 My name is Julie Litchfield. I'm from the University of Sussex. Please do stick up a hand if you can't hear me very clearly. First of all, thank you for giving me this opportunity to participate in yet another way in the conference. It's a very nice field so involved. So let me first of all start by putting some context around this, which will help people understand my feedback. Much of the literature on migration looks at differentials between migrant sending and migrant receiving areas. Andraeia's paper with your colleagues fits very much in this tradition, of this concept of differentials between, for convention's sake, urban and rural areas. Most of you will be familiar with the work of Harris and Tadaro many decades ago, looking at the expected income hypothesis and the idea that the potential migrant compares his or her wage in the rural area with the expected wage. So the wage they might expect to receive in the urban area, which of course isn't just the actual wage in the urban area. It's waited by the population seeking those wages in the urban area. So there's a probability associated to that wage. And then the Harris-Tadaro model goes on to predict that migration will continue until the expected wage is equivalent to the actual wage in the rural area. And that's one of the big criticisms of the Harris-Tadaro model, this idea of an equilibrium which doesn't seem to be observed in practice. Of course there's lots more criticisms of Harris-Tadaro about rationality and the focus on the individual and those sorts of things. And so in response to Harris-Tadaro people moved towards a more household way of thinking about migration, looking at decision making that takes into account potential roles of remittances and those sorts of things. And whilst a lot of us are very attracted to the household model of migration, a lot of us can see that it has real parallels with what we observe in the real world that we can empirically validate some of the predictions of Lucas and Stark and that whole new economics of labour migration. That literature doesn't give us very good direction to do the macro-level work that Andrea is trying to do. So where Andrea's work comes back into the sort of development of the literature is in this attempt to model at a more macro-level migration flows. And in the paper the authors review some of the contributions that draw on physics concepts. So most of us will be familiar with gravity models where we try and model anything from trade flows, FDI flows. Hillel was talking today about technology transmission using these idea of gravity models, the idea that a larger body exerts a gravitational pull on its neighbours. And Andrea's work conceptually, at least in the modelling of the work that they present in the paper, fits into this tradition about using some physical concepts of movement and forces on flows and the particular concept they use is around the idea of torque. So I had to reload into my memory, my school physics understanding as I went through the presentation in the paper about what torque actually means. It's the idea that if you want to move an object through space, what matters is not just the force that you're applying but the direction, the angle of that force. And the analogy they use in the paper is closing a door. So I spent actually more than a few minutes playing with doors in my house as I was trying to understand, yes, I can see the intuition now in modelling. That's why I'm disappointed that you didn't have to go through that as well. But anyway, Andrea's work fits very much in this sort of long tradition of work that uses physics analogies to model flows from one place to another. I think the contribution could be summed up, at least what I took from the paper, the contribution could be summed up in three ways, which distinguish it from the contribution of Harris and Tadaro and from other physics-based models or modelling approaches. And I think one of the contributions is it's not just about the differential between the urban and rural areas, it's actually about the relative shares of people who are suffering deprivation in a particular dimension that we're interested in, whether it's poverty, it could be any dimension, but the paper talks about poverty, education and health. I think a second contribution of the paper is that the mathematical part of the paper is set up so that it can be extended into multi-dimensional spaces. And I think as our understanding of poverty has broadened out from being, as an economist, my understanding of poverty starts with income or consumption, but we've seen, we've all moved along now to think about poverty as being much more multi-dimensional than just income or consumption. So I think that's the second contribution that this provides a way of broadening out the model into a multi-dimensional space. And I think the third contribution which distinguishes Andrea's work from Harris-Tadaro's sort of tradition is that your model doesn't necessarily predict that there will be some equilibrium necessarily, so Harris-Tadaro say there will be an equilibrium because wages in the urban sector are so sticky that they're never going to fall, they're never going to decline to such an extent that the market will clear and there'll be no unemployment. Your model allows, or certainly the discussion of the model allows for the existence of continued migration and that's a useful contribution, I think, or useful difference and then the paper goes on as you saw to illustrate this concept using data from a number of countries along with those diagrams about potential vectors and potential differences between urban and rural areas. In terms of my feedback and points that might be useful for discussion later on, I've got quite a lot, most of my comments are on the kind of conceptual side of the paper and then I've got one or two points about the empirical implementation. I think some people will look at the model a little bit skeptically because they'll say that although you are not trying to model micro level decisions, there is a sort of assumption that people are somehow making a decision to migrate based on these differentials and it was one of the criticisms levelled at Harris Tadaro, this idea of kind of rationality that people actually sit back and weigh up the pros and cons of a potential move but of course we know that migration decisions are often not very planned, often quite unplanned, they can be very chaotic, they might be triggered by quite small events or maybe accumulation of small events that finally lead them to move. I'm reminded yet again of Catherine Hall's presentation yesterday where she was describing very chaotic patterns of migration in South Africa. So I think that might need to be thought about in terms of the model and I think there's also an issue around the implicit assumption about linearity in migration that people move from rural areas to urban areas in one go. I can see how the model could be made much more complex to address this idea of multiple migrations, repeated migrations, temporary permanent migrations and the various dynamics around that but that might be something, that non-linearity might be something to reflect on. Another point to think about is the idea about inter-temporal trade-offs and that people aren't necessarily migrating to become better off. They might be migrating with the hope that they will become better off at some point in the future but at the point in time that we might be observing them, they're not expecting to be better off in that time. There's a lot of empirical evidence that I remember Michael Lipton talking about in the 1980s which suggests that migrants tend to be young, male, risk-loving people so willing to take a temporary hit in their living standards in anticipation of something much better later on. Of course, the household model of migration from Lucas and Start would suggest again that maybe migrants aren't migrating to become better off themselves but actually to assist their families back home and who might not be better off but might just have a less fluctuating pattern. I think there's also a potential issue around this assumption that the rural is the rural and the urban is the urban and I think we have a very good understanding now that actually rural areas are very heterogeneous encapsulating everything from highly commercialised farmers, adopting modern technology, being very outward-oriented, very commercialised, very export-focused right through a spectrum to people who are still in subsistence agriculture and I think that nuance might be relevant for when you're looking at regional differences or country case studies. So, I think in some on the kind of feedback on the comments, I'm wondering if they're on the model rather feedback on the model, is there something about heterogeneity about the rural, heterogeneity of migration experiences and decision making that might need to somehow be captured in this model. It did make me think, I'm not a physics expert at all, that maybe something from chaos theory and those beautiful images we see of fractals and those sorts of things might be the more obvious physics analogy to use but I wouldn't be able to advise you on how to get going. Final comment is on the empirical implementation, so it's nice to see how you've illustrated how the model, the concepts, could be operationalised with data. I think in the paper it would be nice to see some of those descriptive statistics and graphs that you referred to in the presentation, so you mentioned a scatterplot, it would be nice to see that because I think it would be useful to see the data for different countries in the regions to try and understand some of the results that you get even though they are very preliminary. So, for example, why do we get this counter intuitive result of a negative propensity to migrate in sub-Saharan Africa? Is it about the distributions? That might be something that's not the poorest of the poor who migrate, it's a kind of not quite so poor people. I think it would also help to understand if we could see a bit more of the data why Latin America has such a high propensity to migrate. I think if I remember rightly it was four or five times the estimate that you get for Asia and a better fit, so it would be interesting to see the data and what might be gained from that. Thank you.