HILARY GREAVES: (00:06) Hello everyone and a very warm welcome to the Atkinson Memorial Lecture for 2021. This memorial lecture series was set up jointly by Oxford's Department of Economics and the Global Priorities Institute here in Oxford in honor of the late Sir Tony Atkinson about whom Margaret will say more in a moment.

(00:24) The Global Priorities Institute, GPI, is an interdisciplinary institute spanning economics and philosophy. The institute exists to conduct and to promote rigorous academic research that's especially crucial for, speaks especially directly to the decision problems that are faced by an impartial actor trying to do as much good as possible with fixed resources. Within that general remit we're especially interested in longtermism, that is, the idea that often the most important features of our decisions are the effects of those decisions on the much further future on timescales of hundreds of years or even longer. When thinking about that, of course, one critically needs an understanding of the big picture issues concerning what that further future might plausibly look like. And this is one of many reasons why GPI is especially excited about the work of Professor Jones.

(01:11) On a logistical note, when we get on to the lecture, please confine any questions during the talk to clarificatory questions only, reserving more substantive questions for the Q&A session that we'll have at the end. Please also note that the talk is being recorded for posting online. So in particular, if you do ask any clarificatory questions during the talk, those will be included in the public recording. If you do want to raise such a question, please enter your question using Zoom's chat function and then Rossa will call on you as appropriate.

(01:41) And I'll pass you over to Margaret Stevens, who's head of the economics department here at Oxford to say a few more words about Tony Atkinson and to introduce today's speaker properly. Thanks, Margaret. Margaret, you need to unmute.

MARGARET STEVENS:  (02:02) What a bad start. Thank you very much. Thank you, Hilary, and welcome everybody. The annual Atkinson Memorial Lecture is our opportunity both to cement the productive relationship between the Economics Department and the Global Priorities Institute and to celebrate the legacy of Tony Atkinson. Tony's work on inequality and social justice is a source of both pride and inspiration for economists and others in Oxford and beyond. I think that maybe in a game of the first word you think of, the obvious response to inequality would be Atkinson. Tony spent the last 23 years of his career in Oxford, for part of that time, as Warden of Nuffield College and for all of the time as a wonderful colleague and researcher, combining their highest academic standards with his clear sighted focus on solving practical problems on social justice and public policy. His commitment to addressing inequality was not just an intellectual one. He was a natural egalitarian in the way he related to his students, colleagues and everyone around him. So he's really the perfect role model for the Global Priorities Institute.

(03:21) I can't let this moment pass, though, without mentioning another wonderful colleague who we have lost, Professor Peter Neary. Peter had been ill for some months, although he kept that very quiet. So I think it was probably a shock to many to hear that he died yesterday afternoon. It was in the concluding moments of a ceremony awarding him an honorary doctorate at the National University of Ireland, where he was honored as one of Ireland's greatest ever economists. Like Tony, he leaves behind an influential body of work, in his case, on international trade. Sadness that he's not here with us today and great affection.

(04:08) It's now my happier duty and great pleasure to introduce our Atkinson lecturer, Chad Jones, who is well known to everyone who has studied economics through books that feature heavily in macroeconomics courses, especially his introduction to economic growth. Chad completed his undergraduate studies at Harvard in 1989, his PhD at MIT in ‘93 and he is a Professor of Economics at Stanford University. He is an elected fellow of the Econometrics Society and the American Academy of Arts and Sciences. He is perhaps best known for his work on endogenous growth and the role of R&D, starting with his seminal 1995 paper in the JPE and his recent work on top income inequality would certainly have been of great interest to Tony Atkinson and perhaps in the case of his paper on Taxing Top Incomes in a World of Ideas some provocation as well.

(05:06) Today, Chad's going to talk about a semi-endogenous growth perspective where again, the nonrivalry of ideas plays an important part in the story. So the floor is yours, Chad. We're looking forward to your lecture on The Past and Future of Economic Growth.

CHARLES I JONES: (05:24) Wonderful. Thanks so much, Margaret and Hilary and Rossa. It’s really a complete honor and pleasure to be with you today to give the Atkinson Memorial Lecture. What I want to talk about today is material that I've been drawing together recently for a publication in the Annual Review of Economics. And so this is a collection of things I've been working on for my entire career, but also in the last couple of years and it's really nice to bring this together and have a chance to share it as I'm drafting the paper as we speak.

(06:05) Let me say a few words about Professor Atkinson. Obviously, as we all know, he's just famous worldwide for his decades long incredibly influential work on inequality and as Margaret mentioned, this has been very influential in my own work and she highlighted two of the papers that I've been working on quite recently that were very much motivated by Professor Atkinson's research.

(06:32) But for today's talk, I wanted to highlight for you something that you probably know, but I hadn't quite realized. In fact, he was also a growth economist, especially very early on in his career. So after graduating from college, he went to MIT for a year and took a growth class with Bob Solow and served as his research assistant and began the research that evolved into to two important growth papers.

(06:57) So the first that I list here, A New View of Technological Change was a paper with Joe Stiglitz, that built on the blueprint model of Joan Robinson, the notion that technological change doesn't shift out the production function everywhere, but instead might be very local to what your capital labor ratio or your inputs are. I wrote a paper related to that actually, 10 or 15 years ago and hadn't realized that Tony had worked on this. I wish I'd known more about this paper.

(07:26) The second one was The Timescale of Economic Models is very interesting. This was a paper he wrote while he was at MIT and it was incredibly ahead of its time. It was solving numerically for the transition dynamics for three different growth models and looking at this question, How Long is the Long Run? and one of the things he highlighted in that paper is that transition dynamics can last for a very long time. And this is a theme that I'll actually return to later today.

(07:56) Okay. So here's an outline of what I want to talk about. I want to show you a basic semi-endogenous growth model and use that to motivate the rest of the talk. I want to use the model to look at the past of economic growth through a growth accounting exercise. And that will lead to some provocative conclusions about the next two questions. What does the future of growth look like? Could it be slower? Or might it not be slower? Could it could even be faster? And so those are the questions I want to address today.

(08:28) I'll skip the literature review slide in the interest of time, but maybe I'll just highlight the second bullet. One of the things that that I realized while pulling these things together is that the literature on semi-endogenous growth, from one perspective at least, is much broader than you might have expected. Basically, any model that features increasing returns to scale, if you look at it in the right way, is a semi-endogenous growth model. And so, the trade models of Krugman and Eaton and Kortum or Melitz or the firm dynamics models that Melitz and Atkeson and Burstein and others have worked on – sectoral heterogeneity by Rachel Ngai and Bobby Samaniego, technology diffusion models, economic geography models. Many of these models in these literatures could be viewed as semi-endogenous growth models. So I thought that was an interesting point that I hadn't fully appreciated before.

(09:17) Okay. So let me turn now to lay out the basics in the endogenous growth framework for you. And like all growth models, I think a key motivating fact for growth theory is this picture of GDP per person in the United States over the last 150 years. And the really stunning, remarkable fact that you see in this graph is that growth hasn’t departed from a 2% straight line much at all. It's really amazing. You can see the Great Depression here, but even that is just a blip and shortly thereafter, we're back on trend. And so the key growth question, in some sense, that all growth models are interested in is, how is it possible that economic growth can be sustained at a remarkably stable rate for 150 years?

(10:15) The idea of based growth literature really pushed by Paul Romer and Aghion, Howitt, Grossman, Helpman and others – that literature builds on a key insight that Romer won the Nobel Prize for in Economics just a couple of years ago. And that's the nonrivalry of ideas. So the way I like to call it is the infinite usability of ideas. And so what Romer really highlighted for us is that there's a key distinction between objects and ideas, that objects are almost everything we see around us. It's the subject of most of economics – so iPhones, airplane seats, surgeons – basically, most economic goods are rival. If I'm using it, you can't use it at the same time. And that fundamental scarcity lies at the heart of most of economics and Adam Smith's Invisible Hand and everything else. But then ideas are different. Ideas are nonrival, they're infinitely usable. In particular, they can be used by any number of people simultaneously and they never suffer depletion. So think about calculus or computer code or the chemical formula for a new drug or even the design of the new COVID vaccines. These things, once you create the first version of it, it can be used by one person or a million people or a billion people simultaneously and you never have to reinvent the idea. So one of my friends, when Romer won the Nobel Prize, put it this way: if there's an apple sitting on the table between us, you can eat it or I can eat it, but everyone in this seminar can use calculus. A billion people in the world can use calculus or the Pythagorean Theorem, etc.

(12:01) The next point in Romer’s argument, which is going to be the key departure point for the semi-endogenous growth view of the world, is that this nonrivalry of ideas, this infinite usability gives rise to increasing returns to scale. And so let me use a few equations to highlight this for you here. So here's a standard production function. It involves capital and labor, let's say, or you could add other inputs and the stock of knowledge. So A is going to be my notation for the stock of knowledge and a Cobb-Douglas example would be a familiar version of this production function. So Romer’s argument is that there are constant returns to capital and labor holding knowledge fixed. Why is that? Well, this is just the standard replication argument. If you've got a factory that makes iPhones, it uses capital and labor and intermediate goods and other things to make iPhones, one way to double the production of iPhones is to replicate the factory, to build an identical factory across the street with identical intermediate goods, identical capital, identical workers, etc., and then obviously it's going to produce the identical amount of output, so you will have doubled output. So importantly, this replication argument works. It takes advantage of the infinite usability, the nonrivalry of ideas, namely, the design of the iPhone. We don't need to reinvent the design of the iPhone for the second factory. Instead, the original design, because it's infinitely usable, can be used in both factories simultaneously.

(13:32) But what this means importantly, is as long as the marginal product of an idea is positive, if there are constant returns to capital and labor, there must be increasing returns to capital and labor and ideas taken together. And the intuition here is just really simple. The replication argument plus the nonrivalry of ideas, gives us constant returns to objects that are used in production and, therefore, there must be increasing returns to objects and ideas. And this is really the key insight, I think, that Romer won the Nobel Prize for and as I mentioned, it's the departure point, for the semi-endogenous growth view of the world.

(14:10) So with that as background, now we can lay out what I think of as pretty much the simplest version of semi-endogenous growth theory. And you can see the key insights in a very simple model and that's how I like to present things. So this first equation already embodies Romer’s insight. Notice we've got constant returns to labor. There's no capital. I've dropped capital. We could include capital. You can include lots of other things, but again, in the spirit of simplicity, let's just focus on one input.  Solow taught us that capital really doesn't matter that much from a long-run growth perspective, so forget about it. There's constant returns to the only rival input, to the only object to your labor and therefore increasing returns to labor and ideas together. A denotes the stock of ideas and σ here is the parameter measuring the degree of increasing returns to scale in this production function. So Romer’s already built in once we write down that production function.

(15:14) The second equation is the production function for ideas and if we forgot about this last term that I'm highlighting here, if we just had the growth rate of knowledge depends on research, that would be Romer or Aghion, Howitt or Grossman and Helpman. The semi-endogenous growth view of the world comes from adding this A^–β term. This is the “ideas are getting harder to find” term. I think of β as a positive parameter here, any positive number. It could be .5, it could be 37. β measures the rate at which ideas are getting harder to find. And so this idea production function says we produce ideas using research and old ideas and that's where new ideas come from.

(16:03) The third equation is just a resource constraint. We've got L_t people in the economy and they can work as researchers or they can work to make consumption goods. And importantly, as you'll see, I'm assuming the number of people in the economy is growing at an exogenous given rate n and some number 1%, 2% – some number like that. And then finally this resource constraint… You can see, there's only one allocative decision that we have to make – how do we decide how to split our labor into researchers and regular workers and I'm going to follow Solow here and just use a rule of thumb allocation. Let's assume 10% of our labor force works as researchers and 90% work to make to goods.  Romer wrote down a market equilibrium with imperfect competition and patents. You can allocate labor that way. You could look at a social planner, an optimal allocation. You could do things that way. Everything's going to go through. This is just the simplest way to make the points.

(17:02) So that's the entire setup and now we're ready to solve. And when we solve, let's remember that the thing we're interested in, is what's the growth rate of income per person or consumption per person. And so my notation for consumption per person or income per person is going to be y, that's total consumption divided by the number of people  (Y/L)  and you can see from the production function, that's going to be A^σ (1  s̅ ) because that's the fraction of people who work to make goods. This equation already is Romer’s Nobel Prize, in some sense, because it says income per person, y, depends on the aggregate stock of ideas. A is an aggregate, not per person. If this were the Solow model we'd have k^⅓, capita per person to the ⅓ power. Instead, we have the aggregate stock of ideas to the σ. σ could be ⅓. There's nothing about the ⅓ that matters here. It's really that it's an aggregate stock A, rather than a per worker stock, k. And again, this is because of the nonrivalry of ideas. Anytime we invent a new idea, that basically benefits everyone. We invent the COVID vaccine and billions of people are made better off. And so, because these ideas are nonrival, they help everyone.

(18:25) Next obviously, we then have to ask, where do ideas come from? And that's what the production function for ideas was useful for. Along a balanced growth path, the growth rate is Ȧ/A is just going to be some constant. We'll have to solve for that constant in a second, but it's going to be constant. And you can therefore solve the idea of production function. Move A^–β to the other side and you get that the stock of ideas is proportional to the number of researchers, R^1/β. And this again, is an incredibly intuitive expression. It says the more researchers we have, the more knowledge we have. And there's nothing special about this idea production function in some sense. The more autoworkers we have, the more cars we make. The more researchers we have, the more ideas we make. So there's nothing especially controversial there. And it's really these two equations that I've highlighted in blue. We're done now. We put those two equations together and that's it. And both equations are really interesting. People produce ideas. That's the second equation. And those ideas because they're nonrival, raise everyone's income.

(19:38) And so if we combine those two equations, put them together, we get the top equation here, which gives us the level of income along a balanced growth path. So income is going to be growing (we'll solve for the growth rate in the next equation), income is proportional to the number of researchers R_t^γ  where γ  = σ/β, it's the degree of increasing returns in the goods production function deflated in some sense by the rate at which ideas are becoming harder to find. And notice what this is: the more researchers we have, the richer is everyone. Why is that? Because more researchers means more ideas and because those ideas are nonrival, they raise everyone's income.

(20:26) Now, if we want to ask what's the growth rate of income per person, just take logs and derivatives of this first equation. The growth rate of income per person is gamma times the growth rate of researchers and the growth rate of researchers is just population growth. Or again, it's the degree of increasing returns in the goods production function, deflated by the rate at which ideas are becoming harder to find multiplied by population growth.

(20:53) Another way to interpret this equation, it says – the long-run growth rate is the product of the degree of increasing returns to scale, γ, which is the overall degree of increasing returns you can see from the first equation, multiplied by the rate at which scale grows. So Romer told us ideas are nonrival, and that gives rise to increasing returns, but what does increasing returns mean? It means bigger is better. Bigger is more productive. And so the growth rate of the economy is just the degree of increasing returns to scale, multiplied by the rate at which scale is growing. How fast are we getting bigger? And how important is it that we get bigger? That's the growth rate of the economy.

(21:37) Okay. Here's a slide that that helps to give some intuition for the equations that I just gave. So from nonrivalry to growth. With objects, if you add one computer, you make one worker more productive. If you want to make a million workers more productive, you need a million computers. So output per worker depends on the number of computers per worker. That's  the Solow expression. But ideas are different. If you add one new idea, you make an unlimited number of people, any number of people, more productive or better off – so the cure for lung cancer, drought-resistant seeds or the spreadsheet program. Again, if you want make a million workers better off with computers, you need a million computers. If you want to make a million workers better off with ideas, you can just invent the spreadsheet. It can make one worker better off or a million workers or a billion workers better off. And so again, income per person depends on the aggregate stock of knowledge, not on the number of ideas per person. And we know it's easy to make aggregates grow. Solow taught us how to make aggregates grow. Population growth generates growth in aggregates, but since income per person depends on an aggregate, it's easy to make that aggregate grow with population growth. And that's at the heart of the semi-endogenous growth model.

(22:54) So where does growth ultimately come from? The one sentence answer is more people gives us more ideas and because those ideas are infinitely usable, more ideas gives us more income per person. That's the increasing returns associated with the nonrivalry of ideas. So you can see why I say any model with increasing returns is really, in some sense, a semi-endogenous growth model.

(23:20) Let me turn now to some evidence for this semi-endogenous growth view of the world. And this is going to draw on a paper that I wrote with Nick Bloom, John Van Reenen and Michael Webb and published last year. So again, we started with this production function for ideas that I've just shown you and we emphasize the interpretation of β as the rate at which ideas are getting harder to find or to be more accurate, I think, it would say it's the rate at which TFP growth, total factor productivity growth, gets harder to achieve.

(23:55) And looked at this way, I like this Red Queen Interpretation of semi-endogenous growth models, that basically maintaining constant TFP growth requires exponential growth in research effort. In other words if R_t were constant here, notice that A^–β, the fact that ideas are getting harder to find, would slow down the growth rate. So if you want constant growth, you need growth in research. Maintaining a constant rate of TFP growth requires exponential growth in research effort. You have to run faster and faster just to maintain 2% growth and that's the Red Queen Interpretation.

(24:36) Well let's ask, what does the data look like? And what we did in this paper is we looked at lots of different pieces of evidence where we could measure both ideas on the one hand and the research that goes into producing those ideas on the other hand. And so we looked at the aggregate economy. We looked at agriculture and the production of cotton and corn and wheat and soybeans. We looked at health care. We looked at mortality from cancer or heart disease and we looked at firm level data. So we looked at lots of different places. Let me highlight two of those examples for you.

(25:09) The first is from the aggregate economy. And let me go back to the equation one more second. Notice if β were zero, if this “ideas is getting harder to find” term worked there, then the growth rate here, Ȧ/A, total factor productivity growth, would look just like research. Whatever happens to research would be what would happen to the growth rate. So under a null hypothesis of β = 0, that ideas are not getting harder to find, growth rates and research effort should look the same. And so in some sense, we can look at those two series and if they look different, that's evidence that ideas are getting harder to find.

(25:49) So what I've got here is evidence for the aggregate economy. On the left, I've got US total factor productivity growth in blue. And on the right, I've got the number of researchers in the US economy, relevant for the US economy. You want to measure US researchers or OECD researchers or global research. This is a question I'll return to in a second. It doesn't really matter for the purposes of this argument. What you see is your total factor productivity growth has been pretty stable. In fact, it's even declined a little bit over the 20th century. Notice the scales are identical. They go from 0 to 25. The green line says the number of researchers during the 20th century grew by a factor of 23. Growth rates were constant or even declining when research was growing by a factor of 23. Clearly, these two series don't behave the same way and instead, it's the Red Queen model. Exponential growth in research is what was associated with stable or maybe slightly declining growth rates of total factor productivity. So this looks like ideas are getting harder to find. If you back out the value of β, it's implied here, it looks like β is about 3.

(27:04) So this next graph is my favorite example in the paper. It's Moore's Law. It's the famous relationship that underlies Silicon Valley where I'm sitting today. The empirical regularity that the density of transistors on computer chips seems to double every two years. We're doubling every two years. If you remember your Rule of 70 about computing growth rates, implies a growth rate of 35% per year. And the remarkable thing about Moore's Law, is it's a great example of constant growth looking like a straight line on a logarithmic scale. You've seen the graph. It's just a straight line. The growth rate of 35% per year, this doubling time of two years, was maintained for 50 years. People kept thinking it was going to come to an end. And no, no, no. It's just a straight line for 50 years. So I've labeled the growth rate here as 35% per year constant over this entire almost 50 year period.

(28:03) What we did in the paper is we were very careful to try to track down how much research was conducted at different points in time by different firms, by  obviously, Intel and AMD and Samsung, but also firms that  existed in the early 1970s. so Fairchild, Semiconductor, National Semiconductor, other older companies that are no longer with us. And  what we found… And again, we do this seven different ways, because there are different assumptions made in measuring this, but what we found, no matter how we looked at it, is the effective number of researchers had risen tremendously with this benchmark number. There are 18 times more researchers today than there were in the 1970s.

(28:42) And one way of thinking about that, it requires 18 times the research effort today to generate that doubling of chip density than it did in the early 1970s. Again, total factor productivity growth, ideas are getting harder to find. It's harder and harder to maintain this exponential growth. It requires more and more research effort today, relative to the past.

(29:05) If you back out the β here, you get the smallest value we found, which was 0.2. So you think of semiconductors as this incredibly dynamic sector and it is. That's the place where ideas are easiest to find of all the examples we looked at, but it's still the case that β was 0.2. I'll come back to some of this evidence in a second.

(29:27) Let me shift gears to another aspect of the semi-endogenous growth model in the example that I just gave you, which is how long are the transition dynamics? This is the Tony Atkinson question that I started with on one of the early slides. And let's think about it this way. How many years does it take for the growth rate of the economy to move half-way to its steady state? So suppose we start out and suppose the steady state growth rate labeled down here is 1% per year for a total factor productivity growth. That’s a realistic number. And suppose we start out at 2% or 4%. So we start out above our steady state. How long does it take us to fall half-way toward the steady state?

(30:10) With the simple model that I've given you, it turns out, you can solve for the transition dynamics in closed form and you can back out what the half life is and you see the equation here. It depends on where you start and where you end and on this key parameter β, what's the rate at which ideas are getting harder to find? And you can see here I've given us β values for the Moore's Law example for the aggregate economy. I think for agriculture, we found β is a five. So here's the range of βs that we found in our different case studies. And the surprising thing, the stunning thing that you see in this table – these are years – how long does it take before the growth rate falls half-way toward its steady state value? The answer for a typical value of β is measured in centuries. It's 144 or 115 years. It could be even longer. In fact, for the Moore's Law case, it's measured in the thousands of years.

(31:06) Transition dynamics in these idea based growth models for realistic parameter values are incredibly slow. It takes a century or more for growth rates to fall half-way to their steady state. And that has profound implications for empirical work on economic growth because it means that… Research that was being done, changes in institutions, the advent of DARPA and the NIH and the National Science Foundation or Bletchley Park, the Manhattan Project or the space program of the 1960s. These changes are still affecting how we think about growth today. They're still impacting the growth rate of the US and the UK today. Transition dynamics are remarkably slow. So I'll come back to that point again later as well.

(31:54) Okay. Let me shift gears to my second point now and talk about historical growth accounting. So what we've seen in the semi-endogenous growth model is that in the long-run, all growth ultimately comes from population growth and increasing returns to scale. It's the product of those two things. But we can ask a different question, which is historically, if we look at that first graph I showed you – growth over time in the US economy – what does2 the growth accounting exercise look there? Is it all due to population growth or not?

(32:25) To do this exercise, I need to extend the model. Now we need to add capital back in. Capital is going to be denoted by K. Human capital per person is going to be denoted by h. I'm going to think of this as educational attainment. And then I'm introducing this allocation term M. Let me show you the production function. So the aggregate production function for GDP here is Cobb-Douglas K^α (L)^1−α. Human capital per person multiplies labor. So this is total human capital, hL. And then Z is my total factor productivity growth term written in labor augmenting units. So Z in turn is going to be the product of the stock of knowledge and misallocation, this M, and this misallocation term, I would say, is one of the key contributions of growth economics in the last decade – the realization that distortions at the micro level, distortions at the firm level or the plant level, distortions at any micro level aggregate up into TFP differences. So you can think of this M term… With an efficient allocation of resources, M would be one. To the extent that resources are misallocated, M could be less than one. And it shows up as total factor productivity. Then finally, the third equation is just the long-run version of the idea of production function that the stock of knowledge depends on the number of researchers R_t^γ, where γ is the degree of increasing returns to scale.

(34:03) Now if I rewrite the production function, put things together in terms of output per person, you get the equation in blue here. The output per person depends on the capital output ratio raised to some power that depends on the capital share, depends on the stock of ideas, the extent of misallocation, human capital per worker, labor force participation, so I can distinguish ℓ from population, and then it depends on what fraction of the labor force works to make goods instead of ideas.

(34:34) In the long-run, all of growth in this setup comes from population growth. The capital output ratio is going to be constant in the long-run. M is going to be constant in the long-run. It can't be bigger than one. Educational attainment – we spent 20 years in school or something. That's going to be constant. Labor force participation – a constant fraction of people work and constant fraction of people take leisure and the allocation of labor between making goods and ideas. All of these things are going to be constant. So all of growth comes from A_t and growth in A_t comes from growth in researchers R_t, which again comes from population growth. So in in this setup, still once again, all of growth comes from population growth.

(35:13) But now we can ask, what about historically? To what extent did changes in the capital output ratio or changes in misallocation or changes in educational attainment or labor force participation – to what extent did those contribute to economic growth? So if you take this equation and take log differences, that's all I'm doing here. And I'm  writing out… These are the additive growth decomposition that comes from taking log differences. And let me skip this slide for a second and go straight to the growth account.

(35:45) So this is a back of the envelope growth accounting for reasons that I'll get into in a second. But this is a stylized picture of the US since the 1950s. So again, GDP per person has grown at about 2% per year. Where does that growth come from? When you plug numbers into those equations that I just showed you, the capital output ratio is essentially constant, so it contributes nothing. Human capital per person – educational attainment’s been rising throughout the 20th century. It rose at something like one year per decade or a little bit less. When you’re per decade or a little less, what do labor economists tell us? They tell us that each year of education raises wages, raises labor productivity, raises income per person by about 5% to 7%. So if we're adding one year of education per decade, that's 5% or 7%, higher GDP per person per decade and if we put it on a per year basis, divide by 10, that's half a percentage point of growth every year. And that's a remarkable thing, that rising educational attainment basically added half a percentage point of our growth. So out of our 2% growth, fully a quarter of it was due to rising educational attainment throughout much of the 20th century.

(36:04) Similarly, the employment population ratio, the rise in female labor force participation, was a big part of economic growth in the second half of the 20th century. In my calculations, it looked like it was about 0.2 percentage points of growth. So women's entry into the labor force means more people are working, that raises income per person in the economy because we're working harder. And so 7/10 of a percentage point of our 2% growth is due to these inputs and that means total factor productivity growth. The residual here is about 1.3 percentage points. This is in labor augmenting units again, so that's why it's higher than the 1% number you might be used to seeing. But 1.3 percentage points of growth is due to total factor productivity growth.

(37:50) Let me go back to the previous slide now. So total factor productivity growth is the sum of a misallocation piece and the growth rate of ideas. So now we have to ask, how large is this misallocation term? Here, I would say the literature doesn't know. We haven't converged on an answer. There have been some studies trying to measure misallocation and changing misallocation in the US. Bils, Klenow and Ruane look at misallocation in the US manufacturing sector and say there's a lot of measurement error. It doesn't look like there's any trend in misallocation. It looks like misallocation in the US manufacturing sector is pretty constant, so maybe that contributes no growth. I have a paper with Erik Hurst and Pete Klenow and Chang-Tai Hsieh that looks at the allocation of talent in the US economy over the last 50 years. So there what we’re looking at is the following stylized fact – in 1960 in the US, 94% of doctors and lawyers were white men. Today, it's something like 60%. So if you think about what that means, it means in 1960, there were all these talented women and black men and other people who were shut out one way or the other from working as a doctor, a lawyer or manager or other high skilled occupations. There was an enormous misallocation of talent and over the last 50 years, as those ratios have fallen to be more representative of the population, there's been an improved allocation of talent. Talented women are replacing crummy white men as doctors and lawyers and we're getting an improved allocation of talent. What we estimate in that paper is something like 3/10 of a percentage point of productivity growth is due to this improved allocation of talent. So what I'm going to do for my growth accounting is just plug in 3/10 of a percentage point for the misallocation term motivated by that study. But again, that's a back of the envelope type of thing. That number could be different.

(39:49) And then we're left with idea growth and idea growth remember, is just γ times the growth rate of research. What's the value of γ? If we subtract off 3/10 of a percentage point from misallocation, we're left with 1% TFP growth and 1% TFP growth is γ times the growth rate of research. The growth rate of researchers looks like it's about 3% per year. I'll show you some evidence on that in a second. So take a value of γ = 1/3 and you fully account for growth. So that's what I'm doing. And here, I'm splitting it into growth in population, say 1% per year, and growth in research intensity, which would be the rest of it.

(40:29) And so when we break this total factor productivity growth into its constituent components, what we see here is the 0.3 percentage point piece from misallocation. And then basically, 1/3 of the 1% that's left is due to population growth, that's the γ times 1%. If γ is a third and population growth is 1%, that's going to be 0.3 percentage points. And the growth rate of research intensity – what's the fraction of the population that's engaged in research? That looks like that's growing. And so that's contributing the other 2/3 of a percentage point. So here's the full growth accounting for historical growth in the US economy. And the remarkable thing you see here is the long-run component of growth is only this piece. Every other number in this graph would be zero in the long-run, but historically, those other numbers were quite important.

(41:29) So even in this semi-endogenous growth framework, where all of growth is ultimately γn, when you look historically other factors explain more than 80% of historical growth. These transitory factors have been very important, but they are transitory. They have to come to an end. So rising educational attainment – educational attainment went from four years per adult in 1900 to 13 years per adult today. But the 13, you can already see it leveling out. It's been leveling out for the last 20 years. Maybe it's going to rise to 14 or 15 or 20, but at some point, it seems likely to level out and it's already leveling out. So that source of growth, that half a percentage point of growth is already coming to an end. Rising labor force participation – again, already coming to an end. You can see it in the last 15 years with female labor force participation leveling out in the US. Declining misallocation – again , at best, you can have the perfect allocation and then there's no more growth due to this channel. Rising research intensity – the fraction of the population that works in research has to level out.

(42:35) And so the implication of this is quite striking that sure, on the one hand, lots of growth historically is not due to population growth. That's the good news. That's true, even in a semi-endogenous growth framework. The implication is that unless something changes, growth must slow down and slow down a lot. The long-run growth rate is the 0.3% piece, according to the growth accounting, not the 2% piece. And so this implies an incredibly large slowdown at some point in the future, again, unless something changes. And so what I'm going to do in my remaining time, is talk about that slowdown a bit more and talk about what are some things that might change?

(43:21) So the remainder of my talk is divided into these two questions, why future growth might be slower? And then why might it not be? So I've already highlighted through this growth accounting the primary thing I think that one worries about, which is a lot of the factors that drove growth in the 20th century are not long-run factors. They're not factors that are going to be there. And really, the long-run component of growth from the semi-endogenous growth perspective is some number like 0.3, not some number like two. So that that points already been made. Let me turn now to the next two points.

(44:02) And the first one comes to… Look at this research employment number. So again, research is a global activity. Luxembourg doesn't grow because of ideas only invented in Luxembourg. The UK doesn't grow only because of ideas invented in the UK. The US doesn't grow only because of ideas invented in the US. Instead, we all benefit from ideas created all around the world. And so this question of which researchers count, when you're trying to account for US growth is a tricky question because of the diffusion of ideas. So what I'm showing you here are three series.

(44:38) Let me start with blue. This is just if you count US researchers. In green, I've got if you count all researchers in the OECD and then the World number is not truly a world number. It adds in China and Russia, I think, and only goes back to 1990. But if you look at US research, it grew at more than 3% per year from 1981 to 2003 and then slowed down by about 30% after 2003. There's been a slowing already in the growth rate of research by 30% and so in the long-run, that would say economic growth should slow by something like 30%.

(45:17) The OECD, if you look at OECD numbers, you see the same thing. It was growing at 4% before 2003 and only 2.8%, another 33% slowdown in the growth rate of research effort. If you look at the World, it slowed by much less. And I'll come back to that point in a second. So this this second reason to be worried about the future of growth is we're running less fast from the Red Queen model interpretation. We're not running as fast as we used to and in these growth models that implies that growth would slow down.

(45:54) Okay. Finally, notice even if you focus on population growth, there are reasons to be worried about the future. As we all know, population growth has been slowing around the world and this just shows you for high, middle and low income countries, the degree of the slowdown. So I said population growth was something like 1% in the US. Well, if you look in high income countries as a whole, in 1950 it was more like 1.2 and today, it's more like 0.5 or 0.7. Population growth is slowing. Same thing in middle income countries. In low income countries, not yet, but the implication is that as they get rich, their population growths are very, very likely to slow as well.

(46:35) Okay, well, slowing population growth then would be another reason. Maybe the 0.3 is not even 0.3, but in fact, and this is related to a paper that I've just been working on in the last couple of years, the problem is even more severe than that makes it seem. There was a book called Empty Planet published by Bricker and Ibbitson a couple of years ago and that book made a remarkable point. It's totally obvious when you think about it. The point was, maybe the future of global population is not leveling off at 8 or 10 billion people. Maybe in fact, the future of population is that it declines.

(47:11) What's the evidence? Well, look at fertility rates. Look at the average number of births that each woman has and you know that you need that number to be something like 2.0 or maybe 2.1 if you want population to stabilize, and in fact, all around the world fertility rates, women are having fewer than two kids and their fertility rates are plummeting. So if we look at the US and the UK, the number is 1.8. If we look at high income countries as a whole 1.7, China 1.7, Germany 1.6, Japan, Italy and Spain 1.4 or 1.3. As countries get richer, fertility falls and it doesn't stop at 2.0. So this implies fertility rates may be below replacement and population may actually decline in the future rather than stabilize. And so a natural question to ask in the semi-endogenous growth model is what happens to economic growth if future population growth is negative? What if we feed in this Bricker and Ibbitson view that population rather than growing, rather than stabilizing, maybe it's going to decline.

(48:23) So let's assume for the purposes of the model that the number of researchers declines now at exponential rate η. So think of η as a number like half a percent per year or 1% per year. So the number of researchers imagine if it were to fall at half a percent per year, what would happen to economic growth? And you'll notice it's not obvious. I said, in the long-run economic growth is proportional to population growth. If population growth is negative, does economic growth become negative? That somehow seems wrong? And it is wrong. But what exactly happens?

(48:58) Turns out it's easy to answer this question. So go back to the idea of production function that I started out with. The growth rate of knowledge depends on the number of researchers ( R_t ) and then the ideas getting harder to find term, A^–β, and for researchers let's plug in that it's declining exponentially at rate η. If you look at this equation, it's actually easy to integrate. You can integrate it, you can solve for the stock of knowledge, the stock of ideas at each point in time. And in particular, what you realize is that asymptotically, as time goes to infinity, the stock of knowledge levels off. It asymptotes to a constant. And that constant is bigger than our initial level. If we start out with A₀ ideas today, in the future, we're going to have more ideas. We still have positive numbers of people and those people are producing ideas. So we're going to get richer in the future, but the rate at which we get richer is going to fall and it falls so quickly that eventually living standards stagnate.

(50:09) And the level at which they stagnate depends on, in terms of η, how fast does the population decline, if it depends on β, how hard is it to find new ideas. And in fact, another interesting thing you realize is that you could even set β = 0. Go back to the Romer view of the world where ideas are not getting harder to find, the growth rate of knowledge depends on the number of researchers, but the number of researchers is falling exponentially. It turns out, even in the Romer, Aghion, Howitt, Grossman, Helpman view the world, with negative population growth, the stock of knowledge stabilizes. It stagnates. In fact, you could even, if you look closer at this, you could make β negative and the same thing would be true. Ideas could be getting easier to find, as long as 1 > βA₀/η.

(51:02) But the key point here is that this empty planet view of the world, if the number of people is declining, if the number of researchers is declining, then living standards stagnate. And I call this the Empty Planet Result and this slide just summarizes it. But if we look historically, fertility has been trending down. Long ago we used to have five kids per woman, then four, then three, then two and now less in rich countries. What's interesting about this is it illustrates, I think, the importance of macroeconomics. From an individual family’s perspective, there's nothing special about above 2.0 versus below 2.0. Everything's nice and continuous. Whether you have 2.2 or 2.1 or 2.0 or 1.9 kids, everything's nice and continuous across that boundary. But from the macro perspective, from the economic growth perspective, when you aggregate up, this 2.2 versus 1.9 distinction is absolutely crucial.

(52:03) If women have 2.2 kids on average or 2.5 or 3.0, well then we've got positive population growth. That gives us the standard result that I talked about in the first part of this talk, which, let me call now the Expanding Cosmos view. The traditional economic growth view of the world is an expanding cosmos, that we get exponential growth in living standards for a population that itself grows exponentially. We fill the planet with people who are becoming exponentially richer and richer and maybe we fill the cosmos with people who are becoming exponentially richer and richer. It's a very optimistic view of the future.

(52:44) The stunning thing is if women have 1.9 kids instead of 2.3 kids, we get a world of negative population growth and you get this dramatically more pessimistic outcome. You get the empty planning outcome – that living standards stagnate for a population that ultimately disappears. The planet empties of people with a living standard that’s stagnant versus this world where we have exponential growth and living standards for an exponentially growing number of people.

(53:17) And I would say that the surprising thing about this result is it's not some pie in the sky, “this could never happen” view of the world. In fact, if you look at the data, this looks like exactly the world we live in. Fertility rates are falling. There's nothing special about 2.0. They're falling below 2.0 and so unless something changes, unless… If other things are equal, could this be our future? It's much more a possibility than I ever thought. So that paper is called The End of Economic Growth? Unintended Consequences of a Declining Population.

(53:56) Alright. Let me turn in my remaining few minutes to two final topics. First, why might future growth be faster or at least not as slow as the preceding section implies? And then a concluding section where I talk about directions for future research? So I think there are two or maybe three possible reasons why growth might not be as slow as what we've just said. And I think… I'm an optimist by nature and so I didn't want to end on this pessimistic view of the world, this empty planet outcome. And so I think there are some reasons why that view might be too pessimistic, but I'm more worried than I used to be.

(54:35) And these two views are first one I call Finding Lost Einsteins, after a paper by Bell, Chetty, Jaravel, Van Reenen and then Automation and artificial intelligence. And there's one more reason I might mention at the end. So the Finding New Einsteins view – this is an incredibly important point and it's a much broader point than I think people thought about in the past. So the way I like to frame it is, how many Thomas Edisons and Jennifer Doudnas have we missed out on historically, for various reasons? And I think the answer is a tremendous number. And there are different ways of making this point.

(55:20) One way is to think about the rise of China and India and other emerging countries. So China and India are special because they're so large. They each have as many people as the US, Europe and Japan taken together – more than a billion people. And what that says is they’re an enormous number of potential researchers coming online as China and India develop. In 1980, when China and India were incredibly poor, they were too far from the frontier to contribute to pushing the frontier forward, but as they experience 7%, 8% growth per year, those economies get richer, they get closer to the frontier and we've already seen, especially in China, but also in India, incredible research advances coming from those countries.

(56:10) Growth comes from people producing ideas, there are a lot more people in China and India that we can bring online to be our future Thomas Edisons and Jennifer Doudnas and produce ideas that have the potential to make everyone in the world better off. So that's two and a half or 3 billion people that we didn't have 40 years ago from which we can draw on. So that's the first point – poor countries have a lot of people who, as they get rich, can contribute to producing ideas.

(56:39) The second point is one that a graduate student at Stanford, John Felix Brouillette, is working on as part of his dissertation. He's looking at patent rates by men and women. And the surprising fact that he shows in his paper is that in 1976 only 3% of people who received patents were women and maybe even more surprising, we know in the past it was very low, the shocking thing is even in 2016, it's only 12%. We've got a long way to go before all the Jennifer Doudna in the world are realizing their potential. And he estimates that if we were to get rid of those distortions and let those numbers move to where we think they should be, that that could raise growth by 2/10 or 3/10 or 4/10 of a percentage point per year, potentially over the next century.

(57:36) And then finally, there's the original Bell, Chetty, Jaravel, Van Reenen work. Their original Lost Einsteins was primarily about poor people missing opportunities, that if you look, it's the children of rich people who become inventors and the children of poor people disproportionately do not. But we think talent is much more evenly distributed than that and they provide some evidence for that hypothesis as well. And so how many poor people are there who don't have the opportunities to become Thomas Edisons and Jennifer Doudnas that we could take advantage of?

(58:11) If you add all this together, you realize that the number of researchers in the world today – say 1% of the US population, a couple of percent of the European population, the Japanese population – there's lots more opportunities to throw more people at these hard research problems. It's easily imaginable because of the rise of China and India, because of the rise of women inventors, because of the rise of poor people realizing their opportunities, it's easy to imagine that global research effort could increase by a factor of three or a factor of seven over the next century.

(58:49) Now if γ = 1/3 and you triple the number of researchers… You remember the equation I showed you was income per person depends on the number of researchers raised to the γ power, so if γ is a third and we triple the number of researchers, three of the 1/3 is 1.4 so that raises incomes in the long-run by 40%. Or if we could increase the number of researchers by a factor of seven, seven to the 1/3 is about 1.9. That would raise incomes by 90%.

(59:21) To be honest, I was surprised these numbers weren't bigger. Tripling the number of researchers is only a 40% gain in the long-run. That's if γ is equal to a third. I'll come back in my concluding section and talk about what do we know about γ. If you look at the transition dynamics, that 40% increase or 90% increase could raise growth rates by 3/10 of a percentage point for a century. Notice with educational attainment slowing and losing half a percent of growth, this is not going to totally overwhelm that change and so I think there are reasons to be nervous about growth slowing even when you take this force into account, but it is a force that pushes in the other direction that could be quite important. And if γ were larger, it would be even more important.

(01:00:13) Okay. Next point I want to make turns to automation and artificial intelligence. And this has obviously been a very bright area of economic research in the last decade. Joseph Zeira, Daron Acemoglu, Restrepo, other people have worked on automation and economic growth. I have a paper with Philippe Aghion and Ben Jones, where we looked at the automation in the context of the idea production function. What if you could automate the production of ideas? Well, you can see how that could be a very good thing. And so I want to illustrate in a simple way for you how that works.

(01:00:49) So the task based view of the world that Zeira, Acemoglu and Restrepo have put forward says that, imagine production, in this case production of ideas, involves a bunch of tasks. They’re are a bunch of tasks and those tasks can be done by people initially or over time, you can automate those tasks. So those tasks could be done by machines or artificial intelligence. And what if you increasingly automate tasks, what happens to economic growth?

(01:01:19) So here's the idea production function that I wrote down before. I've put the A¹ on this side. So there's the A^–β and then we've got n tasks with exponent α_i where the alphas add up to one. If all the tasks are done with researchers, then there's just an R term here basically, but if some of the tasks are done with machines, let me call them capital, then you get a K term. I'm forgetting about a constant that falls out in front of this production function. But the basic idea is that the production of ideas depends on capital and people and the share of tasks that are done by machines is α and α could increase over time as we automate more and more tasks in the research process. And if α increases, we're putting more weight on the stuff that we can accumulate and less weight on these scarce people that we may be running out of someday. And so,  hopefully, that can contribute to growth.

(01:02:17) How does it work? Remember, if α = 0, that's just the model I showed you before, we get n/β, that's the growth rate of knowledge. With an α in there, capital accumulates. There's a (1 + α + α²), there's a (1/ 1 – α) logic here and so you get (n/β – α) and sure enough, as we automate more and more tasks, as α goes up, the growth rate of knowledge goes up. We  find ideas faster. Machines can replace people and machines are easy to create and they benefit from economic growth. And so this accelerates the growth rate.

(01:02:55) In fact, people talk about a singularity. You can see if somehow β is not too big and α ends up equaling β, then this blows up. You get a singularity. You get infinite income in finite time if there are an infinite number of ideas to be discovered or at least all the ideas you can discover get discovered quickly. So that's an optimistic view of things, I think. To throw one note of caution, I would say automation is something that's been occurring for more than a century. Certainly the automation of research has been going on for a long time. Think about the rise of labs, the lab model of research and the rise of labs, the rise of computers, the rise of the Internet. Producing research today versus 50 years ago is a very different process because we've automated a bunch of those tasks of research. And yet, that automation has not offset the slowing of growth. Growth is not faster. If anything, it's slower. Now, maybe other things aren't equal here, but it does at least raise this question: hey, if automation has been going on for a century, why aren't growth rates higher? And the literature Acemoglu, Restrepo, my paper with Philippe and Ben, have some answers to that question, but I think the question is still a bit out there.

(01:04:16) I'm almost done. I just wanted to conclude with one slide of important questions for future research. And looking back at this literature, I think there are a number of questions that stand out as being incredibly important. And the first one on this slide, to my mind is, it's quite remarkable that we don't know the answer to the question. As Romer taught us, the increasing returns associated with the infinite usability of ideas, that's at the heart of economic growth. How large is that degree of increasing return? So what's the value of this parameter γ ? Or if I were to put it in a different way, suppose we double the number of researchers today, how much richer will we be 25 years from now? The answer to that question depends critically on γ and actually we don't have great evidence on γ. There's some evidence that γ is about a third. I told you a little bit of the evidence. You can get values of a quarter. If you start doing back of the envelope calibrations or estimations, you can get a wide range, maybe from one quarter all the way up to one or maybe even two. And we really need to know this parameter. It's absolutely essential for understanding economic growth or the effect of policies on economic growth, etc.

(01:05:31) Second question, what's the social rate of return to research? And a corollary of that, are we under investing in basic research? Are we eating our seed corn? You look at basic research as a share of total research and the composition has been shifting from basic to applied. Are we eating our seed corn? And is that going to come back to haunt us? Better growth accounting. You remember I mentioned these long transition dynamics, that things that happened 50/75 years ago are presumably still part of our growth today. Well, how much? And what are those contributions? So what's the contribution of DARPA, the NIH, the migration of European scientists during World War II or migration more generally? These are all sorts of accounting questions that we'd really like to know the answer to.

(01:06:14) And finally, the last question that I just alluded to briefly already, automation has been going on for a long time and yet growth is slowing and not rising. Does that mean automation is not going to rescue us the way we might hope? And why not? Okay. I think that's all I have to say. Let me end there. Thank you very much and I guess I'm happy to take questions that Rossa, I believe, is going to moderate.

ROSSA O'KEEFFE-O'DONOVAN: (01:06:40) Thank you very much, Chad. We can't give you a round of applause, I'm afraid, but I think we would be if we could have been doing this in person. Yeah. Thanks very much for a great lecture.