:07that's a great question. So so at the
30:09very end today I I'll try to talk a
30:11little bit um about uh jointly thinking
30:13about innovation, how that frontier
30:16moves over time and adoption uh
30:18together. Um sort of there's these
30:20stylized facts that you know frontier
30:23countries tend to grow at 2% per year um
30:27per capita GDP. That's not always and
30:29everywhere true, but it's a good
30:30stylized fact. And so we have lots of
30:32growth models that generate that. Some
30:35of them generate that with decreasing
30:36returns in the research function um
30:39through having more and more resources
30:41being used even though there's
30:42decreasing returns in the research
30:43function. And some of those models, you
30:46know, that's like the semi-indogenous
30:47growth approach. And some of those
30:49models use uh you know linear returns to
30:51innovation to allow for um balanced
30:54growth. And so this kind of one way of
30:56thinking about is there's models of
30:58innovation that describe the frontier
31:00and then there's models of technology
31:01diffusion that describe how everybody
31:04outside the frontier evolves. And then
31:06it's natural to think about those two
31:08things together. And that's where I
31:10think part of the frontier of the
31:11literature is. So I'm going to just give
31:14you one brief uh you know sentence on
31:17this uh slide and then I'm going to move
31:19to the other style of uh model which is
31:23these idea diffusion models. One of the
31:26things that that h I uh uh what what we
31:30were just talking about was a very
31:31mechanical almost like a physics type of
31:33a model where just technology flows
31:36according to some diffusion but you're
31:37not talking about any countries or any
31:39individuals making choices to try to uh
31:42foster that technology development. So
31:45in this paper what what Jess Benabe and
31:47Jesse Pearl and I were trying to do is
31:49stay within the Nelson Phelps framework
31:51but have there be um investment in
31:54either innovation or an imitation. Um
31:57here innovation has some productivity
31:59sigma and imitation has some
32:01productivity that's given by that Nelson
32:04Phelps diffusion curve but there's going
32:06to be a choice to invest in innovation
32:08or in imitation. And so the law of
32:10motion for productivity is going to be
32:12that Z grows according to how much they
32:16invest in innovation and how productive
32:18innovation is and how much they invest
32:22in imitation or adoption and how
32:24productive adoption is. And so this is a
32:27a way of trying to get some choice into
32:29these models of technology adoption so
32:31we can understand how environments
32:33affect incentives. And so, um, this is a
32:37paper that we worked on. And just a good
32:39side note, if you're trying to learn as
32:41a student or refresh your your
32:42Hamiltonian math, I think this is a good
32:45paper to to look at. We walk through all
32:47the steps very very simply. Um,
32:52and I have some material, but maybe we
32:54can talk about it if anybody's
32:55interested later um, uh, in the Q&A
32:58section, but um, that's just, uh, uh,
33:02starting to get, uh, more decisions, uh,
33:06showing up in these models. And that's
33:07really in these idea diffusion models,
33:10something that I think comes to life a
33:11lot more. So that that's what I'm going
33:13to focus on um, for the next uh, uh,
33:16good chunk of the class.
33:21So when we were developing these idea
33:24diffusion models as a literature, we
33:26were trying to find a microfounded
33:28process of diffusion that could replace
33:31this standin uh for this exogenous
33:34diffusion equation. We wanted adoption
33:36to be costly and the result of
33:38deliberate choice because then you can
33:40say how how can a subsidy uh to to
33:43adoption um affect the growth of you
33:47know low productivity firms or or low
33:50earning workers. Um we can when you have
33:53choice you can say is the economy
33:55efficient? Is there something that the
33:57government should be doing to try to set
33:59rules or or taxes to try to improve the
34:02lives of its citizens?
34:04And we wanted to spend a particular
34:06focus on the many low productivity firms
34:09that exist in in the economy. If you
34:11just do a sort of a plot a distribution
34:14of firms by productivity or size, it
34:18looks somewhat paro- like or a lot of
34:20normal like there's a large mass of low
34:23productivity and small firms and a much
34:26smaller mass of of high productivity
34:28very large firms. And a simple thought
34:31experiment is like how much more output
34:33could we get if we just got these small
34:36low productivity firms to be using best
34:39practices instead of the the the the
34:43practices that are below the frontier.
34:45and Nick Bloom oftentimes with
34:48co-authors John Roberts and John Van
34:50Reinan um have a a literature on
34:52management where they try to empirically
34:54look at sort of in introducing better
34:57management practices uh into lower
34:59productivity firms and a lot of
35:01developing country settings um how that
35:04can help just improve productivity,
35:06improve profits, improve output, improve
35:08welfare. And so that's kind of a a
35:10motivating fact in the back of our minds
35:12that there's so many low productivity
35:14firms out there. Why aren't they getting
35:16better? Can they get better? Is it
35:18efficient that they're not better? And
35:21we also wanted the distribution of
35:23existing technologies to influence the
35:25the choice of adoption. Right? So it's
35:27not just that every person, every firm,
35:30every country knows that there's a
35:32frontier technology. We're all targeting
35:34our adoption to trying to be that
35:37frontier technology. There's a lot of
35:39technologies out there. It's not always
35:41obvious which one is best for you and
35:43your firm. Um and there's a lot of
35:45uncertainty. Um this also uh is in in
35:49the previous example there was no
35:51switching of orders. The the countries
35:53never got you know country one and two
35:56always maintained the same rank in the
35:58productivity and income distribution. uh
36:00if you want to start thinking at the
36:02micro level of firms that's certainly
36:04you know not a good um characterization
36:07of the firm productivity distribution
36:09firm some firms grow faster than others
36:11they leaprog each other um and so these
36:14were some of the things we wanted the
36:15model to develop and the typical
36:18application of these models is to either
36:20firms or workers which allows a
36:22connection to panel micro data which I
36:24think is a nice advancement um uh uh
36:27beyond just thinking about the macro
36:29data that's typically used in the Nelson
36:31Phelps model. So, I'm going to tell you
36:34two papers that that have like
36:36influenced my life to a to a very large
36:39degree. When I learned them in grad
36:40school, they just clicked with me and I
36:43been writing papers motivated by the
36:45ideas I learned in these papers, you
36:46know, for the next decade plus. And so,
36:50one of them is Cordom 1997 and the other
36:53one's Yvanovich and Rob 1989. And then
36:56once you understand these two models
36:58which I'm giving to you in in words very
37:00simply you'll understand the idea
37:02diffusion literature um and sort of see
37:05where to go from there.
37:07So quum 97 is a model of innovation via
37:11the search for new ideas. There's some
37:14idea distribution that's out there like
37:16this platonic world of ideas and we as
37:20humans are trying to find ideas that are
37:22better and better better recipes for
37:26producing goods that we like in
37:28efficient ways. And you're going to
37:30search going to draw from this new from
37:32this distribution of ideas and use the
37:34idea of it's better than the current
37:36idea. And this leads to math on extreme
37:39values. Um, so we're always trying to
37:41get the max to be larger than the one
37:44that we just drew. But if you're drawing
37:46from the same distribution, it's getting
37:48harder and harder to draw an idea that's
37:50bigger than the max.
37:52But if you have population growth, you
37:55get more and more and each person is
37:58somebody who could be drawing ideas from
38:00this idea distribution, you get more
38:03draws.
38:05Even though it's getting harder to get
38:06uh a better idea with any given draw, if
38:10you have a power law distribution of
38:12potential ideas and exponential pal
38:14population growth, that's going to give
38:16you balance growth. So that's a a model
38:19of innovation.
38:21Yvanovich and Rob is a like a proto
38:24model of diffusion of knowledge via
38:27bilateral interaction.
38:30So it's a different model seemingly but
38:32it actually has a lot of connections to
38:33corn.
38:35So there's a distribution of knowledge
38:37across people of ideas with how they're
38:39going to you know uh produce the one
38:42farmer has one idea for how to grow
38:44wheat. Another farmer has another idea
38:46for how to grow wheat, how close to
38:47plant the seeds together, how frequently
38:49to water it, how much irrigation, how
38:52much fertilizer, which fertilizer to
38:54use. That's all sort of encapsulated in
38:56this productivity term. very simple
38:58one-dimensional uh concept. And then
39:01there's random meetings. Farmer one
39:03walks into the bar, meets farmer two,
39:05they talk about their different
39:07techniques and far they they say, "Oh, I
39:10was able to grow this much wheat. I was
39:11able to grow that much wheat." Um and so
39:14they leave the meeting
39:16so that the productivity of farmer one
39:19and farmer two next period is going to
39:21be some function of their productivities
39:24today. And one example of that that's
39:27proven to be particularly tractable uh
39:29is that farmer one and farmer two both
39:32leave with the best technology, the best
39:35way of growing wheat. And so they
39:38compare processes. One method is better
39:40than the other. Well, the the next
39:43farmer said, "Well, I'm going to use
39:44your process and I'm going to go out
39:45there." If you repeat this process over
39:48and over again, you'll realize we're
39:51accumulating sort of the best ideas. And
39:54there's this close connection in the
39:55math between extreme values which is
39:57what Cororm used and differential
39:59equations which is what Yvanovich and
40:01Rob use um where you just accumulating
40:03the max either in a recursive way or in
40:06sort of a sequential way.
40:08And now I think we have some good
40:10background to understand these idea
40:12diffusion models.
40:14So I'm going to give you two versions of
40:16this. One in discrete time and one in
40:19continuous time. My honest answer is
40:22that I wrote this first paper in
40:26discrete time because I wasn't very
40:27comfortable with continuous time. I
40:29didn't know the methods very well. It
40:31turns out it's easier to work with these
40:34types of models in continuous time. And
40:37so my advice is if you feel comfortable
40:41um do a little bit of investment in in
40:43learning some of these continuous time
40:44techniques if this is a style of model
40:47you're interested in working with. but
40:49it's not necessary and I wrote my first
40:51paper in discrete time and everything
40:53works in discrete time just fine and so
40:55I'm going to show you both of them to
40:57try to give people with different you
40:59know uh degrees of interest in working
41:02in continuous or discrete time both of
41:04uh both uh types of students should have
41:06the opportunity to work with these types
41:08of models but I'm going to kind of go a
41:10little bit quicker over the the discrete
41:12time one um but a lot of the intuition
41:15you get from that um carries over to
41:17continuous time. And so, um, here's the
41:21setup.
41:24I'll talk about this in the context of
41:26firms. And so, think about there being
41:28lots of different firms and they're
41:30heterogeneous over their productivity.
41:32And they have the opportunity to either
41:34produce using their current technology
41:36or to search using a new technology.
41:39And and the way we're going to model
41:41this uh searching process is that they
41:43randomly meet and copy a technology used
41:46by some existing producer.
41:49And so this has the idea of cortum 97
41:52that you're searching from a
41:54distribution to try to get a new idea,
41:56but it's not an exogenous platonic, you
41:59know, world of ideas that you're
42:01searching from. there's just a bunch of,
42:03you know, farmers around and you're a
42:05farmer and you're trying to learn the
42:07best technique and so you're drawing
42:09your from the distribution of techniques
42:11that are actively being used at any
42:14given point in time. And so it has the
42:16flavor of a pure effect model like this
42:18Yvanovich and Rob model. And what
42:20happens if you repeat this process over
42:22and over again and you have there be
42:25selection on which firms which people
42:29are choosing to search for a new and
42:31adopt a new technology or which firms
42:33are choosing to keep producing with
42:35their existing technology. That
42:37selection is going to indogenously shift
42:40weight in the productivity distribution
42:42away from low productivity firms towards
42:45higher productivity firms and that can
42:47sustain growth uh in these simple models
42:50with some assumptions we can talk about.
42:53So the aggregate state in this model is
42:55going to be the whole productivity
42:56distribution FT not this is not the same
42:59FT we had in the Nelson Phelps model
43:01where it was just the FT there was just
43:03a a scalar just the productivity of the
43:05frontier. Now the whole distribution
43:07matters and the minimum support's going
43:09to be MT. And so I worked on this paper
43:12with Pearlla. At the same time Lucas and
43:14Mole were working on their paper and a
43:16lot of the economics is similar but our
43:18model happens to be analytically more
43:21tractable because we give uh agents a
43:23binary choice adopt or produce. In Lucas
43:28and Mole, there's a continuum of time 01
43:32that agents can choose to spend
43:34searching or producing. And our our
43:38restriction of the choice set to being a
43:40binary 01 is what gives us a lot of
43:43analytical tractability, but it also
43:45limits our ability to study some other
43:47things.
43:49So now let's just go over this model and
43:51it'll carry over to the continuous time
43:53one too. [snorts] uh in discrete time
43:56fixed measure of firms linear production
43:58with some capacity constraint something
44:00we'll relax later um but for right now
44:03output is productivity so let's not talk
44:05too much about sort of uh uh the that
44:09production side at the firm level
44:12and there's a source distribution for a
44:14new technology fi and so this leads to
44:16the following value function they have
44:19to choose between two options so the
44:21value of a firm with productivity Z at
44:23time T is either produced with your
44:26existing technology Z and get output Z
44:29and then discount it at rate R um you'll
44:32have the value tomorrow of having the
44:35same technology because you didn't
44:36update your technology or you can pay a
44:40cost and in this model that cost is one
44:43period of foregone production. Think of
44:46this as a Schmidz and Holmes switchover
44:48disruption cost where it's costly to
44:51upchange your technology. So you lose
44:53out on production for a period but then
44:55tomorrow you have the value of having a
44:57new technology and that new technology
45:00is drawn from some distribution.
45:03So one equation simple model in some
45:06sense the solution for a firm's optimal
45:09decision can be described by a
45:11reservation productivity threshold. Why
45:14is that? It's very simple here the
45:17productivity sorry here the value of
45:20producing uh with your given technology
45:23is increasing in your given technology
45:25whereas the value of adoption is
45:27independent of your current technology.
45:30We didn't have to model it that way but
45:32if you model it this way you get an
45:34increasing part of the value function
45:36and a constant part. There's a single
45:38crossing which means that optimal
45:40threshold can be described by this uh or
45:42sorry optimal policy can be described by
45:44this threshold. All the firms with
45:46productivity below some threshold are
45:48going to choose to adopt and the firms
45:50with productivity above the threshold
45:52will keep producing with their existing
45:53technology. And this captures the very
45:55simple intuition that
45:58low productivity firms have more to gain
46:01by going out there and trying to find a
46:04technology that other people are using
46:05than high productivity firms. They're
46:07more likely to bump into somebody that's
46:09using a technology that's better than
46:11theirs and then they can upgrade.
46:14And so the key idea is that this source
46:17distribution that firms are going to be
46:18drawing from is related to the existing
46:21distribution that firms are drawing
46:22from. And so here's the the model in a
46:25simple picture. If this is the density
46:28of productivity at time t and this is
46:31the density of productivity at time t
46:33plus one. sort of let's say an
46:35initiative looks something para like
46:37there's going to be some threshold mt
46:39plus1. Below that threshold all these
46:42firms are going to choose to adopt a
46:44technology. They're going to get a draw
46:46from the distribution. They might meet
46:49some people that were also trying to
46:52adopt or they might meet uh or they
46:54might meet some people that were
46:56producing. And so the next period
46:59productivity distribution is going to
47:00look in the following sense where
47:02there's less mass of people below that
47:05threshold and more mass of people above
47:08that threshold. I'm going to make one
47:10more simplifying assumption to make this
47:12model way more tractable and simpler to
47:15think about. And I'm just going to make
47:16the assumption that firms that are ch ch
47:19ch ch ch ch ch ch ch ch ch ch ch ch ch
47:19ch ch ch ch ch ching to search and adopt
47:20a new technology walk through the left
47:22door in the morning. Firms that are
47:25choosing to adopt the techn to produce
47:28and not adopt the technology walk
47:30through the right door in the morning.
47:31And then all the adopting firms only
47:33meet producing firms. They can't run
47:35into each other. That's going to mean
47:37that there's no chance that anybody
47:39meets somebody below the threshold. And
47:42it's going to lead to a very simple law
47:43of motion for how the distribution is
47:45going to evolve over time. And so in
47:48math, we're going to say that the source
47:50distribution here is going to be the
47:52conditional distribution of productivity
47:55above some threshold. And in rational
47:58expectations equilibrium, that threshold
48:01will be the optimal policy that's chosen
48:05by each firm. And so this takes a little
48:08bit time of thinking about um but this
48:10is just like a big K little K argument
48:12in classic you know macroeconomics.
48:15There's some threshold that you know
48:17aggregate capital stock it's related to
48:19the amount of capital the representative
48:21consumers is buying but when they is
48:24accumulating but when they make their
48:25choices they take the aggregate as given
48:27and in rational expectations we make
48:30those two things be equal. It's the same
48:32thing that's going on here. And so what
48:35you get is that the distribution
48:38tomorrow is just the distribution today
48:41truncated at that threshold productivity
48:44level. In math you can write the law of
48:47motion for the density uh as the the
48:49amount of firms at Z um that are uh uh
48:54for for all productivity is bigger than
48:56MT plus one. You're going to have all
48:59the old people that were there and
49:01didn't move plus you're going to have
49:03the new people. This is how many new
49:06people you have. All of the the people
49:08that are that are adopting are the
49:10people that are below the search
49:12threshold. So this is the CDF here. And
49:16then what do they do? They get a draw
49:18from the existing distribution above the
49:21threshold.
49:23And if you just work that math out a
49:25little bit, if you have some initial
49:27condition,
49:29you have that has an initial minimum of
49:32support and you have a sequence of these
49:34thresholds, you can describe the density
49:37at any point in time as a truncation of
49:40the original distribution, the time zero
49:43distributions at these MTS. And so the
49:47distribution is just moving forward in
49:49time, lpping off the low productivity
49:52firms, and they're getting redistributed
49:54into the distribution at higher
49:56productivities.
49:58And in a balanced growth path, normally
50:00we think about just output growing at a
50:02constant rate. But now we have a whole
50:05distribution. So we need a concept of
50:07constant growth, but [snorts] for
50:09distributions, not just scalers. And a
50:12very uh simple one that that most people
50:14work with is you just have the scale of
50:17the distribution changing but not the
50:19shape. Another way of saying that is all
50:22the quantiles grow at the same rate. And
50:25so when you normalize you know let's say
50:27we have geometric growth if you
50:29normalize all the quantiles you know uh
50:32by by the growth rate then you have a
50:34constant productivity distribution.
50:38So that's the that's the whole model.
50:39It's really simple. You have two
50:41equations. One is a a an equation that
50:44describes how the distribution moves
50:45over time and another one that describes
50:48the value uh of a firm taken as given
50:51how that distribution moves over time.
50:53Um there's some fancy math that's uh
50:56associated with that uh called meanfield
50:59games that Ben Mole's been working a lot
51:01uh with uh some some mathematicians. Um
51:05but this is it that that's all it is
51:07just a distribution moving forward in
51:09time and a value function that describes
51:12um the benefits and costs of moving of
51:15of of adoption. And so in this simple
51:18model if you start with a initial
51:21distribution that's paro you can get in
51:23closed form a growth rate that's a
51:26function of the tail index of the paro
51:28distribution where alpha just describes
51:31um uh how fat the paro distribution is.
51:34So a smaller alpha means you have a fat
51:37tail u more variance in [snorts] the in
51:39the distribution all else equal
51:43um and you can have production that's
51:45growing the measure of adopters you can
51:47characterize all of this why do I want
51:49to say here I want to say two things one
51:53is you can have a growth rate that's a
51:56function of the shape of the
51:58distribution
52:00and so a decrease in alpha means you
52:02have fatter tails more inequality
52:05The way to think about this model is
52:07that adoption is a real option and
52:10option values are increasing in
52:11variance. So you might have seen a mall
52:14search model. What happens in a mean
52:16preserving spread in the MCL search
52:17model? You know the reservation wage
52:19changes. It's something very similar
52:22going on here. And so what we developed
52:24is a model that says low productivity
52:27firms have the most to benefit from
52:29adoption, but the amount that they're
52:31going to adopt, which is going to drive
52:33growth in the long run, is going to
52:35depend on um on the technologies that
52:40are out there for them to adopt.
52:44The second thing that I want to say
52:46before I move to the continuous time
52:48version is you can write down a planner
52:50problem which I'm I'm just going to
52:52breeze through here where the planner is
52:54choosing how fast they want that that uh
52:57adoption threshold which firms to adopt
53:00every period how fast they want that
53:01adoption threshold to move over time.
53:04And if you compare the first best the
53:06planners outcome uh and growth rate to
53:09the one that uh arises in the
53:12decentralized equilibrium the planner
53:15gets faster growth and the planner
53:17achieves higher um utility. And there's
53:21an economic mechanism that's going on
53:23here that I think is important to
53:25understand. There are these external
53:27spillovers where firms in in a model of
53:30technology adoption where firms uh
53:33improve their own technology and other
53:36firms can then learn from them and
53:38improve their technology.
53:41The firms may not internalize that
53:44external spillover and therefore may not
53:47be doing enough technology adoption from
53:49the socially uh optimal perspective. You
53:53can reframe that as a free rider problem
53:55where there might be firms that are
53:57sitting back waiting for others to do
54:00all this investment in moving the
54:02productivity distribution forward,
54:04figuring out the best way to to grow
54:06wheat. Let all the farmers meet up in
54:08conventions, talk to each other,
54:10experiment, and then once they figure it
54:12out, then I'll do the the I I'll go and
54:15try to learn which technology to adopt.
54:17And so there's a fundamental reason why
54:20there's uh maybe room for government
54:23intervention or something along the
54:25lines to try to correct this externality
54:27that might show up in the decentralized
54:29equilibrium.
54:32Okay.
54:34So what are the next steps?
54:36I know I've got about
54:37question.
54:38Yes, please.
54:42Question.
54:44Yes. Hi.
54:45Yes. So hey, so is it okay to think this
54:50as the only cost of adoption here is
54:53just stopping your production,
54:56updating to the new technology and then
54:59going forward.
55:01One would think that maybe that's not
55:05enough.
55:06Yeah, that that's a great question. This
55:08is uh I think literally the next two
55:11slides I want to talk to addresses
55:12exactly that. So I'm very happy you
55:14asked. So that was a a the way I viewed
55:17the sort of doing research is sort of
55:19when we're developing a new a sort of
55:22newer mechanism that hasn't been
55:23explored so much do the simplest
55:25possible model you can that still allows
55:28you to explore that mechanism and that
55:30was just a very tractable way of
55:31modeling things. Where we wanted to go
55:34and where the literature went is we we
55:36had the very simple capacity constraints
55:38in that model where output was equal to
55:40to productivity. We wanted to go to and
55:42develop a richer model now of technology
55:44adoption and a bed that's that mechanism
55:47that captures the fact that
55:50low productivity firms are trying to get
55:52better. The how much they want to invest
55:54in getting better and how likely they
55:56are to get better depends on which
55:58technologies are out there but do that
56:00in a much richer macro and trade
56:02international trade model. And so um
56:05we're going to do that. Um we're along
56:07the way we're going to switch to
56:08continuous time. Um, and then, uh, we're
56:12going to talk more richly about costs
56:13and labor and things like that. Um, then
56:16at the very end, I'm not sure we'll have
56:18that much time to talk about it, but we
56:20can talk about what are firms adopting
56:22in the long run. This model here,
56:24because we might not have time to talk
56:25about it too much later, it allowed you
56:27to get perpetual growth via imitation.
56:32Something kind of seems wrong with that
56:34conceptually. And the reason
56:35mathematically we were able to do that
56:38is we just snuck in that the initial
56:40condition is that the the original
56:44initial productivity distribution is
56:46paro which has a fat tail with infinite
56:49support. And what that means is you
56:51never run out of ideas to adopt.
56:55I think for my view on this literature,
56:58these are models that can show you how
57:00technology adoption can contribute to
57:02growth on the short run or the medium
57:04run, but they're not models of long run
57:07growth. For that you need to jointly
57:09model innovation and adoption where
57:12innovation is the process that's
57:13generating these new ideas so that you
57:15don't run out of ideas to adopt. Um and
57:18so we can talk about the role of the
57:20initial distribution that's something
57:22that's come up in these idea
57:23distribution models idea diffusion
57:25models and the literature's address that
57:26I've done some work to address that. Uh
57:29Paco and Ezra Oberfeld have done some
57:31work to address that and others. But
57:33first, we're going to focus on moving to
57:35continuous time and having a much richer
57:37economic model than what I just talked
57:39about. So continuous time, now we're
57:41going to have monopolistic competition
57:43where all firms are the unique producers
57:45of their own variety. Um, and there's
57:47going to be some profit function and
57:48they're going to be hiring labor. And so
57:50this is in contrast to what we just did
57:52where productivity was profits was
57:54output because of uh capacity
57:57constraints. We're going to have labor
57:58as a factor of production and labor also
58:01as a factor of investment where
58:03investment can be in into entry and exit
58:06of varieties and also can be uh
58:08investment in adoption.
58:11So, we're going to have the same model
58:12of indogenous adoption, but we're going
58:14to have um include uh an exogenous in
58:18this paper, exogenous innovation where
58:21firms are going to be bounced around
58:23because they're hit with some technology
58:25shocks. Um in discrete time, it's like a
58:28random walk. Uh in continuous time, it's
58:30geometric brownie in motion. Um and this
58:33is going to allow us to match from
58:34dynamics um which is uh bring a lot more
58:38serious uh calibration and micro data to
58:42the to the literature.
58:44We'll also be able to discuss transition
58:46dynamics not just talk about balance
58:48growth paths. Um and so I'll do all of
58:51that over the next uh few slides.
58:53Is there a question?
58:54Hey Chris.
58:54Yeah.
58:55Yeah. There was a question from the Q&A
58:58about what the advantage of continuous
59:00time over discretet time is. Can you
59:02make sure to point that out as you go
59:03over this model?
59:04Absolutely. I'd be happy to. One thing
59:06is uh
59:09I I'll show you I'll show you what gets
59:10a lot easier. Um one way to look at it
59:13is it took me forever when I was writing
59:15the original paper to figure out this is
59:17the shape of the value function in my
59:19paper in discrete time. It's peacewise
59:22linear with kinks at in every time
59:25period induced at the or kinks at every
59:28productivity level that's induced by the
59:30search behavior of every agent in the
59:32future. Um this is a mess in continuous
59:36time. This turns into like Z over R. And
59:38so it's like a just a lot smoother um
59:42cleaner formulas. But also um it shows
59:45up particularly uh in the law of motion
59:48for the productivity distribution. Here
59:50we had to make some assumptions that you
59:53only meet firms that are adopting and
59:55you don't that are not adopting. You
59:58don't run into other fellow adopters and
1:00:00that was how we were able to get a lot
1:00:02of the tractability in continuous time
1:00:04that comes out very naturally. Um and
1:00:07you can work with differential equations
1:00:09instead of difference equations. we have
1:00:11a little bit more uh mathematical
1:00:13techniques to do that and we also have
1:00:15some good um numerical techniques to do
1:00:18that which I'll point out.
1:00:21So I think I have about 10 minutes left
1:00:2310 uh or so and so I'm going to mostly
1:00:26focus on teaching you some methods and
1:00:29then in the Q&A I'm happy to talk about
1:00:31some more of the economics um behind
1:00:33this. So, I'm going to focus on a paper
1:00:36that I wrote with with uh Peara and with
1:00:39Mike Wah. Um, and uh that'll just but I
1:00:44focus I'm teaching you the papers that I
1:00:46know the best. These are the ones that I
1:00:48wrote. But there's a a whole wide range
1:00:50of literature that uses these sites of
1:00:52techniques. And so, uh, uh, it's not
1:00:54just narrowly, uh, uh, you know, my my
1:00:57papers are the only ones you should look
1:00:58at for technology adoption. And I'll
1:01:00I'll point out some more papers along
1:01:02these lines later. So this is if
1:01:04anybody's familiar with the mellets
1:01:06model of international trade. We took
1:01:08the mellet model of international trade
1:01:11locktock and and barrel just with almost
1:01:13no changes except that we have this in
1:01:15continuous time and we um we added the
1:01:20model of technology adoption. So um we
1:01:23did an asymmetric country version for
1:01:25tractability. We have some consumers
1:01:28with some period uh some expected
1:01:30discounted utility uh very standard. we
1:01:33have consumption of a final good is the
1:01:35integral of a consumption of a bunch of
1:01:38intermediate goods. Um this is the the
1:01:41intermediate goods uh of variety V.
1:01:44They're uh produced with this uh CES
1:01:48aggregation technology. um where there's
1:01:51a measure of varieties omega that are
1:01:53consumed um uh in country I sent and
1:01:57produ produced in country J and they're
1:01:59aggregated all of those varieties with
1:02:01elasticity of substitution sigma. Um
1:02:06this is where all the action is on the
1:02:08firm side very similar to what we did
1:02:10before. There's going to be
1:02:11heterogeneous firms with productivity Z.
1:02:14They're going to have linear production
1:02:15technologies that use labor L. um they
1:02:18faced a fixed cost and an iceberg trade
1:02:20cost to export and they're going to have
1:02:22the option to pay a cost to receive a
1:02:24new productivity draw.
1:02:26And so the incumbent firm's decision can
1:02:29be divided into a static and dynamic
1:02:31optimization problem. And then there's
1:02:33also an entry and exit uh margin to the
1:02:36problem. The static problem takes their
1:02:38productivity as given and they choose a
1:02:41price and an amount of labor to hire in
1:02:43order to maximize their profits market
1:02:45by market. And there's this fixed cost
1:02:48of hiring labor to export to a foreign
1:02:50market and an iceberg trade cost to ship
1:02:52goods abroad. This is super standard. So
1:02:54I'm not going to go through this today,
1:02:56but the paper lays it out in detail. The
1:02:58dynamic problem is is a little bit more
1:03:01um uh interesting, more novel. And so
1:03:05non-adopting firms productivity evolves
1:03:08according to this exogenously specified
1:03:11geometric brownie in motion where the
1:03:13growth rate of a firm as productivity is
1:03:16given by this drift term and with
1:03:19parameter mu and a variance term with
1:03:22parameter epsilon uh where wt is
1:03:24standard brownie in motion. And you can
1:03:27go through the whole paper turning this
1:03:29brownie motion off. turn mu and oopsilon
1:03:31to zero and you get a lot of the
1:03:33intuition but you're not going to match
1:03:35the firm dynamics as well and that has
1:03:37some implications for calibration and
1:03:39quantitative results but qualitatively
1:03:41it doesn't really change the behavior of
1:03:43the model that much
1:03:46incumbent firm is going to choose when
1:03:48to adopt a new technology so draw new
1:03:50productivity Z just like we did in the
1:03:53discrete time version related to the
1:03:55equilibrium distribution fi and xt is
1:03:58going to be the cost of hiring zeta
1:04:00units of labor in order to draw new
1:04:02productivity. So this goes to the
1:04:04question that was asked earlier. Instead
1:04:06of just having a period of not producing
1:04:08um what you now have is a a cost you
1:04:11have to h it's like an investment uh you
1:04:13have to hire some labor in order to try
1:04:15to upgrade your technology. And so the
1:04:18real wage is going to be some component
1:04:19of the cost and then the parameter zeta
1:04:22is how many workers you need to hire in
1:04:23order to upgrade your technology.
1:04:27And then there's an entry and ex exit
1:04:29margin which is going to lead to an
1:04:31endogenous measure of varieties
1:04:34and entrance receive a draw from the
1:04:36productivity distribution as well but at
1:04:38a cost that's higher than the cost of
1:04:40doing imitation. And so this is a a
1:04:43tractable way of of modeling entry. Um
1:04:46it builds on the work of Öza Lmer who
1:04:49also modeled sort of entrance coming in
1:04:51and getting a draw from the incumbent's
1:04:53productivity distribution when they
1:04:55enter.
1:04:56And then in this model, my colleague,
1:04:58you know, Pete Klo always makes fun of
1:05:00me because I I wrote down a model with
1:05:02exogenous death instead of some
1:05:03endogenous creative destruction. This
1:05:06was uh you know, some sacrifice I had to
1:05:08make for attractability in this model.
1:05:10So firms just die at some exogenous rate
1:05:12delta.
1:05:14That's that's the whole basic model. And
1:05:16so what I'm going to do now is just talk
1:05:18to you a little bit about how you solve
1:05:20it, how you set it up. um and then um
1:05:24and then show you very quickly some
1:05:26results before before moving on.
1:05:29So what a firm is doing here is choosing
1:05:31a time at which they want to adopt a new
1:05:34technology. Mathematically that can be
1:05:36reformulated as an optimal stopping
1:05:38problem. This the the you continue using
1:05:42your existing technology until you stop.
1:05:44At the point in time you stop, you adopt
1:05:46a new technology and you have a new
1:05:48value that's associated with using that
1:05:50new technology. And there's a really
1:05:52tight link between optimal stopping
1:05:54times and free boundary differential
1:05:56equations. And so for excellent
1:05:58references, I recommend the the book by
1:06:00Stoki. Um there's a book by Dixon and
1:06:03Pindik and Ben Mole has excellent
1:06:05lecture notes that that go through this.
1:06:07And so the idea is to recursively choose
1:06:10a productivity threshold for when to
1:06:12stop. Just like like we talked about in
1:06:14the discreet time sense, the the
1:06:16benefits of adopting are larger for low
1:06:19productivity firms. If you're super high
1:06:21productivity and you randomly go out and
1:06:23try to meet somebody uh in the techn in
1:06:26in the in the world that's producing,
1:06:28the chances they have a better
1:06:29technology and you're going to learn
1:06:30from them is super small. And so the
1:06:33high productivity don't want to adopt
1:06:34the low productivity do. And that's an
1:06:36endogenous outcome. We can talk in the
1:06:39Q&A section if anybody's interested in
1:06:41sort of what if you could direct your
1:06:43search. Why am I using random search?
1:06:45You know, we we all go and try to talk
1:06:47to the smarter people to learn from
1:06:49them. Uh that's that's an extension but
1:06:51not in the current model.
1:06:53So the math behind what we're doing is
1:06:56that in an optimal stop in time problem
1:06:59the value function and optimal threshold
1:07:01from that problem satisfies a
1:07:03continuation value equation which
1:07:05describes the value of keeping the
1:07:07current technology a value matching
1:07:09equation and a smooth pasting equation.
1:07:12So, uh, I'm going to walk through these,
1:07:15then show you some final results, and
1:07:17then then even though there's a lot of
1:07:18slides left, uh, we don't have that much
1:07:20left to talk about.
1:07:24So, this is a little detour into the
1:07:26math. Just if you going from continuous
1:07:28time, discrete time to continuous time,
1:07:31you know, this is a huristic for how to
1:07:33see how to do that. Just imagine an
1:07:36asset that pays a dividend Z every
1:07:38period. that asset is going to have
1:07:40value equal to the dividend plus the
1:07:42capital gain. And so over a delta time
1:07:45period, you're going to get Z times
1:07:46delta amount of dividends. Then you're
1:07:49discounting um the value of having that
1:07:52Z tomorrow. If you just do a little
1:07:54multiplication and subtraction and
1:07:56division, you get this formula. And if
1:07:58you take the limit as delta goes to
1:08:00zero, you realize this is a derivative.
1:08:02and you go from a discrete time to a
1:08:04continuous time uh flow value of a value
1:08:08function is just the dividend plus the
1:08:10capital gains. Those are classic I call
1:08:13it a Lucas asset pricing formula.
1:08:16Well, if you want to go to my model um
1:08:18of technology adoption, you have the
1:08:21value function in the continuation
1:08:22region. is just going to be the flow
1:08:24value, the profits they get from trading
1:08:28uh their goods to country to to
1:08:31different countries all over the world
1:08:32and selling domestically plus the
1:08:35capital gains.
1:08:37Very simple. If you have brownie in
1:08:40motion where the mu and the epsilon are
1:08:42in zero, you get some extra terms. Um
1:08:45don't worry too much about that. You can
1:08:47read the paper for the details, but the
1:08:50economics is very similar. You have a
1:08:52value matching condition where MT is the
1:08:55adoption threshold. All the
1:08:57productivities below MT are going to
1:08:58adopt. All the productivities above MT
1:09:01are going to keep producing with their
1:09:02existing technology. And this says the
1:09:04value at that threshold of continuing to
1:09:08produce is equal to the value of
1:09:10adopting. And the value of adopting is
1:09:13you get the new productivity drawn from
1:09:16the distribution of productivities over
1:09:18the support of that distribution above
1:09:21the adoption threshold to infinity minus
1:09:23you had to pay some cost in order to
1:09:25adopt.
1:09:27The smooth pasting condition is that the
1:09:29derivative of the value matching uh
1:09:32condition holds with equality and the
1:09:34right hand side doesn't depend on your
1:09:36particular Z and so the left hand side
1:09:38is just the derivative with respect to Z
1:09:41of the value and then there's a free
1:09:43entry condition which is the cost of
1:09:45entry better be at least as big as the
1:09:48value of entry otherwise firms are going
1:09:50to enter.
1:09:53Okay, so now we're basically at the end
1:09:55of the of the of the hard math. The last
1:09:59thing is a kgora of forward equation
1:10:01which describes how the productivity
1:10:03distribution evolves over time. If you
1:10:06want to ignore the oopsilons and the
1:10:08muse and the brownie in motion, just
1:10:10forget about those bottom terms there.
1:10:12And you have the change in the
1:10:13distribution is the following. There's
1:10:16going to be some firms that are choosing
1:10:17to adopt and some firms that are
1:10:19entering their new firms. they get a
1:10:21draw from the existing distribution.
1:10:24Then there's going to be firms at the
1:10:25bottom of the distribution that are
1:10:27adopting. And so you have to subtract
1:10:29all those firms from the distribution
1:10:31because they're leaving. They're
1:10:33adopting. And then they're entering the
1:10:35distribution again as a draw from the
1:10:37existing distribution. And then there
1:10:39are some firms that are dying and
1:10:40because we had unconditional death,
1:10:42they're just dying in proportion to
1:10:44their density. And then the brownie
1:10:46emotion terms, they just bump some firms
1:10:49over the adoption threshold due to the
1:10:51randomness and the drift. And again, you
1:10:54get a solution that's a truncation.
1:10:59You again make the same assumption of
1:11:01initial productivity distribution that's
1:11:03paro. And you're going to get that the
1:11:05the normaliz the the productivity
1:11:07distribution stays paro with the same
1:11:09shape parameter over time.
1:11:12And so we can ask some questions
1:11:16about the model uh and then we can do
1:11:19some quantitative analysis. I'm not
1:11:21going to go through that now, but I
1:11:23wanted to put in the slides for you sort
1:11:25of an example of what are the questions
1:11:27that we can ask with this type of model.
1:11:30Um and what are some of the results that
1:11:32we can we can get out of that. So a
1:11:34simple result is that you can get the
1:11:36growth rate as a function of you know
1:11:39parameters in closed form. uh and you
1:11:41can also get that that it depends on the
1:11:43the ratio of the average profits to the
1:11:45minimum profits. And this has this very
1:11:48economic intuition that comes about in
1:11:50search models that what they're gaining
1:11:52when they get a draw in expectation is
1:11:55the mean productivity that's out there
1:11:57and what they're losing is producing
1:11:59with the worst productivity. And so how
1:12:02good it is to produce with the average
1:12:05productivity compared to how bad it is
1:12:07to produce with the worst productivity
1:12:08that gives you the incentives for how
1:12:10much you want to upgrade. And it's the
1:12:13upgrading through technology adoption
1:12:15that leads to growth. And so that's the
1:12:17type of economics that can come out of
1:12:19this and you can get uh you know all
1:12:21sorts of elasticities of how growth
1:12:23responds to trade costs and things like
1:12:26that in closed form.
1:12:28So last thing that I'm going to say, I
1:12:31have about two minutes I think. Uh I
1:12:33want to tell you a little bit about what
1:12:35you can do with numeric. Uh and this is
1:12:37where continuous time is is helpful. And
1:12:40then I'll I'll uh I'll wrap up and we
1:12:42can talk about innovation and diffusion
1:12:44together if people are interested. And
1:12:47so what we can do is start an economy on
1:12:50a balanced growth path and shock the
1:12:53economy with an unanticipated 10%
1:12:55permanent reduction in trade costs.
1:12:58and then study how the economy transits
1:13:00to a new low trade cost equilibrium.
1:13:03This is something that's very classic to
1:13:04do in economics, right? There's some
1:13:06shock that happens. You're going to be
1:13:08in a new equilibrium, but you don't jump
1:13:09there right away necessarily. Well, the
1:13:12way we did that is you characterize the
1:13:14math problem as a differential algebraic
1:13:16system of equations and then we use a
1:13:19professional solver in order to compute
1:13:21the transitions. This avoids us having
1:13:24to do our own PTE partial differential
1:13:27equation solver that has finicky
1:13:29dependence on grids. This is kind of
1:13:31like if you're using an optimizer like a
1:13:34Newtonian method. I don't go and write
1:13:36up my own optimizer every time. I use
1:13:38the people at Intel or or you know or
1:13:42Stanford that are professionals that
1:13:44write that stuff. And so in the
1:13:46background what's happening is there's
1:13:47some upwind finite difference methods
1:13:49that you can see Ben Mole's notes for.
1:13:51But what I want to advertise is that if
1:13:54you go to this GitHub link, there's
1:13:55replication code for this paper written
1:13:58in Julia and I think pretty good
1:14:00documentation that includes a really
1:14:02simple warm-up case. So if this is a
1:14:04type of model that you're interested in
1:14:06learning, there's a place you can go for
1:14:08the code and documentation that you can
1:14:10really learn step by step how to work
1:14:12through it. And you can get figures like
1:14:14this where upon the trade cost shock uh
1:14:17imports to GDP skyrocket pretty quickly
1:14:20and then just grow a little bit longer.
1:14:22But the measure of varieties produced
1:14:25domestically has a long and slow
1:14:27decline. And you can think about what
1:14:29happens to consumption productivity
1:14:31growth. There's a bit of a jump and then
1:14:33a continued extended growth. And you can
1:14:36think about the welfare impacts of such
1:14:38a thing. And so I think I'm I'm hitting
1:14:40my time. So I'm not going to have time
1:14:43to talk about uh diffusion and
1:14:44innovation. Uh but I'll just mention
1:14:47that there are some nice models that try
1:14:49to address the the issue that if you
1:14:52write down a model of adoption and you
1:14:54want to see how it generates growth, it
1:14:57can't really generate growth in the long
1:14:58term through imitation alone. And so
1:15:01people have modeled innovation and
1:15:03adoption together in order to to to see
1:15:06where long run growth can come from. And
1:15:08a key message I'd like you to take away
1:15:11is that
1:15:13adoption can affect long run growth even
1:15:16in a world where innovation is the
1:15:18driver of new ideas and adoption can
1:15:21contribute to growth in the medium run
1:15:23and the short run even without thinking
1:15:26about innovation. So it's still
1:15:27interesting to think about technology
1:15:29adoption um along the way. And so um
1:15:33I'll just give you some some pointers to
1:15:36um uh Paka and Ezra Oberfeld's paper and
1:15:41to my paper with Jess Benabib um in
1:15:44econometric forthcoming that walk
1:15:46through some of these issues. So let me
1:15:48conclude now. Um technology diffusion
1:15:52sort of broadly defined as everywhere.
1:15:55Cross-country diffusion affects the
1:15:56distribution and dynamics of per capita
1:15:58GDE across countries. It's a large
1:16:01reason we think that poorer countries
1:16:03grow faster um than richer countries. Um
1:16:08diffusion across firms can affect the
1:16:10distribution and dynamics of firm size
1:16:12and profits. And the diffusion of
1:16:14knowledge across workers can affect the
1:16:16distribution and dynamics of wages. You
1:16:19can see a very nice paper here uh
1:16:21thinking about how peer effects across
1:16:23workers can affect how good they are at
1:16:26working in the future.
1:16:28What I tried to provide today were some
1:16:30simple models that can be used to
1:16:31structure the analysis uh of macro and
1:16:34micro productivity dynamics. I admitted
1:16:36a lot of great papers. What I really
1:16:38wanted to do is just give you a
1:16:40framework for thinking about diffusion.
1:16:42And so much work remains to improve the
1:16:44models and I hope you're all going to be
1:16:45part of that in the future. And part of
1:16:48that is by confronting them with more
1:16:50data micro and macro. And you can see
1:16:52nice work by Brooks Donovan and Johnson
1:16:54using RCTs and survey data in Kenya to
1:16:57try to see how important the diffusion
1:16:59of knowledge is in their context or Koig
1:17:02Song and Zilla to think about using R&D
1:17:06and productivity growth data in China to
1:17:08think about the importance of the
1:17:09diffusion of technology and innovation
1:17:12for the rapid growth of that you know
1:17:15developing uh now quite rich uh country.
1:17:19And so I'll I'll finish there. Um,
1:17:20thanks for everyone's attention and I'm
1:17:22happy to stay and sort of take part in
1:17:24the Q&A.
1:17:26Thank you.
1:17:29Okay. Yeah, go ahead. Sorry.
1:17:31Okay. Thanks. So, um, in this lecture we
1:17:34talk about the search model in which um,
1:17:36agents can adopt the new technology
1:17:39without any friction. For instance, the
1:17:40friction due to patents or any other
1:17:43informationational friction I say. And
1:17:45in a recent paper by accident
1:17:48artist
1:17:50when they talk about the diminish
1:17:52business dynamism they the mechanism is
1:17:55based on the assumption that the
1:17:57diffusion between the technology leader
1:17:59and lagger has decreased over time. Um
1:18:01so um so this is something which is
1:18:04different from the our ideal model here.
1:18:06My question is do we really observe this
1:18:10decrease in technology diffusion over
1:18:11time? Is is there any empirical uh
1:18:14foundations for for this assumption?
1:18:17It's a great question and it's a super
1:18:19tricky one and part of the issue is
1:18:23there's a there's a sense in which we're
1:18:26theory ahead of measurement because we
1:18:29don't have a ton of great data on
1:18:33technology diffusion itself. And so like
1:18:37if we do innovation there's a lot of
1:18:40measured data on R&D. Um there's patents
1:18:44uh which people use and neither of those
1:18:45are perfect but we have some measures
1:18:48that we think might be proxies for
1:18:49innovation. I think we don't have as
1:18:51good data on the diffusion of
1:18:54technology. There's a couple places
1:18:55where that's not true. And so in survey
1:18:58data um some people um look at uh
1:19:02surveys that say are you using a new
1:19:04technology in your firm and is that new
1:19:07to you or is that new to the industry
1:19:09itself trying to separate did that firm
1:19:11innovate or adopt. So that's one type of
1:19:14data we have. The other two things we do
1:19:16is one is you can think of technology
1:19:18embodied in capital and you can look at
1:19:20the flow of capital across countries and
1:19:23then the other thing that people do is
1:19:25they write down theories that link
1:19:27technology adoption to some observables
1:19:30and then use the measure of observables
1:19:33to try to back out how much technology
1:19:34diffusion is happening. And some people
1:19:36do that with models of international
1:19:38trade saying the more two countries
1:19:40trade in goods and services maybe the
1:19:42more ideas flow between countries or you
1:19:46can write down models in which the there
1:19:48are productivity dynamics induced by um
1:19:53uh adoption and innovation and there are
1:19:55patterns of how much adoption is
1:19:57happening and how much innovation is
1:19:59happening in movements in firm dynamics.
1:20:02And so that was kind of the approach
1:20:04that we were taking in in this paper
1:20:06that I didn't tell you about this this
1:20:08recent econometrica paper um where uh
1:20:12the the widening of the distribution or
1:20:15the compression of the distribution over
1:20:17time uh might be in and sort of how much
1:20:22low productivity firms are growing
1:20:23compared to high productivity firms are
1:20:25growing might give you a sense of how
1:20:26much adoption or innovation is
1:20:28happening. There's some research that
1:20:30suggests that um there's been a slope.
1:20:33Oh, it was IMF research. I think it's
1:20:35that there's been a compression of the
1:20:37distribution of of the firm size
1:20:39distribution over time and that might be
1:20:42a sign that there's more adoption and
1:20:44less innovation happening from the lens
1:20:46of my theory, but it's very hard to have
1:20:48direct measures of diffusion. Uh so it's
1:20:51very hard to give you a direct answer
1:20:52whether it's been increasing or
1:20:54decreasing over time.
1:20:55Okay, thank you.
1:20:56It's a great question.
1:20:58Okay, Chris. Um, thank you. I I can see
1:21:03one probably still needs to do a lot of
1:21:04mathematics to have a full grasp of the
1:21:07of the lecture. Uh, but I just want to
1:21:10uh look at it from the uh point of view
1:21:14of research and development R&D as an
1:21:16important source or driver of innovation
1:21:20basically. Now, what is the role of
1:21:22financial development in this in this
1:21:24case? I I cannot see anything of that in
1:21:26the model or is there a particular way
1:21:28one can factor this in because it's is
1:21:31important finance drive R&D and so u how
1:21:35do we treat the inequality among uh
1:21:38countries with respect to the level of
1:21:40financial development and of course
1:21:43access to funding for R&D
1:21:46that that's an absol That's a fantastic
1:21:48question.
1:21:49A short answer is a lot of the models
1:21:52that I talked about and a lot of the
1:21:54models related models in the literature
1:21:56have not yet developed uh an answer to
1:21:59that question. And so I would say that's
1:22:01that's a bit of a hole in the literature
1:22:03is trying to develop a model where you
1:22:06you you incorporate the financial
1:22:08frictions uh and level of financial
1:22:11development into the story. So that's
1:22:14just a acknowledgement of sort of where
1:22:16the literature a part of the literature
1:22:18is. In the Nelson and Phelps style
1:22:20models, um, one of the things that we
1:22:23were thinking about is sort of how much
1:22:25human capital a country has affects its,
1:22:28you know, quote unquote absorptive
1:22:29capacity. How much can it perform R&D
1:22:33and how much can it adopt technologies?
1:22:35You can similarly write into that
1:22:37equation the level of financial
1:22:39development of different countries and
1:22:42that can affect the the rate at which
1:22:45they grow via innovation and and we do
1:22:48have models of of how financial
1:22:50frictions affect innovation. Um but it
1:22:53can also affect their ability to adopt
1:22:54technologies. And so I I don't know of I
1:23:00can't off the top of my head think of a
1:23:01great paper to point you to that does
1:23:03that. But in in the the Nelson and
1:23:05Phelps style model, it's relatively I
1:23:08think straightforward to try to um do
1:23:10that analysis and see uh empirically how
1:23:12important the financial um development
1:23:15of a country is in in that.
1:23:18Okay. Thank you, [snorts]
1:23:20[clears throat]
1:23:20Chris. I have three questions from the
1:23:22from the Q&A. Um the first is related to
1:23:26um the it probably could be related to
1:23:29the slowing diffusion question that you
1:23:31first were asked. It's by Matias Cortez.
1:23:34Is the shape of the distribution of
1:23:36productivity across firms stable in the
1:23:38balanced growth path? No changes in
1:23:40between in between firm inequality. Is
1:23:44there a way to think about this in the
1:23:46context of recent evidence on growing
1:23:48between firm inequality? I'm thinking
1:23:50specifically about growing between firm
1:23:52wage inequality and I wonder if there is
1:23:54a way to link these models to these
1:23:56patterns.
1:23:57It's a it's a fantastic question. So,
1:23:59can I take one question at a time?
1:24:01Yeah, sure. Yeah, that's a fantastic
1:24:03question. So the models that I showed
1:24:05you um were models in which the
1:24:08productivity distribution shape remain
1:24:11constant over time. They are in my
1:24:14opinion good models of how the the the
1:24:18technologies that are available for
1:24:20adoption affect the incentives to adopt,
1:24:23but they are bad models for
1:24:25understanding what determines the shape
1:24:28of the technology distribution itself.
1:24:31And so um what we tried to do in in this
1:24:35paper is let's write down a model in
1:24:39which the shape of the distribution
1:24:41itself is endogenous and comes out of
1:24:44the varying forces of how much adoption
1:24:47is happening versus how much innovation
1:24:49is happening. And so um here we can do
1:24:53counterfactuals by thinking about sort
1:24:55of subsidies to innovation or subsidies
1:24:58to adoption infor in increased
1:25:00enforcement in patent protection. uh
1:25:03differences in ability for firms to
1:25:05license technology over time and how
1:25:08those changes would lead to a change in
1:25:10in the shape itself of the productivity
1:25:13distribution which captures a lot of
1:25:15what you were talking about sort of
1:25:17changes in in in firm inequality. If you
1:25:20wanted to then link that to worker
1:25:22inequality, uh, wage inequality, I think
1:25:25you need a slightly richer model of
1:25:27wages, uh, or heterogeneous workers, um,
1:25:31than than we've developed thus far. But
1:25:34that's something that seems like a very
1:25:36doable next step. So, it's a great
1:25:38question to say sort of where does this
1:25:40shape come from, right? If you think
1:25:41about trade and models, um the shape of
1:25:44the the the distribution is what shows
1:25:47up in this ACR formula for welfare gains
1:25:49from trade. Sort of where does that that
1:25:51parameter come from? This is one theory
1:25:53of that. Um but when you have endogenous
1:25:57movements in productivity, then you have
1:25:59a theory that can help to to answer
1:26:02these uh questions that you're asking um
1:26:05in a fundamental way.
1:26:08Thanks, Chris. And then I guess it's
1:26:10actually a series of questions by the
1:26:11same person about uh firm market power.
1:26:14So I'll I'll combine the two questions
1:26:16and you can address them at the same
1:26:18time. Is it possible to study a discrete
1:26:20number of firms in an economy in this
1:26:22setup? I'm thinking about something like
1:26:24igopoly model. So firms have market
1:26:26power. And then he says can you explain
1:26:29conceptually conceptually technology
1:26:31diffusion versus business stealing? both
1:26:34are firms increasing productivity based
1:26:37on other firms. What is the difference
1:26:39in terms of modeling etc.
1:26:42Yeah. So there's a couple papers that I
1:26:44didn't talk about but I mentioned a
1:26:47little bit at the very beginning. Um um
1:26:50actually let me let me pull those up. Um
1:26:53this paper by um Akjet Aes and Impoliti
1:26:57and another paper by Sha Cleo and Nath.
1:27:00They work within the creative
1:27:02destruction framework but also think
1:27:04about technology diffusion as sort of if
1:27:07there's a different um products and the
1:27:11productivity of producing each product
1:27:13can evolve on a on a ladder and firms
1:27:15sort of step up on rungs of the ladder.
1:27:17you can conceptualize that sort of
1:27:20moving up a rung on a ladder on a
1:27:23product um is building on what the
1:27:26previous inventors did getting to that
1:27:28rung in the first place. And so you can
1:27:31bring a lot of the creative destruction
1:27:33models to thinking about uh technology
1:27:36diffusion with that perspective. I think
1:27:39what's a little bit different and what
1:27:40we were trying to think about is we
1:27:43think that
1:27:44within product within certainly within
1:27:48sector but even within narrowly defined
1:27:50product that's relatively homogeneous um
1:27:53there's a wide distribution of
1:27:56production techniques being used to
1:27:58produce that product. And so in the
1:28:00models that we just talked about um
1:28:03there's a lot of low productivity uh
1:28:06firms that are existing um and producing
1:28:09these these goods um and they could be
1:28:12just upgrading to better technology. In
1:28:14the creative destruction style models
1:28:16usually have like the best uh firm
1:28:19producing that particular type of good.
1:28:22And so it's it's in my mind more
1:28:24developed for having sort of frontier
1:28:27firms that are pushing out the frontier
1:28:29and not so much for having lots of firms
1:28:31that are well within the frontier and
1:28:33how they get better. And so what we
1:28:36wanted to do is try to think about
1:28:37having models where you can have
1:28:39frontier firms pushing out the frontier,
1:28:41but there's just a distinct
1:28:44process by which low productivity firms
1:28:46upgrade their productivity that's
1:28:48different from these frontier firms
1:28:50doing R&D. And so that's kind of a a way
1:28:52of conceptually uh making these
1:28:54different in terms of market power. You
1:28:57can do both. Um you can you can have
1:29:00market power in both. In the the trade
1:29:03and growth paper that I I wrote with
1:29:05Pearl and Wisa, we did monopolistic
1:29:06competition. So it wasn't very sort of
1:29:09interesting markups, but you can have
1:29:11different uh demand functions or
1:29:13production functions that allow for
1:29:14variable markups. Um, and there are
1:29:17creative destruction style models that
1:29:19also allow for thinking about markups.
1:29:22So, I think it's a a useful thing to try
1:29:24to combine. Um, and I don't think one
1:29:27model type of model or the other has an
1:29:29obvious advantage in that respect.
1:29:31Any other questions from the front row?
1:29:33Okay, we have one last question uh from
1:29:36Dumbala Coutella and maybe this is a a
1:29:39better question for Lauren uh next week,
1:29:42but um are there any behavioral
1:29:44explanations of firms learning new
1:29:47technologies from others? I think they
1:29:49have in mind behavioral economics.
1:29:51Yeah, absolutely. So um so this is a not
1:29:55work that I've personally done. Um, this
1:29:58is in some sense work that I've done is
1:30:00an asif uh representation of firms not
1:30:05being able to necessarily find and adopt
1:30:08the best technology. And so I've done
1:30:10that in a random search way, but you
1:30:12need some theory of why there's a better
1:30:14technology that could be used and why
1:30:17it's not being used. And so one theory
1:30:19could be it's hard to find that
1:30:21technology. Another theory could be it's
1:30:23too costly to adopt that technology.
1:30:26Another theory could be stubbornness in
1:30:29some sense. I don't want to adopt that
1:30:31technology. That you can call that
1:30:33behavioral or you can frame that in it's
1:30:35risky to choose a new technology. I know
1:30:38it works for other people, but if I
1:30:40implemented it in my context, I don't
1:30:42know if it would currently work. So, uh
1:30:44I don't have any great evidence to point
1:30:47you towards how to distinguish between
1:30:50sort of stubbornness or riskiness. Um,
1:30:53but I think what you're pointing to is
1:30:55that there has to be some reason why uh
1:30:59better technologies exist and they're
1:31:01not being used when they're non-rival
1:31:03when it's physic when it's feasible for
1:31:06them to be in used. Um, one thing you
1:31:08can do is in this Brooks, Donovan and
1:31:10Johnson RCT paper, they were trying to
1:31:13match um, entrepreneurs with mentors and
1:31:17you can see sort of which techniques the
1:31:20entrepreneurs adopted and didn't adopt
1:31:22and why. And so you can get once you
1:31:24have survey data matched to these RCTs,
1:31:28you can go in and sort of survey the
1:31:30individuals and try to figure out what's
1:31:32going on and why. or you have to develop
1:31:34very sharp predictions about how a
1:31:38behavioral theory um of non-rational
1:31:42behavior would differ from rational
1:31:45behavior. And that's very tricky because
1:31:47a lot of times the same behavior can be
1:31:50described well by both models if you
1:31:52just have a richer sense of what the
1:31:54rational agent is concerned about or if
1:31:56you give yourself enough flexibility to
1:31:59choose the behavior of the non-rational
1:32:01agent.
1:32:04Okay, thank you. Uh, I want to thank
1:32:06Chris. Um, especially he originally was
1:32:09supposed to go in a few weeks. Uh, he
1:32:12made some references to Lauren will be
1:32:14talking more about some micro technology
1:32:17diffusion in um in agriculture
1:32:21uh next week. Um, and Ben Mole will be
1:32:26talking more about continuous time
1:32:27methods. Um um but Chris, we we had
1:32:31originally scheduled him for Good
1:32:32Friday, so we moved him. He was very uh
1:32:36kind and flexible to move to today. So,
1:32:39if we could all unmute uh those of you
1:32:41who have access to your microphones and
1:32:43give Chris a round of applause. I want
1:32:45to thank him. [applause]
1:32:50And uh we will see you all uh next
1:32:53Thursday. Um thank you. Bye-bye now.
1:32:57Thanks. It's my pleasure.
1:32:58Thank you for Lauren.
1:33:00Thank you
1:33:00Lauren Kirsty and Mandy once again.
1:33:03Yeah. Thank you.
1:33:05My pleasure. Look forward to reading the
1:33:08research that you do and I can learn
1:33:09from you.

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