 Thanks very much for coming. Let me just set the outset. Thank Wider for inviting me to speak here today. So this is brand new work, actually. It's the first time any of us are presenting this. So your comment and feedback is greatly appreciated. And it doesn't have inequality in the title, but it is a paper about inequality and growth. And that's the core part of it. So it's called Public and Private Expenditures on Human Capital Accumulation in India. And it's joint work with Gerard Lum at Indiana and John Stone, who is now at Weber State University. So the broad motivation is based on two strands of the human capital growth distribution literature. So there's a huge set of papers in both. But in the top, when you ask, how does public education spending influence economic growth? Typically, the mapping is from public expenditures to human capital accumulation to growth. And there are a variety of assumptions made on that relationship, on the human capital accumulation function. So there's papers here that some of you may be familiar with or not. And there's many, many more that explore this nexus. There's also an equally large literature on the effect of public education spending on wealth distribution dynamics or income distribution. Horace Mann, the father of US public education, is famously quoted as saying, as public education is one of the greatest equalizers of the condition of men. And there's been an attempt to formalize this in the context of models where income dynamics are stochastic. And there are all kinds of interesting results about what happens in the steady state of the distribution of income. Is it ergodic? Is it non-degenerate? And conditions under which these outcomes obtain. And coming back to inequality and growth is a little new for me. I was working a lot on this stuff about five years ago. And even there, in the context of majority voting endogenous growth models, kind of the Alicina-Rodrick-Barrow distributional conflict and growth models, there were some nice results about complete factor holding convergence. In other words, the median voter equilibrium led to the growth maximizing outcomes in the long run. So this is kind of an aspect of the literature that I like and that I'm interested in. And it's been worked out in a variety of kind of different contexts. To make these models tractable, often simplifying assumptions are used. So for instance, Lucas only considers a private input in human capital accumulation. Or if you typically have composite inputs and you model the human capital accumulation as a Cobb-Douglas type, then you get unitary elasticity of substitution. Or if you have public spending and private spending, these models end up being difficult to solve unless you assume rows equals to 1. So you make simplifying assumptions to characterize the balanced growth path. And that ends up being an approach that some papers take in this literature. So what we want to do is look at the point of departure from two standpoints. First, we want to construct an abstraction that is useful to understand public spending on education investments in a developing country context. So this is an abstraction. We want to make this useful. In other words, we want to make this have features that are typical of developing country context. So what we're going to do is we're going to allow for the imperfect substitutability of public and private education in a child's human capital accumulation. So we'll allow for both public spending and private spending, but they don't necessarily have to be perfect substitutes in the model. So that's one of the features we're going to. And there's a lot of evidence that suggests both of these inputs are related in the accumulation process. Another thing that we're going to allow for is a complementarity effect. In other words, we're going to allow for the parental human capital to positively influence a child's ability. So if your kid has a fifth grade math and your father is only second grade math, then the father can't meaningfully contribute to the intellectual development of his child or her child. So we're going to model that additional term also in the human capital accumulation equation. So those are two things we're going to do. We're going to allow for the imperfect substitutability. So allow for both public spending and private spending to be substitutes, near substitutes, or more complementary. And we're also going to allow for the fact that the parental human capital complements the child's human capital. Provided that the parental human capital is above a particular threshold. And I'll talk about that a little more. We're going to look at a cutoff in the distribution of human capital. If the parent's human capital is above that threshold, then the parent meaningfully contributes to the child's intellectual development. So that's the second feature. But we also allow for non-homothetic preferences. And I'll explain how that works in a second as we go along. But this is also going to be crucial for looking at the effect of some of the controversial experiments we conduct vis-a-vis raising public education, spending, and understanding how that affects inequality. Having non-homothetic preferences is going to be important for the effect that higher public education spending has on inequality in the model. Once we write out, and as I said, we motivate this because we want a useful abstraction to think about what should be the optimal level of public education spending in a developing economy. We run a series of counterfactual experiments. So we think of raising public education spending in a particular state of India. And I'll talk about that in a second from, let's say, X to Y, which requires us to raise taxes to do that. And raising those taxes are going to have an effect on the transitional path for private investments in education, human capital growth, consumption levels, and income levels. So we're going to write out the transition path. So Francois Bourguignon was talking a little bit about in the morning about how we don't focus enough on transition paths. So this model is going to yield outcomes going 100 years down the line. For a particular exogenous tax financed increase to get public education spending up to a particular level. And the way that we're going to finance that additional public education spending is through a variety of tax instruments. We're going to fool around with a consumption tax and thresh out the effects that this has. There's generally equilibrium effects that this has on those four things that I just talked about. We're also going to look at the changes that income taxes have on a higher public education spending, human capital growth, consumption, inequality, as well. And then we're going to do the same thing by increasing the center state transfers. So in India, the fiscal transfer is usually provided out of central tax revenues to states. And states are either net contributors or net receivers of these tax revenues. So we're going to look at a pure windfall, in some senses, of an exogenous increase in the proportion that the center gives back to a region to a state, and see what happens to growth and inequality in this situation. And the model is basically a calibrated model. I won't have much time to talk about the calibration, but in the paper that is loaded up on the website, there's the details are there. I'll just run you through that very briefly. And the experiments we are conducting is the reason why this is an India project is that we have public education, state gross domestic, net state domestic product ratios for 15 Indian states in 1985. And they range roughly from 2% to 4%. In other words, these regions, these are big states. And in India, studying states is interesting, because some states in India have 200 million people. Other states have 100 million people. So these are very interesting units of economic analysis. But we have a distribution of these public education to state GDP, state numbers. And we're calibrating the model to the median of that distribution, to the median state. And then the question we're asking is what if that particular state or that region wants to go upwards? We'll just take the second highest public education spending ratio, and what if it goes down for some reason? Which is not really the realistic question here, but the question that is realistic is if a particular state, the state of the median of the distribution wants to ratchet up its public education expenditures to the highest public education expenditures, what kinds of effects does that have on growth and inequality in the long run through all these different things that are feeding into the human capital accumulation equation? So that's a rough gist of it. And let me give you a brief glimpse of the results. So if we raise public education spending to a tax financed increase, we're going to get economic growth. We're going to get higher economic growth. But in some ways, this is the main result of the paper. There's going to be a trade-off. There's going to be a growth and equality trade-off. Whether you finance that additional expenditure through a consumption tax or an income tax is going to matter for the growth and equality trade-off. And our result is that if we finance this additional education expenditure increase by an increase in a consumption tax, that is actually more friendly for growth and less it reduces inequality, but not by that much. But if we did the same thing, if we financed that additional increase in expenditures on public education by an income tax, that tends to be a little less friendly for growth, but more friendly for reducing inequality. So that's the crux of the result. In that sense, it matters how you get to the top of the distribution in terms of that higher spending on public education. It matters what tax instruments you use. And the general equilibrium of it works out why that's the case. And the answer to this is going to be behind the competing substitution and income effects that these tax increases imply for household private choices. In particular, if the government is going to raise higher public education, fund higher public education investments, households are going to be compensating by reducing their private investments on education if they're substitutes, but if they're complements, we'll show that you can even get crowding in, for instance. So that's the kind of rough road map where this is going. And then what we do is, since we can't analytically solve the model, because we have this row not being imposed equals to 1. So that creates a little bit of a complication. But when we computationally solve the model, we show that even though you're financing this higher public education investment by a tax finance increase, the effects on growth in the long run are not very, very different from whether you use either instrument. And that's also the case for the change in inequality as well. So computationally, the differences are even 80 or 100 years down the line, roughly across 2, 2 and 1 half percentage points. So you don't really get that much of a difference in the computational effects. OK, now let me give you a glimpse of the model. So as I said, one problem with doing this kind of research with referees is if you add three features and say, OK, these features capture the essence of a developing country context, the referee says, well, give me 10 more and the paper's rejected, right? So then there's this trade-off between tractability and trying to make sense of it. So what we think are important features that drive our results are preferences. So there are n overlapping generations that live for two periods. And they essentially have one choice to make, which is to spend their after tax income, which is 1 minus tau L WT HT. HT is the human capital. WT is the efficiency wage and tax on labor income is tau L, which is a parameter between 0 and 1. They're going to spend that on consumption, on consuming the final good. And there's no physical capital in the model. So savings is taking the form of investing in the education of your child. Now the child's human capital as an adult will be this, HT plus 1. So if the parental human capital is above a particular threshold, H bar T. So we have a distribution of human capital. So we're going to let H bar be the fifth percentile of that distribution at any given period T. So that means that if you're above the fifth percentile, you intellectually contribute to the human capital of your child. So if you're above it, HT times AT is the complementary term, right? And you get this AT, HT to the delta. Then this is the public education component here. This is in per capita terms, so there are no congestion effects. And this is private education spending. And this is the efficiency of that private education investment spending. So those are the things that go into the human capital accumulation of the child who becomes an adult in T plus 1. If your human capital is less than this H bar T, then this term doesn't exist here. And you just get this over here. So non-homathetic preferences, we have this complementarity threshold, which is based on a cutoff on the distribution of human capital at time period T. And there's a simple budget constraint that the household faces that constrains his or her optimization problem, which is that the tax adjusted. So this is a markup on the consumption, on the price of consumption. Plus education investments has to exhaust all after tax income. Now, to think about this transfer formally, and this is as simple as possible as a representation you can think of. And you can quibble with it, but we think this is fairly kind of accurate in terms of capturing what we're going. So they're anti-families. ETs the per capita. So anti times ET is the total public education investment. That's coming from taxing household consumption. So big CT is all the consumption that's going on. Tau sees the tax on that, so that's a tax revenue. And then big TT is the transfer. That's the transfer that states are going to receive from the center that's going to help fund that public education investment. In per capita terms, if I divide both sides by NT, I'll get the per capita public education investment. And the way we think about the central state fiscal transfer is that it's going to be basically given back to the state as the tax collected on the efficiency wage multiplied by aggregate human capital multiplied by this parameter delta. So all these are exogenous. The delta, the triangle, tau L and tau C are all exogenous parameters in the model. If you get delta to be greater than 1, you can think of this state being a net receiver of federal funds. And if it's less than 1, then you can think of this particular region being a net contributor of federal funds. OK, so when you solve this, you can manipulate. And this is going to be key in understanding under what tax instruments you have income effect and substitution effect. And under what tax instruments, you only have a income effect. But you can see what happens here is that if you raise the price of consuming, you're basically going to end up with wanting to shift to your educational investments. Can I borrow three minutes into my Q&A time? Is that possible? Or are you going to be? I may need to eat into two or three minutes of it if that's OK with you. But great, thanks. So OK, so you solve the model. And this is going to be important here. If you look at an interior solution, your private educational investments are going to be negatively related to the public education investments. So if the government funds more Big E, then your private E goes down. It could be that it funds a lot of Big E, so your private actually goes to 0. So the question is under what condition is private E greater than 0? So in equation 3, E bar is the maximum amount of E that the household can undertake. Because if it doesn't consume anything, it still has to do this subsistence consumption stuff. This is its wage income. In theory, that's the maximum amount of E that the household can undertake. So the threshold that emerges there is that as long as the human capital is greater than this, then there's a positive E that comes out of the model. And then these are just the comparative statics that come from the first order condition of the household, where we haven't assumed rho being equals to 1. That's a special case. So this is what the dynamics will be. The dynamics of the model will be pinned down by whether a household human capital is above that subsistence threshold and whether it's above the complementarity threshold. If it's above both, which is this case here, the complementarity term kicks in, and the household spends on private E. So that's the first part. If human capital is greater than the complementarity part, that complementarity term comes in. But if it's less than that H hat, that subsistence threshold hat, the household doesn't spend anything on private E's. If HT is less than the complementarity part and less than the subsistence threshold part, you don't get private E and you don't get the complementary part. So that's a characterization of the dynamics of the model. So that's what we're going to calibrate. From HT, we'll go to HT plus 1 using those equations. OK, one last thing. When rho is equals to 1, we just get this. OK, so here is the calibration strategy. We have seven moments for this state. We have genies in 85 and 205. We have the growth rate across this period. The median state turns out to be a state in South India called Pamiladu in terms of its public education spending shares. These shares, as I said, range from 2% to about 4.5%, 5% in 1985. So we have seven moments. We have this. We also have this. We have the public education expenditure shares. We have the private education expenditures shares in both periods. And we have the genies, which are based on survey data, on consumption expenditure survey data. And on the basis of this, I won't spend time on this. But on the basis of this, we get here's the original data and that's the model. So we're able to pick parameters in a reasonably good way, actually. That mimics the seven moments that we have in 1985. And you could get more parameter combinations that give you these moments. And so in the end, we do a sensitivity analysis that on a lot of these parameters. OK, so now let's take the first counterfactual experiment, which is we want to go to the second highest state in the distribution. So we're asking if we're going from roughly 3.42%, that's Tamil Nadu in 1985, to 4.24%, what's going to happen to the general equilibrium of this economy? What's going to happen to growth? What's going to happen to inequality? That's the question we're asking. So here's what's going to happen. If you finance that increase by an increase in tax on consumption, you're poorer. You're being taxed more. So your private education investments go down. That's the income effect. But if you increase your tax on consumption, which makes you want to consume less, the substitution effect means that you push towards private investment in education. You substitute out of consuming the final good towards investing in the human capital of your kid. But there are also these other effects. This is going to mean that from the budget, you have more ET available. And that's going to lead to ET falling. So ET falls because of the income effect and this effect for the budget constraint. So the substitution effect, it goes up. So tax is increased, biggie is increased, and two channels are pushing small e down and one channel is pushing small e up. So how does this work out? If you look at the time trajectory, so these are the transition paths for this economy, on E. So you went from roughly 2 to 2.8. That's what you need to raise it to in order to get to that 4.24 term, where you were at 3.42. So you're going from 3.4 to 4.24. You need to raise the tax on consumption from 2% to roughly 2.8%. What you see in the dot is you see that your private falls because there are two mechanisms which are moving private down and one that is moving it up. And you get, so therefore you get a reduction in private. Then if you look at human capital growth, it's roughly kind of, it rises, but by less than 3%. Human capital growth is just income growth in the model because output has just been produced by human capital. So you get an increase in growth. This just gives you an increase in the level of human capital over time. And this gives you the insight into what happens on inequality, on the genie. And the key mechanism here is that because you're facing a higher tax on consumption, your after tax income falls. But because you have non-homothetic preferences, your privates are going to fall proportionately more for richer households than poorer households. So that leads to a compression in the distribution of HT plus 1. And that leads to downward pressure on inequality. Now the key contrast here is that if you want to move to that upper point in the distribution and you do that by financing it by an increase in the tax on labor income, you have a rise in your labor income, which means your private falls, you invest less privately on the child's human capital. This is also going to lead to ET falling. But you don't have the substitution effect anymore, because you're not financing this by high consumption tax, financing it by an income tax. So both these lead to ET falling. You don't have this compensating increase in ET coming through the substitution effect. So ET falls by more compared to the first case. If ET falls by more, HT plus 1 increases by less. But HT plus 1 over HT is the growth rate. So the growth rate increases by less. So a tax-financed increase in education leads to growth increasing by less. Finally, is that 23 minutes? I'm done. OK. Pure windfall. Outlet ends up being higher consumption. A lot of it goes into higher consumption. It doesn't go into private education investment. So in the paper we talk about ranking these three things. And since the chair is telling me that I need to keep quiet now, here we report a lot of the sensitivity results, because we want to make sure that our results are robust across a variety of different parameters in the model. And I can talk to you more about this towards the end to conclude. This is a way to think about these kinds of experiments in developing country contexts. And when you have a tax-financed increase in public education investments, you're going to end up with a growth and a growth equality trade-off. In other words, it'll matter how you fund that additional higher public education expenditures. But computationally, we show that these effects are not large. And another thing that I didn't talk about was that we end up with, if a large chunk of the population, in other words, doesn't benefit from the complementarity. In other words, if parents don't intellectually contribute to intellectual development of their kids, we thrush this out also. Higher public funding doesn't really have less of an effect. Thank you very much. And sorry for going over time.