 going also on sort of trying to find a kind of a good marriage between macro and finance, combining insights from both fields to push the boundaries of our knowledge. So please. All right. Thank you very much for the introduction. Thank you for inviting me to this conference. I'm going to present this paper which is joined with Francois Gouriot at the Chicago Fed. And it's called Accounting for Microfinance Trends, Market Power, Intangibles, and Risk Premium. So I want to show you a couple of stylized facts by way of introduction. The first one, you've probably seen a graph of these sorts thousands of times over. It documents the decline in the real interest rate in the US, but that's a worldwide phenomenon since the early 80s. And a lot has been written as what could be causing this decline. A lot of the potential explanations have been proposed. For example, one prominent explanation is an increase in the worldwide supply of savings, perhaps driven by demographics or by excess savings in emerging markets. One thing that's surprising, though, especially if you're coming at it from the perspective of this explanation, is that not all rate of returns seems to have declined in parallel. So in particular, if you try to estimate the return to private capital in the economy, you find something that's more or less stable. So this graph sort of documents the diverging trends between the real interest rates. That's the blue line. And you see that it's declining over the sample. And the red line, which is a rough measure of the marginal product of capital, which is due to Gom Rupert and Ravi Kumar at the St. Louis Fed. And what they do essentially is to compute the profit rate in this economy. So you look at the part of income that's not going to labor. And you divide that by the value of the capital stock. And that gives you a measure of the return to capital. You see that there are some ups and downs, but there's certainly no downward trend in this return. So you have a growing gap between the risk-free rate and the return on private capital, which, again, is surprising if you think that the driver for the decline in real interest rates is an increase in savings that should drive all rates of returns down. In parallel, this is not what we're seeing. So something else must be going on. Another thing that's surprising, and this comes really from looking at financial data, is that stock valuations have only increased moderately over the sample. So this is plotting the price dividend ratio in the US. And you see that there's a lot of volatility in the late 90s. That's the NASDAQ bubble. But if you remove that, there's a bit of an increase in the price dividend ratio over the sample, but only a moderate increase. And again, that's surprising if you come at this from the perspective of the fact that there's been an increase in the worldwide supply of savings, because that should have driven interest rates down a lot, and that should have driven valuations up a lot. And in fact, we only see a slight increase in valuations. So the price dividend ratio is high from a historical perspective. But if you confront this price dividend ratio with a very low level of interest rates far into the future, it's actually relatively low. So again, something else must be going on. And yet another fact that's a bit surprising and a bit inconsistent with this increase in savings supply hypothesis is that investment has remained very tepid. So this is a plot of the investment to GDP ratio. And you see that it's stable or declining a bit. And that's not consistent, again, with an increase in the global supply of savings. We should drive up the capital stock and the investment rate. So once again, something else seems to be going on. So there's been a lot written over the past 20 years, and especially over the past 10 years, about these different facts. And here I've listed some of the prominent hypotheses or explanations that have been put forward. For example, the global savings glut or slowing productivity growth, rising market power. That was the topic of the recent Jackson Hole conference, technical change, the rise of intangibles, and a smaller literature on maybe some secular trend in risk premium. So all these explanations and all these papers pretty much focus on a subset of these facts, one or two. And what we want to do instead is to look at all these facts jointly, because we think that these explanations have ripple effects for all these different facts. So if you try, for example, to explain the decline in interest rates by an increase in the world supply of savings, then you're going to have to confront the fact that investment didn't increase all that much and things of that sort. So we think it's important to look at these things jointly. And in particular, we think it's important to look at macro facts and finance facts jointly. And you'll see that I'll draw a very stark comparison in the sort of exercise that you can do if you try to impose the discipline of matching financial moments compared to an exercise where you discard these moments and say, look, finance is too complicated. I'm just going to do the macro. And you're going to be led to very different conclusions. So that's what we're going to do today. I'm going to document some of these macro finance trends. So some of them I already showed you. There are a few more. And then I'm going to put forth a very simple model, really like an accounting framework, which is going to be a little modification of the Neoclassical Growth Model, and try to estimate this little model and show you some baseline results, some counterfactuals. The baseline is not going to allow for intangibles. I'll introduce that later as an extension. And you'll see that we're going to be led to the conclusion that it didn't play a major role for the sort of things that we're looking at, which is the reason why we're leaving it out of the baseline. Then I'll compare our macro finance exercise with the macro macro exercise. And I'll try to explain why the macro finance exercise is much more sensible and leads to a much more sensible conclusion. And then I'll wrap up by showing you some more reduced form related evidence for one of the things that we're going to emphasize as being important, which is a secular increase in risk premium. So we're going to split the sample in 2000. And we're going to start the sample in 84. So the reason we're not starting in 1980 is because there's a lot going on with inflation in the very early 80s. And that's pretty much over by the mid-80s. So that's the reason for these dates. Later on during the talk, I will show you some estimates that go back in time to the 1950s. So you see the averages of these different variables on these two samples. And the last column is the change in these variables. So you can recognize in this form the trends that I already talked about, the decline in the interest rate, the relative stability of gross profitability, the fact that the price dividend ratio has only increased slightly, the fact that investment to output has gone down, but investment to capital is relatively stable, declined just a little bit. A fact that is very important and has been discussed a lot that initial is the decline in the labor share. So it's very significant. There's a 4 percentage point decline in the labor share between the two samples. And there's another little thing that's going to play some role is the fact that if you look at the relative growth, the price in the relative price of investment goods, it used to decline a lot during the first part of the sample and that rate of decline slowed down. So there's less investment-specific technical change than there used to be. But the effect is not major. So we want to account for all these things together and try to understand what structural underlying phenomenon might be driving them. And it's very important to look at them jointly as you will see. So we're going to use this accounting framework. And in this accounting framework, we want to make room for the most prominent explanations that have been put forth to explain some of this phenomenon. In particular, we want to allow for market power. And we want to allow for risk aversion, risk premium, and things like that. That's going to be the finance part of the model. And this is going to motivate these small extensions that we're going to do to the neoclassical growth model. So we're going to introduce monopolistic competition. That's to make room for market power. And we're going to introduce abstains in utility and some risk. And the risk is going to take a specific form. And that's mostly for attractability. It's going to combine productivity shock and capital quality shocks. And I'll show you exactly why that particular formulation is tractable for us. So abstains in utility is important because if you want to match these asset pricing facts, it's very important to disentangle attitudes towards intertemporal substitution and attitudes towards risk. And abstains in utility allows you to do that. So given this model, what we're going to be able to characterize is a risky steady state where all the big ratios, the macro big ratios and some finance big ratios are going to be constant. And we're going to be able to pin down this risky steady state in closed form. So it's going to be very transparent the way the model operates and very transparent the way the parameters are going to be recovered from the estimation. So I'm not going to give you the full details of the model, but I want to give you a gist of it. So these are the preferences. So you recognize an abstain in utility formulation. VT is utility. It's an aggregate of consumption today and utility in the future. Sigma, or 1 over sigma, really, indexes the intertemporal acuity of substitution. And theta is the degree of relative risk aversion. Ct is per capita consumption. There's going to be population growth, and population is NT. And beta is the discount factor. And I'm going to work a lot with the discount rate formulation. So that's 1 over beta minus 1. Labor supply is going to be inelastic, and that's something that could be relaxed. So for example, market power, markups, is going to suppress factor supply. In this model, the only factor that has some elasticity is capital. So you'll see that it will lower the capital stock. It will lower investment. But it won't do anything to labor supply. If you added labor supply elasticity, it would also suppress labor supply. But we took that out from the baseline estimation. Production is very simple. You have differentiated goods. The elasticity of substitution between these goods is epsilon, and the markup is going to be inversely related to epsilon, and that can be time varying. The production function for each of the varieties is going to be constant returns to scale. In fact, cop Douglas between capital and labor. And you see that you have two forms of technology shocks here, ZT and ST. ZT is going to be a TFP trend, and it's going to be deterministic. And ST is going to be the stochastic trend, which is going to incorporate the shocks that are going to be encapsulating the risk in this model. So in our formulation, basically, you can think of ST as being constant unless there is an extreme event. It could be a disaster, or it could be a bonanza. And if that happens, the realization of chi is either negative or positive with some small probability. That's the framework we're going to be working with empirically. So you can aggregate this economy. You get an aggregated production function, which is also cop Douglas and has this familiar form. Capital accumulation is standard. There are two little twists. The first one is the QT in front of the XT. XT is investment. So QT is the relative price. It's going to be the inverse of the relative price of investment goods. So it's going to be the efficiency of investment that's going to capture this relative decline, this decline in the relative price of investment goods. And then you see that capital is hit by this QT shock. So that's the trick that we're going to introduce. And it's really for attractability is that this shock QT, which is hitting the productivity of labor, is also hitting capital. What that's going to do is that you're going to be on a steady state with some constant big ratios. A shock is going to hit, and you're going to transition directly to the new steady state. So there's going to be no transitional dynamics. So you're always going to be in this risky steady state. And for that reason, the model is going to be amenable to a close form characterization. So a key equation in the model is going to be the Euler equation. In fact, that's the only behavioral equation in the model. mt is the stochastic discount factor, and RT plus 1k is the contingent return on capital. And it has two parts. The first part, alpha y over mu k is going to be the rental rate of capital, how much you can run your capital for in the next period. And the second part, 1 minus delta over QT plus 1 is going to be the capital gains. And the price of capital is moving around, so there could be capital gains and losses. And you see that everything is multiplied by this shock, KT plus 1. So the return on capital is going to be risky through this variable. But all the other variables are like y over k is actually going to be constant. So just a quick remark to warm up to the model. Why is alpha y over mu k the relevant measure of the rental rate of capital? Well, you have this cop dog less production function. Alpha is the technological share of capital, the elasticity of the production function to capital. But you have market power. So if there was no market power, alpha y over k would be the return to capital. Alpha y would be the share of capital. You divide the stock of capital. You get the rental of capital. But because you have market power, the rental share is going to be depressed. And that's why it's alpha over mu. That shows up in there. Finally, you have the resource constraints, so goods can be either consumed or invested. So as I told you, there's going to be a risky balanced growth path in this economy. We're going to assume that Z, which is TFP growth, N, which is population growth, and Q, which is the growth in the efficiency of investment, are going to grow at constant rates. So then you're going to get a risky balanced growth path where all the variables of interest are going to be basically scaled by a common stochastic trend. So there's a deterministic trend. That's the T. And there's a stochastic trend. That's the S that incorporates the different productivity and capital quality shock that could be accumulating. So for example, output is going to be T times S times a constant Y star. Investment X is going to be T times S times a constant X star, et cetera. And you see the expression for the deterministic trend as a function of the underlying structural trends in this economy. So uncertainty is not going to affect the trend component. It's going to be incorporated in these constants, in these Y stars, and these X stars, and the equivalent for the other variables. So risk and uncertainty, as much as market power and things like that, are going to affect this risky steady state, these big ratios, in a way that I'm going to characterize. But you're always going to be in this risky steady state. No transitional dynamics. That's why it's going to be closed form. That's why it's going to be very transparent. So just to reinforce the point, this is a graph that illustrates what could be going on. This is not meant to be empirically realistic. So here you see some trends, and there are some little blips. So the blips are the capital quality shocks and productivity shocks. So you see that they hit output, consumption, and investment in a parallel way. When you have one of these shocks, and in this case I've drawn negative shocks, the realized return on capital is going to be very low. And then you revert to a period where you don't have any shock, and the return to capital is going to be higher than the risk-free rate, because there's going to be a risk premium. And so the expected return on capital is going to have to compensate for the risk. That's why it's above the risk-free rate. So now let me characterize the big ratios. And again, don't focus too much on the nitty-gritty details of the expressions, but just the logic of how the model is working. So there's one parameter that's going to be very important. And you see that as a function of the underlying structural parameters, it's a complicated expression that involves attitudes towards intertemporal substitution, risk preferences, the amount of risk, the amount of patience. And this R star is going to be the expected return on equity. So not the R star that we usually talk about, which is the risk-free rate, but the expected return on equity. It's going to be a very central variable in this estimation. From that, we can get the user cost of capital. So the whole Jorgensen notion of the user cost of capital. So what is this user cost? Well, you have to compensate capital for the risk it's bearing. That's why the expected return is R star. You have to compensate for depreciation. That's why you have to add delta. And you have to compensate for the capital loss because the capital is getting cheaper over time. So that's why you have the GQ over there. And the rental rate has to compensate exactly for that. That's the logic of this expression. And importantly, R star is not the risk-free rate. So a lot of implementations of the whole Jorgensen formula plug in for this R star the risk-free rate. For example, an important paper in this market power literature is the paper by Barkai. And he estimates a markup with the user cost approach, very much like this one. And he plugs in the risk-free rate for R star. And as you've seen, the risk-free rate is plunging over this time period. And so you're going to be led to the conclusion that the user cost of capital is going way down. OK? And because of that, you're going to be led to the conclusion that the profit share is exploding. And if the profit share is exploding, that means that the markup is exploding. And they're going to find very high estimates of the increase in the markup over this time period. And if you have an increase in R star, an increase in risk, that's going to mitigate this increase in markup. So that's going to be one of the important conclusions that's going to be coming out of the model. Continuing with the big ratios, you see the capital output ratio here. So we have to multiply capital by its price to divide it by output. So Qt is the relative price of capital as a function of output. So this ratio is unit less. And you see the expression for this ratio. And it's very intuitive. So if the technological capital share of capital alpha, the elasticity of the production function to capital is higher, you're going to have more capital. If the market power parameter, if markups are higher, you're going to get less capital. Why? Because if you want to exercise market power, if market power is being exercised at the economy level, output is being restricted. So there's not that much need for investment and for capital. So that's why the mu is in the denominator. Similarly, if capital is very risky and leading to a very high R star, then that's going to deter investment. We can compute another sort of big ratio which is relatively new. It's not in the standard macro or growth literature. But it was one of the motivating style aspects that I've gave you, this spread between the marginal product of capital that seems to be relatively constant over the sample and the declining risk-free rate. So NPK is this return to capital. And it's the profit rate divided by the value of capital. And we're taking the spread between that and the risk-free rate. And you see, there are three things that could be explaining this spread as a matter of accounting. The first one is depreciation. So if you invest in the risk-free rate, your capital doesn't really appreciate. If you invest in capital, it does. So you're going to require a higher marginal product to compensate for that. That's the first term. So it could be, for example, that there's some action in the depreciation rate or in the investment bias technical change over the sample that would explain the behavior of this spread. The second component is rents. So there are markups in this economy. There are pure profits. These pure profits are there only if mu is greater than 1. And these profits are going to show up in this accounting measure of the marginal product of capital. So part of the gap that's developing between this measure of NPK and the risk-free rate could be pure profits, economic rents. And finally, the last part is the gap between the expected return on equity and the risk-free rate. So if the risk premium is rising, if the expected return on equity is relatively constant and the risk-free rate is falling, that's going to open up a gap again between the NPK, the measure of NPK, and the measure of the risk-free rate. So these are the three possible explanations at this stage for the increasing gap between NPK and RF. Depreciation slash investment-specific technical change, rents, and risk. And you see that because this gap is increasing over time, it has to be trans in these things. So it has to be that depreciation has increased over time, has to be that rents have increased over time, or it has to be that risk has increased over time. And to give you away a bit of the punchline, what we're going to find is that it's about 50-50 between rents and risk. And depreciation is going to play a relatively small role. The price-dividend ratio is another financial big ratio. And it's given by this garden growth formula. So GT is the growth rate of TFP. That's going to be the growth rate of dividends as well. And so the price-dividend ratio is going to be 1 over R star minus GT. And importantly, again, in this ratio, what we should plug in is the expected return on equity and not the risk-free rate. The risk-free rate has declined a lot. The price-dividend ratio has only increased slightly over the sample. If you plug in the decline in the risk-free rate that we've observed in the data, the price-dividend ratio, which is high, should be even higher. So the fact that it has increased only moderately is going to be an indication, according to our estimation, that R star, that the risk-free rate has increased. That R star has not declined as much as the risk-free rate. And finally, you can get the equity premium as the gap between the expected return on equity and the risk-free rate. And it's a function only of risk aversion, the parameter theta, and the amount of risk, which is governed by the shock, kT plus 1. You can also characterize the other big ratios. This is the investment to capital ratio. So investment to capital alpha and mu are not going to enter in there. And the reason that you just need, in steady state, you just need to replace the capital stock. And that's what this equation is saying. But the investment output ratio is going to depend on alpha, on mu, and on R star. So if alpha is higher, then you're going to get more investment. If mu is higher, more market power investment is going to be lower. And if R star is higher, if there's a lot of risk in the economy, then investment output is going to be relatively low. And finally, you get the shares of income. So the labor share is 1 minus alpha over mu. So what could be driving down the labor share is either a technical change away from labor and towards capital, or an increase in market power. The capital share is alpha over mu, and the profit share is mu minus 1 over mu. So when mu is equal to 1, no markups, the profit share is equal to 0 and recover the standard formulation. So let me try now to implement this accounting framework. What we're going to do is fit the model to these two subsamples and assume that we're in these risky steady states in these two subsamples. So it's obviously a bit of hand-waving there, because we're transitioning from one risky steady state to another risky steady state with different parameters. So there's got to be some transitional dynamics. And we're not going to take care of this transitional dynamics in the baseline. So what we do in the paper is we have an extension where we incorporate the transitional dynamics and we show that it doesn't make a big difference. The drawback is obviously that we're doing some violence to the mapping between the model and the data. The advantage is the transparency of the exercise. So you're going to see exactly how things are identified. Another thing that's a bit tricky if you want to really sort of match the model dynamically is that you have to take a stand on expectations. So you have this trend that you see in the data with the benefit of hindsight. What you don't know is what's in the agent's minds when they form their expectations in real time. And that turns out to be pretty important. So if you do something that's very forward-looking with a lot of foresight, the transition looks a bit crazy. But if you assume that there's a lot of uncertainty or some myopia, then it behaves a lot better and you get results that are very consistent with what I'm going to show you. So here are the nine parameters that we have to estimate and the model is exactly identified. So we're going to introduce exactly nine targets for these nine parameters. So let me talk you through them and through what I'm going to interpret them to represent. So beta is the discount factor and I'm going to take that to be a saving supply. So if the representative agent gets more patient, that means that the desire for savings increases. We're going to have... The risk is going to take this disaster form. So you either have no something completely deterministic or with some probability you have a very bad shock, a disaster, or you have a very good shock, a bonanza. Okay? And I'm going to take a stand on the severity of the disaster. I'll show you that later, which is in line with what Barrow has done and estimate this P, the probability of a disaster. But really for a lot of the estimation, the only thing that we're going to need is the amount of risk and not the specific form that we're imposing. Mu is market, it's market power. You have Tiff P growth, population growth. Alpha is the technical share of capital and if alpha changes, we're going to interpret that as a factor of bias technical change. So the identification is almost recursive. There are things that are completely direct. So the rate of population growth, of investment prices of Tiff P, employing to population ratio, that you read directly from the data from matching the corresponding B ratios. You can infer a delta from the investment to capital equation. You can infer our star from the price dividend ratio using the garden growth formula. You can, given these quantities, you can infer alpha and mu by observing the labor share and the measure of marginal product of capital. So you see how mu is determined, for example. It's a function of the gap between the MPK and the user cost and of the difference between one and the labor share. And you see how the technological parameter is estimated. From that, you can infer what the ERP is. And for some of the other moments like beta, for example, or P, then we need to put a little more structure on the model. And so we're gonna put this structure and that's gonna be irrelevant for the identification of alpha, the technological parameter, and mu, the markup. It's gonna be relevant only to estimate things like beta and P. So these are assumptions that we're going to make. The risk is gonna take this disaster form. So with probability one minus two P, nothing happens. With probability P, you have a bonanza. With probability P, you have a disaster. And the expectation of the shock is equal to one. These are the preference parameters that I'm picking. It's relatively standard for a macrofinance calibration. Risk aversion is relatively high. We have to match a high risk premium. So it's 12, but it's not crazy. And the IS is equal to two. And the shock size is equal to 15%. So from that, we're gonna recover beta, P, and VH. So here are the estimated parameters. And you see their value in the two different samples and then the difference. So the discount factor beta, that's the saving supply. So you see that it has increased a little bit. So there's some room for an increase in general saving supply over the sample. The markup, according to our estimates, has increased from something like 8% to something like 15%. So it's an increase of roughly 7%. It's a big increase in the markup. It's much smaller than some of the estimates of the increase in the markups that you might have seen in the literature and that don't take into account this finance perspective, this the possibility of a rising risk premium. So the barca estimates, for example, increase a lot more than this estimate. You see that the disaster probability, the amount of risk in the model increases from 3% to 6%. So there's going to be an increase in risk premium and that's what's going to be tempering the rise in the markup. The Cobb-Douglas parameter is relatively stable. And you'll see that's going to be one big difference with the macro-macro calibration where it's going to be moving in weird ways. If you try to decompose the spread between the marginal product and capital and RF, the spread has increased from 11% to 15%. That's a change of 4%. And it's accounted 50-50 by rents by an amount something like 2% and by the risk premium, something like 2%. So the reason this gap between the MPK and the risk-free rate is opening is because there's more risk and because there are more rents. And it's about 50-50 between these two explanations and depreciation plays a minor role. You can look at the income distribution. So this is the labor share. You see that it's declined. The true capital share, the rental share, the technological capital share declined also and the profit share has increased. You can also do rolling window estimation. So these are 10-year rolling windows. And what you see, for example, here is the total spread between MPK and RF. It's increased from eight to something like 16. And you see that it's driven by the green and the red. So the green is the increase in rents in market power and the red is the increase in risk. So this explanation, the rolling window gives a little more role to rents compared to risk. This is the income distribution as a rolling window. So the red line is the true capital share. The green line is the profit share. And you see that it's increasing from something like 15 to something like 15. And the blue line is the capital share that you would plug in a solar residual. So that's the true capital share that we're not measuring plus the profit share, whatever is not going to labor. And that's increased from 30 to 35% because the increase in rents is bigger than the decrease in the true capital share. This is the composition of expected returns. The red line is the expected return on equity. You see that it's relatively stable. The green line is the decline in the risk-free rate. And the blue line is the gap between the two. And you see that we're documenting, according to this estimation, an increase in the expected reap premium from something like 4% to something like 5.5% over the sample. We can also use the model not just to do estimation and accounting, but counterfactuals. So for example, you can do a counterfactual. So we're doing a counterfactual. It's a nonlinear model. So we're doing them one by one. Okay, what's the contribution of each parameter if you keep all the other parameters constant? So the variable that we're trying to decompose is like output or investment, the equity premium, et cetera. And we're looking at the contribution of beta of mu of p. So you see that for output, the increase in saving supply is increasing potential output, but the increase in market power is decreasing potential output and the increase in risk is also decreasing potential output. And overall, potential output is down because of these evolutions by something like 0.3%. Investment is down quite a bit by 5%. And again, you have these countervailing effects. The increase in saving supply is pushing investment up. It would have been 17% higher, but because of the increase in market power and the increase in risk, investment is actually down. And the contribution is about 50-50 between market power and risk. The equity premium is higher and is explained entirely by the increase in risk. The risk-free rate is lower and that's explained about 50-50 by the increase in saving supply and 50-50 by the increase in risk. Okay, so there's more risk in the economy. People are, there's some precautionary savings and that drives down the interest rates. It's an important factor, almost 50% of the decline in the risk-free rate. Finally, for the price dividend ratio, you see that if you only had the increase in beta, the price dividend ratio should have increased by 31% in fact, it increased only by 7%, by seven points. And so everything is explained by the increase in risk and by some of the other factors. You can add intangibles by assuming that we're mismeasuring the amount of capital. So the idea is that there are some investment that we're not capitalizing. We're treating them as intermediate expenditure. Really they're building some kind of capital stock. So we're underestimating investment, underestimating the capital stock. And if you do that, then you overestimate the marginal product of capital. Okay, because the profit rate is accurately measured. You see that in the data, but the capital stock is too low compared to what it really is. So that means that in the spread between MPK and RF, you're gonna have now something that's gonna be mismeasurement of intangibles. And if that mismeasurement is rising over the sample, then that's going to account for some of the increase in the spread. But even if we make a relatively, a rather extreme assumption, it's not gonna change that much to the estimation. Okay, there's just, I mean, even if you assume that the mismeasurement increase from 10% to 20% of capital, okay, which is very large. The share of IPP in investment is about 6%. So that's a very large increase in intangible that makes a minor difference to the estimation. And interestingly, the part that's being reduced in the contribution of the spread between MPK and RF is the rents part, is not the risk premium part. So if you do a comparison with a macro estimation, so macro estimation discards risk in the model and discards the price dividend ratio. That's the way you do typically RBC or New Keynesian models. You say, well, we don't know the equity premium, it's too complicated, we don't know how to explain it and things like that. So you discard these financial moments and you estimate the model without the price dividend ratio and without the risk. So a macro calibration. So what you have is a much bigger increase in beta. It would be 2.8%. We only have 1.2%. The increase in market power is gigantic. Okay, it goes from 16% to 33%. So it's a 17% increase in the market. This is colossal. Okay, much bigger than the 7% that we find. Because this increase in the market that you need to explain the gap between MPK and RF is so big because you give no room for risk. So the market is increasing a lot. That means the labor share is gonna go down like crazy. But of course the labor share declined, but not that much. So you actually need to have technical change that's biased towards labor to sort of stabilize the labor share. So you see that the alpha coefficient, the share that goes to capital, declines from 18% to 12%. It's a 6% decline, it's very large. So if you do this macro calibration, you're led to the conclusion that we've seen labor bias technical change in massive proportions over the last 20 years, which I think will strike you as very counterintuitive. This is comparing as a rolling window on a very long sample from the 1950s onwards the macro estimation, which is the solid line and the macro finance estimation, which is the other line. So I'm showing you two parameters, beta and mu. You can focus on the second one, mu, market power. You see that if you do the macro estimation, you see this huge increase in markups from the 1980s to the present, but it's the trough of the 1980s. There's also a big decline in the markup from the 1950s onwards. So huge swings in market power. The macro finance estimation produces much more stable estimates of the markup. And the reason for that of course is that risk is moving around and is picking up some of the slack. I don't have time for the related evidence on risk premium, but if you try to estimate the equity risk premium with all the available methods that are out there, and I really mean all the available methods, what you find is an increase in the risk premium. You should put very large standards around these estimates. It's very hard to estimate the risk premium in real time, but this is what you find with all these methods and it's roughly in line with what we get. You can look at risk in other places. In particular, you can look at risk in the bond market. So here this is the Gilchrist and Darsec spread, for example. You see that it's increased a bit. The BA spread, the AAA spread have increased a bit. VIX is the one that doesn't work so well. A realizable has increased quite a bit. So the evidence for increasing risk premium in equities comes out more strongly. It comes out a bit in the corporate bond market. The VIX is a bit the thing that looks odd. So let me conclude. This was an accounting exercise disciplined by a standard neoclassical framework. The key was to study all these macro finance trends jointly. You cannot estimate them separately because an explanation that you're proposing for one fact has ripple effects for the other fact. The substantive conclusion that we reach is that there's an increase in macro risk, a secular increase in macro risk over the sample, that plays a role that's as important as market power. So we're not saying that there's no increase in market power, we're saying that the increase in market power is much more limited than what you've seen in some other papers. And we could also extend this framework to incorporate other explanations like an open economy and other targets and things of that sort. Thank you, Manuel. One of the papers claiming its market power will be presented tomorrow morning. So this paper will be discussed by Jalma Ventura. Very good. Okay, first of all, let me thank the organizers for inviting me here and to discuss precisely this very interesting paper. This is a paper that wants to cover a lot. It's a paper that it's very ambitious. And it's a paper that it's actually quite interesting and provocative in the results it has. The way I'm going to discuss it is I'm going to go through the paper a little bit as I read it and give you some of the comments that came to mind as I went along, okay? Let me be precise first on what the paper does. It gets a little bit caught, but it's okay. So basically the first thing that you see from the paper is that what Emmanuel and Francois do is basically to take a standard Ramsey model, like we study in textbooks like the first class in your banks macro or graduate macro class and you add two elements to it. The first is abstinence in preferences. That plays no real role other than giving you the ability to break the two coefficients of inter-temporal elasticity of substitution and the coefficient of risk aversion. And the second one is to add monopolistic competition which is to give some market power and have a role for this market power. Everything else, the model works exactly like the standard Ramsey model. That was one of the first surprises I got because when I was thinking about macro and finance there's been a lot of research in macro and finance understanding how important is finance for macro and so on but there were no financial frictions whatsoever in the model. So that was in a sense a bit of a surprise for me. I was expecting how introducing some frictions in financial markets would help us understand some of the issues or so on and so forth. That's not the case. We can go back to a standard macro without these frictions and perhaps the models have a lot to tell us just as long as we do take the possibility of risking into account. And that's what comes from the next assumption. The next assumption says we add a shock that keeps the economy in the steady state but it creates risk and they do that in a very clever way. They have a shock that when happens it changes both the capital stock and the effective labor supply in exactly the same way so that it doesn't affect the capital labor ratio. And as a result it does affect however the risk on your consumption because when it's a negative your consumption declines you can work less your capital is worthless when it is positive the consumption increases and that risk in your consumption ends up being affecting all the prices in the economy in a very simple way. I think this is an interesting aspect of the model. Then what they do is to take that model and calibrate it twice. The first time they took at the average of a series of variables the most important ones are the ones that I put in the slide the gross profitability, gross capital share, investment capital ratio, the risk-free rate, the price dividend ratio and they look at the averages for 1984-2000 and they calibrate the model, they use particular there are nine but in the matter of fact with these five is enough and five variables okay or nine and nine variables depending on how you look at it and that gives you exact identification for that period and then you take at the averages of these variables for the period 2001 and 2016 and you get different values of the parameters you compare them and somehow you attribute to the different changes in the parameters the importance on the difference on the values of these variables. One of the, when you do that basically what you are comparing these calibrations you get some output which is like this this probably is gonna be hard to read it's taken exactly from the paper but this is the bottom line it's just to give you a little bit what this is going after. So here for example, this is not working there is no, the pointer works? No, you don't see it, no? No, okay well you see on the vertical side you see gross profitability, measure capital share risk free rate that's what we are trying to match. You see on the top the different parameters beta is a discount rate or what is called a supply of savings mu is the market power or the markup P is this probability of disaster delta is the depreciation rate alpha is the coefficient in the production function GN, GZ and GQ are different growth rates growth rates of the labor force of productivity, total factor productivity GQ is the growth rate of the price of investment so the relative price of investment and consumption goods and N bar is the share of the whole population that is working, okay? So these variables on the top are the parameters that we are calibrating and we calibrate using data for the variables that are on the column and what you see is a target change over the two periods and that's the difference and then these numbers there in this matrix tell us how much of the change of that particular variable is due to the change of a particular parameter so for example you see gross profitability on top was 14.101 in 1984 2000 then it increased to 14.89 and of that increase you can see that better actually doesn't explain much it explains actually the opposite and it has to be made up by market power by P which is the risk probability and alpha delta a little bit alpha doesn't play a role and so on and so forth all the variables, you see? So that is kind of a distribution of who is guilty for that particular change, okay? And that's the output of this at the end of the day you say there were all these changes there were these changes in the parameters these were the shocks, the one on the top and each of them is guilty and then the whole paper goes into the narrative of describing these numbers what do they tell us and in particular these numbers tend to tell that P plays an important role P plays an important role and P is risk okay the probability of a disaster happening. Let me tell you a little bit about the questions about how to use that the paper is very well written you can see that also from the presentation which was very clear on all the results and I want to talk a little bit about the kitchen how this is cooked The first thing that I have as a question to Emmanuel and Francois is how did they choose the time periods? Why did they choose 84 to 2000 and 2001 to 2016? Obviously it seems that it breaks the sample exactly in the middle and that could be one of the things but if there are a bunch of shocks that make the economy change you would like to break it at the time where the shocks happen basically this is more like trends than like shocks and if you go a little bit I don't know why this is not okay now so for example for some of the variables when you look at the long-term real interest rate these are the two periods obviously it seems like a smooth change rather than a big break for some others like the gross profitability I'm not so sure there's a big change or not the price dividend ratio that definitely seems a little bit arbitrary to make it in the middle of the at the moment with the dot-com bubble basically burst and then the investment GDP ratio you also don't see a huge change I would like to ask whether the results are sensitive to other breakpoints they do something later on in the paper which is to look at the long time series of 50 since 1950 and look at rolling windows of 11 years and some of the results are similar although the paper in the version I got didn't comment too much about the similarities of this long sample and the one that you do here it would be interesting to see whether you break it a little bit later around the crisis or a little bit earlier before the bubble whether the results would be very similar or very different I don't know since there was a little bit of change in financial markets during these periods I would like to understand a little bit more that then there is another comment I would like to do in order to produce this table to compute the numbers on the right basically they do quite a complicated procedure in which basically these are averages of contributions of many possible changes but let me be clear today nine variables change and I want to decompose what is the contribution of each of the variables of course I could do something assume eight change and one didn't and then that would be the difference that I observed between that exercise and the exercise in which the nine change could be the contribution of the other variable but I could say non changes and one changes but I could say three change five don't change and one what difference does it make well these results are the average of all possible combinations and I don't know how to interpret that very well and I would like perhaps a little bit of help in interpreting that probably sticking to the usual one of saying all change except for one might be a little bit better and probably I wouldn't be surprised if the results are similar but I think it would be a little bit better for interpretation the main comment I want to do is about the identification strategy and the central role that the Gordon formula plays in this identification strategy basically when you go and you calibrate the model the first thing that you do is to obtain growth rates of population TFP price of investment goods and ratio of labor of two population from data that's why they say that in fact you are only measuring five variables what so ever and then you take one formula which is the Gordon formula there the price dividend ratio is one over R star minus GT GT is a combination of the growth of productivity and population okay and you say and you estimate R star from this formula and this R star is going to be the key piece that will help you get all the ratios right or wrong and all the other variables and once you have the R star then you can calculate the risk premium and given the particular formula that they have on the risk premium that gives you the P the risk premium depends on risk tolerance to risk depends on the magnitude of the disaster these are fixed and what we get is the probability of the disaster the same R star gives you the time preference row plus some risk adjusted growth measure given by the model one over the inter temporal elasticity situation the second term is all given and Roy's estimated based on R star and some numbers on this so the savings shock the row is obtained from R star the same from the market power the marginal product of capital is obtained as the average product of capital in the economy which is a reasonable thing the depreciation some labor share I less but you get R star there so basically all the numbers that the paper obtains are based on this Gordon formula to really trust the Gordon formula has it done very well over this period I want to conclude just by telling you that the time I use that forward on formula it did very poorly actually I it was I tried to use some net present value formula to calculate the value of assets in the U.S. together with Vasco Carvalho at at Cambridge and with Alberto Martin sitting here and we went and we took the value of assets of the United States from 1950 to 2008 and we used the formula to calculate the net present value that we took from Schiller which is standard which looks like the has a special case the Gordon formula so basically we computed estimated the cash flows we computed expected returns out of sample assumptions and so on and we found that the formula does extremely bad exactly in the period that we are analyzing and I am wondering are you so confident about the Gordon formula even in its most simpler form which is a fixed price to dividend ratio and some productivity growth taken from national accounts and total factor productivity for bizarre I would somehow try to think about what happens if there is a bubble you have written on bubbles and you have argued in some of your papers that they have been an important element perhaps it would be interesting to introduce some bubble component and see how as you change the bubble component some of your results can change and you can use some of the some of the estimates of these bubble components as a as a residual from these calculations of the Gordon formula to see whether the things change a little bit overall nevertheless as I tell you we all can pick on one particular thing this is trying to put lots of facts together I just happen to think that the Gordon formula is not going to work for assets and there are various papers that show that this is my main comment thank you okay thank you gentlemen we have six minutes for Q&A so floor is open for questions for Emmanuel Frank? Just two short questions about some of the sources of what's behind the main changes which I understood is beta on the one hand or at least if I think about the fall in the equilibrium we were interested in beta and the probability of of a disaster the beta should I I mean so if you look at the literature on what can it explain over time and across countries real rates demographics and population aging in particular is probably one of the more robust variables so my question is that what you think is the main factor behind that and what does that then imply for how these things will evolve in the future and have you done extension with an OLG type of model where you could capture this more directly and on the disaster probability I mean another fact or trend I think which is still there is the sort of the great moderation now that has been sort of an interruption but at least the Rogoff in the recent sort of paper claims that actually when you look through that it's still it's still there that kind of contrasts a little bit with sort of the idea that risk has actually increased now of course these are different types of risks so I was just wondering whether you've thought about about about that all right Amanda you want to respond yes well thanks a lot Jaume and thanks Frank for the question and I'll start with Frank and finish with Jaume so in the model you the decline in the risk rate as you correctly noted is explained by roughly 50-50 by two forces the increase in beta and the increase in P so beta is the patient's parameter the representation is more patient and P is the disaster probability it's the amount of risk so obviously the and and this links to a comment that Jaume made it's a model that's extremely simple there's a representative agent which like aggregates all the sorts of imperfections that we might think are in there like financial frictions and things of that sort and so for example risk aversion could be increasing over time and that could also be driving the increase in the equity risk premium and this increase in risk aversion could come at some times because the financial sector is stressed we're comfortable with that interpretation even if the model doesn't have that level of detail for beta I think demographics is precisely the sort of things that we think that beta is capturing but again it's a bit of a reduced form at this stage because we have observed this sort of an evasion so if we we thought about extending the model uh... to uh... incorporate these particular details and to do uh... an olg model uh... you know where you have a rich uh... life cycle component where you can really think about life cycle savings and uh... their implications for aging we didn't do it because partly it's quite complicated partly because i think there's a lot that we felt we don't know uh... about how to discipline that model for example uh... we don't know enough i think about how uh... retired people versus active people invest their portfolios so it could be for example that when you retired you're more conservative in the way you invest your portfolio okay and so that would tend to make so aging in that case would not only make people more patient but it will also make them more risk averse on average so it could be that uh... demographics is behind the increase in p the in beta and the increasing in p so i think it would be very interesting to open up that that black box but i think we'd also need to not just like ramp up the modeling but bring in more more data that we we weren't exactly sure uh... where to get that thing that would be a very interesting extension for the increasing p and like the the the great moderation well as you as you noted in your question the risk in our mall takes a different form it's this disastrous that sort of looming over the economy and affecting asset prices and investments and things like that but you wouldn't see it in day-to-day volatility or year-to-year volatility so on the face of it is consistent with the great moderation i think like the this clash is also a bit what we're picking up when we're looking at the vixx uh... you see that the vixx is not increasing that much uh... between the two samples and the vixx i think is picking up more of the great moderation sort of thing than the the disastrous that we're thinking so i think the class that you that you saw is also showing up in these some of these alternative measures that we're looking at uh... so i think you have to be open to the possibility that there are other sources of risk than just a year-to-year uh... volatility uh... in uh... in output let me move to uh... to to jump in so uh... your first comment was about the the level of uh... stylization in the model are the lack of texture and it's true that we don't have financial frictions for example it's not because we believe that financial frictions are not important obviously they are we just wanted to write something that was very simple and then interpret some of the parameters is a bit reduced forms stand-in for other stories that you could be uh... you can be telling so i think it's the style of of the paper and there are pros and cons if you bring in more texture then you have to discipline more details of the model that you're not sure about it's a world of trade-offs uh... basically for uh... you had another comment which was about the time period and uh... and the fact that we're splitting the sample into so there was a bit of a disagreement between the two co-authors there uh... i thought that to capture these trends would be better to do to put more emphasis on the rolling windows and for us was more attached to to the split the reason we put the split there is first because it's in the middle of the sample so it's relatively neutral and i think like based on some uh... other narrative evidence we think that there's kind of a bit of a structural break that happens there so if you look at the price dividend ratio for example i mean that sort of neutralizes the nasdaq bubble you know uh... it's uh... it's imperfect and i think it would be a good idea to explore the sensitivity to to different breaking points or to comment more on whether the rolling window estimates are consistent with uh... the break in the middle uh... for these tables that try to decompose the effects of the different variables so these are really to be interpreted as counterfactuals of course it's a non-linear model so to assess what's the contribution of one particular explanation uh... is difficult uh... in a linear model you know you have five things that are moving and if you sum these five things that adds up to the whole effect in the non-linear model it doesn't work like that and there's some arbitrariness as to how you do this decomposition so we decided to do in this particular way but i guess probably we could document some robustness with respect to that and in particular show the particular specification that you had in mind and finally for identification so uh... a quick comment on this the first thing is uh... the uh... the garden growth formula per se so we rely on this for the estimation that's absolutely correct uh... then we do this robustness in the conclusion where we look at different ways actually all the possible different ways that you could estimate the aqueous premium so there's a large literature on this uh... there are different methods so there are these time series methods they're based on some elaborations basically of the garden growth formula where kembel and shiller are doing basically you try to forecast dividend growth and and then you back out uh... the expected return and and the risk premium from there so all of these methods document and increase in the risk premium that's in the ballpark uh... of of what we have you also have cross-sectional methods so cross-sectional methods they look at stocks that have a higher beta than others so risk your stocks and then they try to look at the different in realized returns between uh... between stocks of uh... of different categories or price-division ratios of stocks of different categories so it's not estimated of the time series but of the cross section and these methods also find an increase in risk premium of course like you can quibble with uh... the fact that the capem is not fantastic model that's different debate the bubble uh... one of the things i think our break in two thousand is doing is to neutralize a bit this ramp up in the price dividend ratio and the collapse so there's one big event in valuations which is basically the end of the nineties and then the price of an racial increases spikes and then crashes and one way you might want to go about modeling that is deviated from the sort of models that i've been writing and uh... that we've been writing here and to incorporate let's say a bubble for example and the only thing i can say is that by sort of putting this split in the in the middle or by doing these long rolling windows we're trying to like smooth that out basically so in essence i think we were trying to do is to look at longer trends uh... in valuations and maybe smooth out some of the bubbles that maybe appear at shorter horizons but uh... that's the that's the way i think about it anyways thanks a lot thanks Emmanuel so here the ECB we actually present both the R-star from the textbook and the R-star in your model to the governing council and so also with a variety of methods we see that equity cost in the euro area has remained stubbornly high and so does this watch that the risk premium has increased over the past 10-20 years so very consistent with the evidence you have for the U.S. okay so it's time for coffee and we can double up on coffee we have half an hour break and uh... see you back at about quarter to twelve