 Okay, I guess that we can restart. I see that many came back into the window. So let me welcome Emina Camura, our second keynote speaker. It's a short introduction of Emmy. She's a Chancellor's Professor of Economics at the University of California, Berkeley. She's a botan research associate and co-director of the Monetary Economics Program of the MBA and co-editor of the American Economic Review. We all know Emmy's work. She's a hugely influential in macroeconomics. And for that, she also received the many awards. For example, the John Bates Clark Medal for her influence on economic thought. I'm not gonna summarize here the contribution of Emmy. I guess that the best is actually to leave the floor to her for her presentation. Let me just say that the title of the presentation is the slope of the Phillips curve. Evidence from the U.S. States. And this is joint work with Jonathan Nazzel, Juan Ereño, and John Stainson. Emmy, the floor is yours. You have 35 minutes. In the meanwhile, people will post a question in the chat and I will read them at the end of your presentation for the QA session. Please proceed. Thank you very much. Thank you very much for that gracious introduction. And it's great to be here. If only virtually, it's really nice to see these kinds of events continuing and in fact, increasing as we're all sort of recovering from the COVID crisis. So let me share my screen. So this presentation is joint, is it's based on joint work with Joe Hazel, Juan Ereño, and John Stainson. So Joe and Juan were two of our former graduate students now at LSE and UCSD respectively. And if you haven't met them yet, I would certainly recommend doing that. Let me also say that I know that everybody in this audience is extremely knowledgeable about the topics that I'm talking about. So I very much encourage your questions and comments. So the topic of this paper is the soap of the Phillips Curve, something that as I said, I know that so many of you are intensely knowledgeable about. So let me move fairly briefly through this introductory portion. So there are many formulations of the Phillips Curve, but here's one formulation. This is the New Kinsley Phillips Curve. On the left-hand side, we have inflation as a function of expected future inflation and then the gap between unemployment and the natural rate. So this is reflecting some kind of measure of the output gap of demand shocks. And then finally, there's this new term, which reflects cost per shocks. So this is talking about these various drivers of inflation that are sort of central in the literature, the role of expectations, the role of demand shocks, and finally the role of cost per shocks. Now this presentation is going to be trying to think about this object cap up, the slope of the Phillips Curve, which is the response of inflation to demand shocks. So loosely speaking, how much does an increase in aggregate demand affect inflation? I think that the episode that has probably affected most American economists' views about the slope of the Phillips Curve the most is the Volcker Disinflation. So during the early 1980s, Paul Volcker dramatically raised interest rates. This was associated with a big recession. Unemployment rose dramatically and inflation fell dramatically. And so many people have interpreted this as pretty strong evidence of a steep Phillips Curve. And this is the way that this is often taught in intermediate macroeconomics classes. But relative to at least this interpretation of the Volcker Disinflation, the period since the 1990s has looked sort of like a sequence of puzzles in the sense that we've appeared to see a much more muted response of inflation to unemployment. So for example, during the Great Recession, we saw an increase in the unemployment rate that was comparable to the magnitude of the increase in the unemployment rate that happened during the Volcker period. And yet inflation, while it fell, fell by much less. Similarly, you could say that there was a missing reinflation in the aftermath of the Great Recession as the economy recovered. Unemployment fell very dramatically. But at the same time, we did not see a huge increase in inflation. We know not to say that inflation didn't show any cyclicality. Inflation certainly did fall a little bit during the Great Recession and rose a little bit in the recovery, but it wasn't on the same order of magnitude as the changes in inflation that we saw around the Volcker Disinflation. I should also apologize sort of at the outset. I'm speaking very much about the US experience. And I know that at this conference, I have many people in the audience from Europe, but I do think that while I'm speaking specifically about things that have happened in the United States, the reality is as many of you know that other countries, many other countries around the world have had similar experiences to the Volcker Disinflation. And I sort of encourage questions and discussions about how those experiences have played out in other countries in the Q&A period. So this fact that there seems to be this contrast between less response of inflation to unemployment in the last two decades relative to earlier is something that has led to a pretty widespread discussion of the Phillips Curve in macroeconomics. The question has been asked many times whether the Phillips Curve is getting flatter, whether it might be hibernating, whether it might just be completely dead. And this observation has led to broader concerns about the Phillips Curve as an analytical tool, whether perhaps this change in the slope of the Phillips Curve might reflect some kind of an important flaw in the New Keynesian model. So while this idea of the Phillips Curve flattening, I think is one of the main narratives that we have to talk about the changes that have occurred since 1999 or so in the US economy and also in various other economies, there is an alternative explanation one could think about for this set of facts. And this explanation has been emphasized in particular by Bernanke and Mishkin and by various others under the heading of the anchored expectations hypothesis. So this is the idea that when Volcker came into office, it wasn't just that he raised interest rates and that this may have led to a decline in inflation through the Phillips Curve, but it's also clear that there was fundamental regime change that occurred at the Federal Reserve and that this regime change may have affected the people's long-term expectations about inflation. And then in fact, these changes in people's long-term inflation expectations may have played a crucial role in why inflation fell so much during the Volcker disinflation. So from this perspective, this offers perhaps an interpretation of why the more recent period would look so different because while there was clearly an important regime change that occurred around 1980 when Volcker came into office, things have been very different since the late 1990s when long-run inflation expectations have been incredibly well anchored. And this is of course also exactly the time period in which it's looked like inflation is so much less responsive to changes in unemployment. So just to give you some sense of what these facts look like for the United States, here's a graph showing long-run inflation expectations from the survey of professional forecasters. That's the gray line and core CPI inflation. That's the black line. And you can see that while these moved almost one for one for many periods during the 1980s and early 1990s, by the late 1990s, long-run inflation expectations had actually stabilized. And interestingly, these kinds of facts actually look quite similar both for professional forecasts and for consumer forecasts of longer-run inflation. So this is sort of some suggested evidence that perhaps there is an alternative explanation aside from a massive flattening of Phillips Curve for why it might be that inflation appears so much less responsive in the recent period. Now, why is it hard to tell apart these different explanations? A massive flattening of Phillips Curve versus this anchored expectations hypothesis that there's this other factor that may also be important and which is ultimately around in the form of long-run inflation expectations. Well, a crucial reason and something that I'm sure those of you who've worked on trying to estimate the Phillips Curve are intensely aware of is that this equation has a lot of endogenous variables in it and they're co-moving and it makes it really difficult to tell the difference between these different hypotheses. So one thing that flows directly from my sort of story about the 1980s and the United States is that this was a period in which long-run inflation expectations were co-bearing pretty strongly with unemployment and that makes it very hard to tell the difference between a very steep Phillips Curve and a big decline in long-run inflation expectations because both things were happening at the same time. And this is natural in a situation where you have a regime change but it's imperfectly credible. So as a consequence, the regime changes associated with an increase in unemployment. Now, this is certainly something where a lot of work has tried to in various ways control for the effects of inflation expectations but it's very challenging for econometric reasons. And so this issue of how do you tell the difference between the role of inflation expectations and the slope of the Phillips Curve in situations where the two things unemployment, the unemployment gap and long-run inflation expectations may be correlated is one of the challenges, the very important challenges that researchers face when trying to estimate the slope of the Phillips Curve. A second issue is sort of a classic problem that one always encounters in trying to estimate the slope of one equation when the data that you're seeing are coming from a system of equations. So the most familiar example of this is sort of the econ one-on-one example of demand and supply curves. If you're seeing prices and quantities and they come from some market, then it's going to be hard to tell whether you're tracing out the demand curve, you're tracing out the supply curve or you're looking at some kind of mishmash of both. And that challenge also arises in the context of Phillips Curve estimation. So while I've been emphasizing the idea that we would like to estimate the slope of the Phillips Curve, so that's the coefficient on this demand shock term, there can also be supply shocks which shift around the Phillips Curve. And that clearly complicates the estimation of the slope of the Phillips Curve. And in fact, some of the recent research in this area, so both paper by Fitzgerald and Michelini and a more recent paper by McLean and Tenreiro have emphasized that at least in simple models, this problem can sort of be arbitrarily bad in the sense that in simple models, monetary policy has the ability to completely offset all demand shocks. And in that simple world, the only variation that's left in inflation is variation associated with supply shocks. So that's exactly the wrong kind of variation for estimating the slope of the Phillips Curve. So potentially this kind of endogeneity problem can be arbitrarily bad. So these are some really important empirical challenges and I think this speaks to why it is that even with a long and venerable history, we're still struggling with trying to really understand the empirical facts about the Phillips Curve. So in this context, the natural question to ask is whether it would be possible to expand the set of data that we can use to estimate the Phillips Curve because there's just so much going on in the aggregate data that it's hard to tell the difference between these different effects. So one way of expanding the scope of data that we can potentially use is to look at cross-sectional data. And a recent literature has indeed tried to do this. So going back to this paper by Fitzgerald and Michelini and then several other important papers that have followed up on that, a number of papers have tried to ask this question of whether we can get more out of the data by trying to use not just aggregate evidence on inflation and unemployment, but also evidence from smaller geographical units. And one of the things that some of these papers have emphasized is this idea that I just mentioned that potentially this could help with the endogenated unemployment rate, this issue of demand and supply shocks that I just mentioned. Because while it's true that in at least a very simple model, it's possible for monetary policy to completely offset all demand shocks, leaving only variation associated with supply shocks to estimate this of the field script, which again is exactly the wrong kind of variation. This would never be possible at the regional level. At the regional level, if you think about California and New York, since there's only one interest rate for the whole United States, you're never gonna be able to offset all demand shocks in both states at the same time. And there's gonna be some demand variation left over. So that offers the hope that you could at least do a little bit better in terms of identifying the reaction to demand shocks as opposed to supply shocks. So that's one potential advantage of trying to estimate these equations using regional data. We're gonna emphasize another advantage which has to do with expectations. So another advantage is that long run inflation expectations at least in times of big regime change like the period after the Volcker Disinflation are gonna tend to move together across different regions or different states, the United States. So this is true in the data, but it's also what you would think in a simple model. In a simple model, you're all in the same country, you're in a monetary union, and the central bank is setting long run inflation, the inflation target, not just for one state, but for the whole country. And so this is gonna mean that long run inflation expectations are common across different states within the union. And from an empirical standpoint, that has the advantage that we can sort of difference out the effect of these long run inflation expectations using time fixed events. So this is gonna be a sort of dip and dip approach to estimating the slope of the field script for those of you who are familiar with that, with that language, if you're not, I'll go through exactly what I mean. Now, there are some very important questions that arise when thinking about how to relate the slope of the regional Phillips curve to the slope of the aggregate Phillips curve, because it's really not obvious at all how they're related. And in fact, there's been a broader discussion in macroeconomics about when and to what extent we can use evidence from cross-sectional data to really answer the questions that we are interested in as macroeconomists. And again, I wanna emphasize this is often not obvious and perhaps particularly not obvious in the case of inflation because when we think about regional Phillips curves where we're talking about relative prices, whereas at the aggregate level, we might imagine that we're not talking about relative prices. So it's natural to kind of immediately wonder how these objects are really gonna be related, a regional Phillips curve and an aggregate Phillips curve. So that's gonna be another dimension on which we're gonna try to contribute by developing a sort of simple benchmark model in which you can see exactly what the relationship is between the slope of the regional Phillips curve and the slope of the region of the aggregate Phillips curve. And in fact, we're gonna show that the regional Phillips curve slope is gonna be very informative about the slope of the aggregate Phillips curve. Another thing we're gonna do is to try to develop some data to actually estimate regional Phillips curves for the United States. This is a little bit of an idiosyncrasy of the US statistical system that historically inflation indexes were not released by the Bureau of Labor Statistics at the state level. This has to do with concerns that they've had about sampling error and how users might interpret noisy series. But in any case, historically it wasn't possible to download these kinds of data series even though the underlying micro-data were actually there. And so we're gonna construct those series and our hope is that those data will be useful for projects beyond ours. But these might be issues that are less of a problem in some other countries where the data infrastructure is somewhat different. And then finally, this regional data is going to give us new possibilities for identification. So we're gonna construct a new instrument to try to focus on demand variation at the state level and estimate the slope of this regional Phillips curve. So just to preview the results, our main finding is that we're going to estimate a fairly modest slope of the Phillips curve even going back to the late 1970s, modest in the sense that if we plug this slope into, if we use this slope that we estimate for the 1970s and 1980s to sort of simulate inflation responses in the modern world to unemployment changes like the unemployment that occurred during the Great Recession, we're actually going to predict relatively small movements in inflation, sort of similar to what we saw in the actual data. So in that sense, these slopes are consistent with the fairly modest responsiveness of inflation to unemployment that we've seen in the recent period. So how is this consistent with what happened in the book for disinflation when we saw a huge response of inflation to increases in unemployment? The way it's consistent is because according to our estimates, the majority of the decline in inflation that occurred in that period was really a consequence of changes in long run inflation expectations. So this regime change idea. We do find some flattening of the Phillips curve, I should say between the early and the later parts of our sample, but it's not quantitatively important in explaining, I'm explaining basically the behavior of inflation because the slope is already quite small. So now let me talk a little bit more about what I mean when I talk about the effects of expectations on inflation versus the slope of the Phillips curve because I think this can be a little bit of a confusing statement given that these are all endogenous objects. Perhaps you're thinking, what do I really mean when I say that expectations might have a separate effect on inflation from a demand shock? Given that if there is a demand shock, then there's gonna be a fact on expectations. So these things are jointly determined. Can we really think of these as separate forces? And I think that's exactly a reasonable concern to have. And so let me do a little bit of an algebra that can allow us to come up with an equation where it's easier to see the separate and distinct role of these different forces. So in particular, I'm gonna do a little bit of algebra by just solving forward this first Eucanian Phillips curve equation is the same equation I showed you at the beginning with inflation on the left-hand side and then expect an inflation and unemployment minus the natural rate on the right-hand side. I can solve this forward by recursively substituting inflation into inflation expectations on the right-hand side. And then I get this equation which gives inflation as a discounted present value of future unemployment. So this is pretty intuitive. It's saying that inflation today isn't just determined by unemployment today, it's determined by people's views about unemployment going forward. But now I'm gonna do one more thing which is to decompose unemployment into two components, a long-run unemployment component and then a deviation from this long-run value, Utilda. So now, again, not doing anything complicated but just substituting in this decomposition into this discounted present value of future unemployment. I get two terms. One reflecting the discounted present value of single-clone employment and the other reflecting long-run unemployment. And then one last step is to use the fact that in the Eucanian Phillips curve there is a relationship between long-run unemployment and long-run inflation. If I substitute in that relationship then I get this equation at the bottom, which I think is pretty intuitive. So if you look at this equation, what it's saying is that inflation is gonna move one for one with beliefs about long-run inflation in the future. So think about this as the inflation target of the central bank. So this is sort of the lesson that you might have been taught in intermediate macro that if the central bank commits to a very different long-run inflation target that can have a big effect on current inflation. And in addition to this long-run inflation expectations term there's this discounted present value of cyclical unemployment. So this is the slope of the Phillips curve that I've been talking about all along. And it's a discounted present value of future cyclical unemployment because it doesn't just matter what unemployment is today it also matters what it's going to be say over the next few years. So one more thing I'm gonna do for expositional purposes. This is not something that we actually use in our analysis but it's sort of useful just to get intuition for these equations. So suppose that we were to assume that unemployment cyclical unemployment followed an air one process. Then we could solve out for this infinite sum using a standard formula for infinite sum to get this last equation. So this last equation really sort of looks similar to something you could estimate in the data on the left hand side you have inflation on the right hand side you have unemployment cyclical unemployment multiplied by this side term. And then you have these long-run inflation expectations on the right hand side as well. So a few things to say about this equation here. One comment as I kind of emphasized is that this long-run inflation target is a major determinant of current inflation and has a coefficient of one. So current inflation moves one for one with this long-run inflation target term. And this is true regardless of what the slope of the flow to current dates. So the slope of the bills can be very small and yet the response to this long-run inflation expectations term can be very high. And you can see how this can be a very fundamental empirical challenge because it means that potentially inflation can move in response to this long-run inflation expectations term even without any movement in the cyclical unemployment term. And so potentially if there is a correlation between the cyclical unemployment term and long-run inflation expectations that can pose a major empirical challenge and that's sort of what I'm arguing happened during the Great Recession. It was very hard to tell the difference between these two factors because it was both true that cyclical unemployment rose a lot and also true that the long-run inflation target fell considerably. So potentially this is a very important source of omitted variables bias. So now let me move on to a model where we can think about how this aggregate, this kind of aggregate Phillips curve formulation relates to what we might get using regional data and how to interpret these things from the structural standpoint. So the model is gonna be very standard, sort of the type of model that you've probably mostly seen many times before, except it's gonna have these multiple regions. So there'll be two regions. Each has a tradable and non-tradable sector. There's no labor mobility between regions but there's perfect labor mobility between sectors within each region. And then most importantly, there's a monetary union between which encompasses these two regions. So that's gonna be important because it means that for example, the inflation target will be common across the two regions. So various standard assumptions on the household and firm side, you know, there's CES demand on the household side, there's Calvo price setting with perhaps the one exception of GHH preferences on the household side. Now in all of this, we're sort of making some starkly simple assumptions. The logic for that is that I'm gonna show you a benchmark case in which the relationship between the aggregate and regional Phillips curve is gonna be particularly stark and simple. But of course, you know, I think it would be interesting to think about, you know, generalizing these assumptions in a long various dimensions. So what do you get out of this? So the aggregate Phillips curve, which is the second equation here, is the same as what I've been showing you all along. So this is just the New Keynesian Phillips curve. But we also can derive a regional Phillips curve for non-tradables. And that's gonna look very similar to the aggregate Phillips curve, except it's gonna have this additional term, which, you know, I can call a terms of trade term, has to do with relative prices between tradeables and non-tradables. And intuitively, this is gonna be a thing that's gonna bring you back to PPP in the long run. So it's actually not gonna be very important from an empirical standpoint. In practice, we're gonna estimate the coefficient on this term as being quite small. And that's related to the fact that we have a pretty flat Phillips curve that we're estimating. But it's gonna be quite important from a theoretical standpoint in terms of just thinking about how you get determinacy in this model. The other thing that I wanna highlight is that in this simple model, and again, you know, we have made a number of sort of stark simplifying assumptions, the slope, the coefficient on unemployment here is kappa in both cases. It's the same. So this is sort of the basis for the statement that at least in this simple model, you can learn a lot about the slope of the aggregate Phillips curve from looking at the slope of the regional Phillips curve. Now, notice that I'm talking about non-tradables here. That's something that comes out of the model, but it's also very intuitive. The intuition is that if you think about tradeables like think of gasoline, if you consider running a regional Phillips curve regression with time fixed effects, what's gonna happen? Well, if the gasoline prices are the same across all the regions, then the time fixed effect will absorb all variation in the gasoline prices. And the coefficient on local unemployment will be zero. And that would be true regardless of how responsive gasoline prices truly are to economic conditions. And you're just getting that zero on local unemployment because of the fact that gasoline is priced nationally as opposed to being priced locally. So that's the sense in which what you really can learn from these regional Phillips curves pertains to goods or services that are priced at the local level. So in most of what we do empirically, we're going to focus on services prices for this reason. Now I'm gonna do a similar sort of solving forward exercise to what I did for the aggregate data starting with this regional Phillips curve and then solving it forward exactly in the same way as I did with the aggregate data. And so just as before, I'm gonna end up with terms that are discounted present values of cyclical unemployment and a long run inflation expectations term. Empirically, this long run inflation expectations term is gonna be proxied for by time fixed effects in the data. Now, one more time, if we just for expositional purposes, suppose we were to assume that the cyclical unemployment process followed an error one, then we could solve out for this infinite sum using standard formulas and we would get this equation, which actually looks a lot like what people have estimated in the data in this regional Phillips curve literature. So this equation here has inflation on the left-hand side on the right-hand side, it has unemployment multiplied by side and then has the terms of trade terms that often hasn't been included as an empirically, it's not so important, but theoretically it's important to make the model sort of make sense. Then we have a time fixed effect and a supply shock term. Now the one thing I want to highlight here is that the coefficient on cyclical unemployment here is psi and not kappa. Psi and kappa are closely related. So here's the formula for psi in terms of kappa, but they're not the same. And the crucial difference between them is that psi is kappa adjusted for the persistence of the unemployment rate. So remember that this term here, it comes from kappa multiplied by discounted present sum of discounted present value of future unemployment rates. And so the issue is that the response to unemployment today in this kind of solve forward version of the Phillips curve, it's not just a response to current economic conditions. It's also a response to the fact that unemployment is a very persistent variable. So if unemployment is high today, you expect it to stay high, probably at least for a couple of years. And as a consequence, the coefficient on current unemployment is gonna be much higher than just kappa. It's gonna need to be kappa adjusted for the persistence of the unemployment rate. The reason I'm belaboring this point, which is sort of a point about arithmetic is that from an applied standpoint, many of the specifications people have estimated for regional Phillips curve really are estimates which pertain to psi and not kappa. So that is an issue in terms of relating the estimates from the regional Phillips curve literature to the estimates from the aggregate literature, which would focus more on kappa. And there's this sense that estimates for the regional Phillips curve literature tend to yield higher slope parameters than estimates from the aggregate Phillips curve literature. And our sense is that a considerable amount of this difference can be accounted for by this sort of mechanical issue that the regional Phillips curve literature tends to be estimated psi whereas the aggregate literature, both the theoretical literature and the empirical literature is often focusing on kappa. So it's a sort of a mechanical point but one that I think matters for the applied literature. So briefly, we construct these new state level inflation indexes for the period from 1978 to 2018 that we think have a number of advantages relative to the existing data. And we're gonna focus on the behavior of state level inflation for non-tradables which is basically gonna be state level inflation for services. Then what's the variation on the right-hand side that we're gonna be looking at? Well, here's a plot showing unemployment for California, Texas and Pennsylvania. And so it's gonna be differences in state level unemployment that are gonna be contributing to our estimates of the slope of the Phillips curve. So it's gonna be the fact that, for example, Texas has an extra recession in the late 1980s. We're presumably having to do with the fact that it's an oil state or the fact that California has a much bigger increase in unemployment associated with the greater recession. So these are gonna be the kinds of differences across states that will help identify the slope of the regional Phillips curve because as I said, it's gonna be sort of a different type of estimate. So what do we get out of this? Well, let me just repeat here our regional Phillips curve. So now, as I've sort of alluded to earlier, we're not gonna use this AR1 assumption in our actual estimates, although I think it's useful expeditionally. So here I'm just writing out the infinite sums, no solving for these with the assumption of AR1. Although, to compare it to the prior literature, we're also gonna consider this kind of specification which you could get by making this AR1 assumption. So this is the type of equation that we're going to want to estimate and we're gonna use a fairly standard sort of GMM approach to do it. What about identification? So there's this issue of demand versus supply shocks that I've emphasized in an important challenge. So here we're gonna- I mean, you have five minutes. You have five minutes, just looking at it. Sounds good. So here we're gonna use two different approaches. One, we're just going to sort of rely on the time fixed effects to capture the supply shocks and use live unemployment and relative price instruments. The second approach is this new tradable demand instrument that is gonna be sort of a new feature that we can rely on from the regional data. So while I don't have time to go into the details of this tradable demands bill over instrument, for those of you who are familiar with this idea, it's kind of similar to a bar take instrument that we're gonna use to construct proxies for demand shocks at the local level. So we're going to estimate this structural equation for the Phillips curve using these two approaches, either OLS or this instrument. So I mixed that up a little bit. It's GMM that we're gonna use to estimate CAPA here, but we also, as I said, for similarity to the existing literature we have, this type of reduced form equation. And here we're going to be using similar instruments, but just estimating this reduced form equation. So what do we get out of this? Well, a first conclusion is that it really matters to include time-fixed effects. So when we don't include time-fixed effects, then we actually get basically a slope of zero for this region Phillips curves. When we do include time-fixed effects, however, we get considerably statistically significant slopes on the Phillips curve. And so again, you should think about the inclusion of these time-fixed effects as picking up the role of these long-run inflation expectations. Now, perhaps more interesting than the slope of the Phillips curve over the whole time period is this question of how it's changed. When we don't include time-fixed effects focusing on CAPA, which is the estimate of the structural slope of the Phillips curve, then we get a massive flattening of the Phillips curve. So the Phillips curve appears to flatten by a factor of 100. On the other hand, when we do include time-fixed effects, we get a much more modest flattening. So now if you look at this row here, the Phillips curve flattens from a slope of about 0.01 to a slope of about 0.005. And the results are quite similar using our two identification approaches, either lagged unemployment or using this new instrument we construct using the regional data. It's maybe easier to kind of understand this in pictures. So the version on the left-hand side is showing the relationship between inflation and unemployment when we don't include time-fixed effects. And there you see a tremendously different relationship in the first part of the sample period before 1990 where it looks quite steep and the second part after 1990 where it looks almost completely flat. In contrast, once you take out time-fixed effects, then while you do see some flattening between the first part of the sample period and the second part of the sample period, it's much more modest. And so there's this really dramatic effect of controlling for time-fixed effects, which on our model are proxying for changes in long-run inflation expectations. So now to ask the question of how steep our estimates of the Phillips Curve really are, a sort of useful exercise is to take our estimates from these cross-sectional Phillips Curves and then just plug in the aggregate data and then ask if we use our estimates of the Phillips Curve and of Kappa and then plug in aggregate unemployment data, what would our estimates imply for variation in inflation in the recent period? And would the variation be too large or too small? So this is what we do. I'm not gonna go through all of the details, although I do wanna say that it's fairly important that we're gonna do the same thing that we do for non-tradables, also for rent because the shelter component, the housing component of the CPI is one of the most cyclical components, as some of you may know. So we're gonna do a similar exercise for rent and the estimates I'll show you will be including the housing component. So here's what we get from that analysis. The gray line here is the prediction from just this fitted equation where we take our slope of the regional Phillips Curve and plug in the aggregate data and the black line is the actual data. So the first thing I want to say is that both lines are taking out the rule of long-run inflation expectations. So what I'm plotting here is inflation minus long-run inflation expectations. And once you do that, the amplitude of both lines is much diminished. So notice that in most cases, the data on inflation minus long-run inflation expectations, it doesn't vary by more than 1%. So that's the first comment that most of the variation that we've seen in inflation is associated with variation in long-run inflation expectations. A second comment is that there's actually pretty reasonable co-movement between the predictions of, based on our regional Phillips Curve data, which is the gray line and the black line for the period since 1990. And that just reflects the fact that inflation has tended to fall during recessions and has to rise during booms just not by very much. The period when actually there's the biggest disconnect between the predictions based on the regional Phillips Curve analysis and the actual data is the period around 1980. And a natural interpretation of that is that this set of predictions I'm showing you is set of predictions that there were only denominations. And I think it's natural to think that you need supply shocks to explain the period around 1980. But there's a sense in which this is kind of the opposite of the conventional wisdom in the sense that actually our analysis is pretty consistent with the period since 1990, it's really the period around 1980 or something like supply shocks to explain the data. So let me say one more thing before I kind of conclude which is that my analysis has really been putting a lot of emphasis on the role of long run inflation expectations, which in the empirical work is proxied for by these time fixed effects. But I really haven't said anything interesting about how to return. I know that in this conference, a number of you have been kind of commenting on these issues. I think this is an incredibly important issue. It's a very important question, how the monetary authority can change people's beliefs about long run inflation expectations. And even though there's been quite a bit of work on this in economics, I think it remains something that we don't understand very well and something that we're more research is very welcome. Because we know that there are many times when people don't seem to adjust at all in terms of their long run beliefs about inflation, but other times it seems that these beliefs do adjust rapidly. So examples would be the end of the Volcker disinflation which I just showed you, but also the end of hyperinflations. So, in the case of a Volcker disinflation, how did it happen? Do I think it was an accident? That inflation expectations fell so rapidly during this recession, probably not. Politics were probably very important. There was a fact that there was this massive recession and yet Volcker didn't get fired. And perhaps this was really crucially important in changing beliefs about the long run monetary machine. But at the same time, I think that's a fundamentally different mechanism from the conventional mechanism of a Steve Phillips curve where you're holding the monetary machine often. So let me stop there. And I would be very open to any questions and comments. Thank you, Amy. Thank you for the very nice presentation. I am still waiting. People can post the questions in the chat. I actually have one question myself. So I wanted to ask one of the great thing about this paper is really the fact that you managed to explain what we do when we do this regional estimation of Phillips scores. I have to say the truth. I mean, really in the literature, I like those estimations but I didn't fundamentally understand them. Thanks to your paper, I guess we have a much better insight. One aspect that comes from your model is the fact that you can get rid of these inflation expectations by the time fix effect. But that's also coming from a relatively simple theory. And I was also thinking that when you think about what happens empirically, it might be that there is a secular component in unemployment in different states which can differ a lot across states. That would challenge your assumption that you can get rid of that term. So how do we think in those terms? Do you have any insight into that? It's a very good question. So let me say first that just in terms of what the data look like, you might be surprised by how much co-movement there is across states in people's inflation expectations and particularly the long run inflation expectations and particularly with regard to a big event such as the local disinflation. So in terms of how the data look just in terms of like some first reaction that one might have, there is a lot of co-movement and that kind of lines up with what you might expect from the data. But just to respond to your bigger conceptual point which I think is an important one, yes, absolutely there could be reasons for secular changes in inflation in one state versus another. And basically that would introduce an error term which we didn't have in our model. And then that becomes an issue of identification and that becomes where the instruments become important. So then the question essentially is whether the variation associated with these secular changes that might be leading to different long run inflation expectations or long run inflation in different states is correlated with the source of variation that the instruments are picking up. So just to give a concrete example so we can think about this a little more easily, imagine that there's some state like Florida which has an aging population relative to some other states which don't have this aging population. So that might have some impact on relative inflation rates perhaps because of different consumption baskets or something like that. Then the question effectively, so that's gonna introduce basically some component of the error term which has to do with demographics. And then the question of whether that would bias our estimates is essentially one of whether that component of the error term would be correlated with the instrument. And so I think our hope is that our instruments are sort of picking up more kind of cyclical variation that wouldn't be associated with these type of long-term secular trends. And so we would hope that I wouldn't be a source of bias but I think that's the way to think about it. That you could think about adding more error terms associated with kind of issues you're describing and I'm sure they're there. And then it really just becomes a question of whether those sources of the error terms are correlated with the source of identification we're using to estimate some of the risk. Thank you, sounds, yeah, it did sounds very interesting thing to look at. And I see now that there is a question in the chat by Peter Karadi, but I think that essentially he was asking something very similar to what I asked. So let me read it out. Very insightful presentation. I see the theoretical point about how regional estimation can help eliminating the long-term inflation expectations. Are there evidence about regional known variability in measured long-term inflation expectations? What might be particularly interesting whether regional long-term expectation are influenced by regional as opposed to national activity and inflation? Yeah, it's a very good question. And we've actually only recently been kind of looking at this, you know, we don't have anything sort of formally written out, but we've been looking at this a little bit because, you know, exactly, it is a good question. And our initial impression is that it is actually remarkable how much movement there is in these regional inflation expectations. So it appears that people are thinking a lot about the same factors in different states in forming their long-run inflation expectations. The data aren't great, but they're, you know, for the United States, you can't get it at the state level, but at the regional level, you can get some information about inflation expectations. That's what I'm facing that statement on, but I think that would be very interesting to see more. Thank you. I see now that the question came in by Hassan Naplousi. Correcting the regional estimate psi for the persistence of unemployment requires an assumption about how forward-looking firms are. We know from the forward guidance literature that the New Canation Phillips School is too forward-looking. Could we possibly draw different conclusions from a model where firms are not as forward-looking? Yeah, that's a great question. Something I didn't really have time to comment on, but, you know, you could say there's a little bit of a tension in some sense, and the fact that I am using this is sort of solving forward to convert between psi and kappa. That's the one place where we're sort of explicitly, in some sense, using rational expectations. One comment I would make is that the way that we're using rational expectations is really just in people kind of knowing how long the recession is going to last. So, you know, as a first kind of comment, I think that it is much easier to be rational about the idea that you think that on average, you're in a recession now, you're going to be in a recession for the next few years. That's an easier way to be rational than, for example, to be rational about the future distribution of the inflation factor or something like that, just because, you know, you have more sort of experience with that type of episode. So that's the first comment. But we have been very concerned with the issue that you described. So we've actually redone our analysis for various different values of beta, the discount rate. And, you know, there is quite a bit of robustness in terms of the findings and in response to different values of this beta. So it's not super sensitive to that. That was something we were concerned about for the reasons you described. You know, that said, I think this question of how you might interpret these facts in the context of a less rational model is a very interesting and reasonable one to ask. The good thing about our analysis is that aside from this issue you're pointing to about the relationship between beta and Kappa, but other than that, you know, we're taking out the long run inflation expectations term. So how that gets formed and how rational it is in some sense becomes a new point. And in that sense, you know, we're putting a lot less weight on rational expectations than in other estimation approaches. But you're right, that in the relationship between Kappa and Psi, you know, intuitively that conversion depends on how long people expect their session to last. And to the extent that they think it's going to end right away or something like that, that's going to lead to a different implication for the structural parameter than if they're more rational about that duration. So I think it's a very interesting question or certainly more could be done. Great. So Wemi, thank you very much for the insightful presentation and the nice Q&A. Really happy to have you here.