 Thanks everybody for coming. I'll go straight into it. Even though we've seen quite a bit of growth in Africa in the last few decades, or in the last decade perhaps, there's no doubt that there's a comparatively limited industrial base. There's also relatively limited industrial diversity in Africa today in sub-Saharan Africa. Of course, we know, and this is the topic of this session, there's a literature that actually a set of models that predate modern neoclassical growth models. And these are sort of kick-started by Arthur Lewis, not necessarily Martin Rebellion's favorite economist, apparently. But I and I imagine my other co-presenters today will also use these models. So within this literature on dual economy, models, theory, and empirics, there's a sort of natural lineup of topics that you could look at. Are there differences between sectors in terms of their productivity growth, or their productivity level, are there factor product differences, marginal product of labor differences, or marginal product of capital differences? Of course, these two are linked. So the tradition has been to kind of look at what the sectoral differences are in these magnitudes, and then to do kind of counterfactual analyses. What would happen if Malawi had the TFP level of the United States? Not necessarily always very meaningful, but that's not for me to judge. Here's some of the authors. So what's new in our analysis is really questioning the production technology. Is the production technology really the same in all these countries if we just look at one sector? So is the shape of the production function for an Ethiopian tech farmer, is that production function the same as for a Kansas sorghum farmer? Or in the manufacturing sector, do Sri Lankan garment firms really have the same shape of production function as the German car plant? And part of this research will show that technological heterogeneity doesn't change the qualitative implications of productivity improvements, but it has very significant impact on the quantitative implications, and especially the speed of structural change. So apologies if this sounds a bit grand, but this is part of my research program I have. And please also apologize. I apologize to you for pretending that these are very important papers. You will never have heard of any of these. And of course, there are many other people working in this area, so obviously the two co-presenters today. So what's really going on in this literature? First of all, we looked at agriculture. So this is also together with Francis Thiel. We looked at agriculture and we wanted to see whether we can model agriculture in a way that reflects this diversity that has been mentioned from Hayami and Ratsan in the 1960s onwards, where people always say maybe we should model the production technology to be different across countries. That's what we did in this paper. Then there's another paper which has been around for a long time, and that's why I just name it here as the paper with a title that's nowhere near as funky as the No Mangoes in the Tundra paper, and that's on manufacturing. And here the idea is to show that there are technology differences across countries, and these are a function of the specialization that countries undergo in terms of their manufacturing and their export arrangements. This paper here is published and indicates how we really are making a mistake if we just look at aggregate economy data. And I think that's something quite popular these days. So many of you will be aware of the work by Danny Roderick, including with Margaret MacMillan, but he recently published a paper on the QGE on convergence in manufacturing. So this idea of going away from the aggregate economy data and going more towards sector-level data, given that now a lot of this is available, this is something that I'm very sympathetic to. This paper on agricultural technology and development will be mentioned more in due course. So what am I doing in the present presentation? Well, first of all, this is work in progress, but I'm trying to revisit lots of these theories looking at what drives growth in an empirical dual economy model, but accounting for this notion of technology heterogeneity. So rather than take you through the paper, which is obviously on the website, I'm going to use most of my remaining 15 minutes to try and sell you two ideas. And those two ideas are technology heterogeneity and then how we could probably model productivity. So technology is really the shape of the production function. So if we have a cop-dog's production function, those are just the coefficients on the factor inputs, most simply capital and labor, for instance. Now the radical, the new idea here is that different countries have different technologies. As to where those might come from, I think we can explain quite well in the agricultural context, where we have these agroclamatic requirements. You can't just plant mangoes in the tundra. You need to take into account these external factors, and they will probably affect what you plant and what sort of agriculture you engage in. But there's a host of other reasons why we think technology could be different in agriculture. A question mark is very important here when we're saying, well, if countries have different production functions, is that set in stone? And is that something we need to work around? Or is that subject to change? And this is an important question that so far we haven't really addressed. Then we have productivity, the manner from heaven, or the endogenously created productivity that drives technical progress, that drives growth to a certain extent, and that's the height of the production function. So I just want to make really this distinction between technical progress that a country comes up with, and then spillovers. So we're all standing on the shoulders of giants, so any technical progress that's developed in Silicon Valley is the product of other technical innovation that has taken place either there or in India. I'm saying India because a lot of Indians these days work in Silicon Valley. So perhaps this distinction is very fuzzy, but I just want to emphasize that what we often measure as country-specific productivity growth is really an amalgamate of what countries have come up with themselves and other ideas that spill over. How can you improve technical innovation, or technical progress in your country? You can invest in R&D and carry out efforts to improve innovation. But you could also try and capture more of these ideas that come over from elsewhere, absorptive capacity. So for instance, in the US, these are high, I forget the exact title, but the visas for highly skilled individuals, there are means and ways of capturing ideas that are from elsewhere, from outside the country. So productivity has a global element. There's global technological progress. There's a local element, which means a regional element perhaps, and then country-specific. And of course, whenever we have productivity comes into our marginal product of labor calculation. So very simple graphs to illustrate. These two countries have the same shape of the production function, a very simple one just in labor, because we can then present it in this two-dimensional space. But as you see, they have the same technology, they have the same shape of the production function, but different productivities. So the height of the production function differs. In contrast, these two countries have different technologies. This is a linear technology, and this is a curvilinear technology, but they're basically similar in productivity. So I'm going to go a little bit into this paper, which is with my co-author Dietrich Walroth, where we start out with an empirical motivation. We're looking at agricultural production in 128 countries, and we allow this production function to have different coefficients on the inputs. Now, inputs are labor, measure for capital stock, which is tractors, and then we have fertilizer, land, livestock, and over a very long time horizon. And what we observe if we look at the implied labor coefficient, which is our main technology coefficient in the later theoretical section, that there's certain kind of correlations between what share of a country's arable land is in which climate zone, and what this coefficient is, on average, across a total of 128 countries. So countries in the more equatorial and equatorial and highland zones seem to have higher labor coefficients than those in the temperate or arid and cold climate zones. And just as a test, whether we're just capturing something slightly different here, maybe income, there's a similar pattern here, although the lower middle and income countries are clearly not conforming to this simple relationship. So we're not talking about anything causal or so, but this is an observation. So maybe there's something systematic about labor coefficients. So what would happen if we start out with a labor share in agriculture of 80% and then we have different sizes of productivity shocks? A, what would happen to the labor share if we calibrated our model to the case of South Korea? So you can see when you have a higher labor coefficient, 0.55, then your agriculture labor share will decline much slower than if you have a smaller labor coefficient. And in return, what does that do to real output per capita? The lower coefficient countries can basically grow much faster than the higher coefficient ones. So just to illustrate that more, we measured the improvements that we identified in South Korea. Arguably the single biggest success story in the 1950s and 60s, South Korea was at the same level as Ghana in terms of income per capita. So they have seen a 270% increase in total factor productivity, 250% increase in wages, and an 80% increase in population. So these are then the counterfactuals. If we look at these three types of coefficient, high labor coefficient, intermediate low. So you can see starting from 80% agricultural labor share, all of them have dramatically reduced their labor share in agriculture, but there are tangible differences between these three cases. And perhaps one of the most striking insights is the labor productivity, which is partly due to the amount of labor in the sector, but also the output increase. So we have three times more output per worker in agriculture in the low coefficient than in the high labor coefficient case. And this has very tangible impacts on real income per capita. So what could you take out from this paper? What's the story? Maybe some regions with high labor, maybe they've actually done quite well in terms of getting productivity increases. So maybe there's not such a barrier to productivity improvement in these countries than we previously thought. But the pessimistic view is that if you have a high labor coefficient, then structural change is really slowed down dramatically as compared to a low coefficient case. So if this is really structural, if countries in, say, the equatorial regions of the Earth, if their agricultural productivity is such that they have a, sorry, their agricultural technology is such that they have a high labor coefficient, then it will take them a long time to achieve something as career, even if they had exactly the same shocks introduced in the model. OK, so I've got five more minutes now. So I'm going to introduce an alternative set up which has to do with how to model productivity. This is a lot of algebra. But what do I really want to indicate? So productivity is something unobservable. Let's pretend all of you are employed as typists. No, actually, you're writing down every single word I say. What happens if I turn the light off? Well, maybe some of you really have some kind of night vision goggles, and they can still write. But others can't. So what does that mean? They're unobserved global shocks, me turning the lights off, but they have heterogeneous impacts. Think of a global oil shock. It probably has a different impact on different countries, depending on whether they're exporters, net of oil, or importers of oil. But then there's also more regional localized effects. So if Robert suddenly starts talking to Maggie really loudly, maybe that part of the room, the people around them, they're kind of distorted. They can't really pick up on what I'm saying. So if I'm monitoring the productivity, the output, the accuracy, and how much you have understood of what I've been saying, or how much you've written down, then probably those guys over here, they're not affected. But these guys over there are affected. So what's this phenomenon called? It's called cross-section dependence. Just the idea that if you're in Canada, what goes on in the United States is probably really important for your economy. Now, let me tell you something quite surprising. In cross-country empirical analysis, that's not taken into account. There's no taking account for the fact, where are you within the sort of global space, if you think in a geographical manner? Where are you in the room? Are you sitting over with Justin, or are you sitting with Robert in terms of your relationship to other people? So we're modeling this in our papers using common factors. And there's strong ones, which would mean there's global shocks, and they have a different impact on different countries. And then there's weak ones. The weak ones are these localized effects, where they really just affect some of the people in the room. And then we use some methods to, even though these are unobservable, these factors, given that we have time series data for a lot of countries over 30, 40 years, we can actually account for them. We can kind of blend them out, which is quite amazing, and there's a substantial literature on this. So what do we do in this paper? Three minutes. So we use the same data as in the previous paper, which is quite a unique World Bank data set, Kregor, Don Larson, Rita Butzer, and Jan Mundlach. And this is investment series for agriculture and manufacturing. So the agriculture bit is really amazing. So that's why you can then directly compare your sectoral production functions. We have 40 countries over a 30-year time horizon. I'm not going to go into great detail. Basically, these heterogeneous technology estimates using these common factor frameworks give you, let's say, these technology coefficients on capital, and these would be the implied labor coefficients. And these are the ones that we're using for the later analysis. So first of all, we can see that sectoral TFP growth differences are actually not that substantial. So if these are the means, the robust means, this would be 2.4% per annum in manufacturing, 2.3% in agriculture. This is quite a different result from what the seminal paper in this literature is perhaps Martin and Mitra 2002, and they found that agriculture had higher total factor productivity growth. Then we can have a look at sectoral TFP levels. So these are different estimators for agriculture. These are different ones for manufacturing. The lower ones are always the ones that are favored by theory and residual diagnostics. But what I want you to look at is just the standard deviation. So we can see if we use a standard way of measuring TFP levels by looking at the intercepts of a production function. We get a very, very high variation. You can also see the range is quite substantial. More than three times the variation that you get if you use one of these heterogeneous parameter estimators. And similarly, manufacturing half the variation. So what does that mean? People have thought these differences in TFP levels and the differences in TFP growth rates, they are everything. They matter the most when we look at whether this is aggregate economy data or sector level data. But what our research suggests is that, well, you're really leaving out this guy here, this beta I. You're leaving out the technology heterogeneity that I tried to illustrate a little earlier. And then in terms of the marginal factor products, we can show different assumptions lead to different outcomes. Perhaps this is a more interesting graph. This gives you the relative marginal product of labor between manufacturing and agriculture. So if these were the same, then this country does not seem to have any distortions. There's no misallocation of labor. If you have a much higher value in agriculture, then that means more of these people should be in manufacturing. They should be shifted. But clearly, there's some kind of barrier. There's some structural problem why they cannot shift into agriculture. And what these numbers mean are these other ratios. So the marginal product of labor in Madagascar in manufacturing is 3.6 times that in agriculture. Now, these numbers might not mean very much to you. But again, what do we see? These numbers are very, very modest compared to what you get in a model where you do not, where you assume everybody has the same technology, be it in agriculture or be it in manufacturing. So to summarize, this is tentative results, the ones that are presented towards the end because we made a change to the estimation. So things will inevitably change. But what's quite clear is that this idea of technological heterogeneity, different production functions across different countries, not just across sectors, has a very significant impact on measuring these kind of sources of growth structural change. There's not much evidence for higher TFP level in agriculture. Again, that's speaking to Martin and Mitra. And this duality, this massive, the ratio of marginal product of labor between manufacturing and agriculture seems substantially reduced here. So perhaps it's quite obvious for you already what I should do differently here, because you've probably completely lost you. But some of the things that I didn't have too much time into discussing here would be how do these results really match with what was there in the literature already? And perhaps also motivate a bit more, why do we think there could be technological heterogeneity, bring up some theoretical, like some proper economic theory, and then perhaps also compare the empirical results with some results from a calibration exercise? Thanks very much.