 Well, first of all, I would like to thank ACV for the invitation. It's great to be here. I have a lot of material and very little time, so let me just cut to the chase. So let me start by showing you a picture, which I've been showing my students since 1989, I guess, and which I find fascinating. Of course, I've been updating it every year. I didn't have the perfect foresight at that time. So what this shows is the evolution of the unemployment rate in the US and in the Euro area since 1970. And clearly, the two variables behave very differently. In the following sense, if you look at the US unemployment rate in red, you see large fluctuations that are associated very strongly with the US business cycle. With a clear tendency to revert to some nearly constant mean. Whereas if you look at the Euro area and employment rate, it seems to wonder about some seemingly upward trend without any tendency to gravitate towards some resting point. Now, in the language of time series analysis, we would call a variable that behaves like the US unemployment rate, a stationary variable. And one that behaves like the Euro area unemployment rate, a non-stationary variable, or a variable that has a unit root that has a random walk component. Now, to be sure, I mean, I'm not the first one to make this observation. Olivia Blanchard and Larry Summers in their seminal paper 1986, I believe, called Hysteresis on the European Unemployment Problem, which was published in the macroanalyl, made that point very forcefully. And they also provided a potential explanation, which I will get back to later on. Now, this characterization of these two variables, which seems clear just by a casual observation of the series, can be formalized using some statistical tools. So for instance, for those of you who are familiar with these simple statistical tools, this is the autocorrelation of the two variables. Again, the Euro area in blue, the US unemployment rate in red. For the US, it decays very rapidly, like I would expect from a stationary series. And for the Euro area, it remains very close to one, even if you increase the order of lags of the autocorrelogram. Again, very much consistent with this characterization I mentioned earlier. In fact, if you perform some formal unit root tests, you conclude that the US unemployment rate is a stationary, in the sense that you can reject the unit root for that variable, whereas you cannot reject it in the case of the Euro area. If you try to fit using conventional bug jankings approach, the univariate models that fit the two series best, you get the following models, again, for the sample period I mentioned earlier, 1970, 2014, using quarterly data. For the US, it's a simple AR2 process for the Euro area. It's an AR1 process for the first difference in the unemployment rate, for the change in the unemployment rate. Of course, this has dramatic implications in terms if you take it literally, which I'm not asking you to do, but if you take it literally, it has dramatic implications for the evolution of the two variables somewhere down the road. And just to illustrate this, let me show you a simulation. Again, this is not a forecast, a panic. It's a simulation that is a draw from that two fitted statistical processes for the two variables, a simulation from 2015 to 2050. And you can see how in this particular draw, the unemployment rate in the Euro area keeps diverging from that in the US, whereas in the US, it keeps fluctuating, but always around some constant value close to 5%. OK, so what I do in this paper is to take seriously this notion that the unemployment rate in the Euro area can have a unit root, can be non-stationary, behave like a random walk, and I try to understand what may be behind that unit root, what are the sources of that unit root. And well, I cannot do or I don't know how to do this in a vacuum, so I need some model that helps me organize my thinking about this. And what I do is I use a version of a New Keynesian model similar to the ones that most central banks are using these days for simulations of alternative monetary policies and so on. It's a formulation of that model that allows unemployment, or it introduces unemployment. And in the context of that model, I can make three hypotheses on what that source of the unit root can be. The first one is what I will call the natural rate hypothesis, the second, the long run trade-off hypothesis, and the third, the hysteresis hypothesis. And I will explain what those are to you. So what I do is to assess empirically the merits of those three hypotheses, and I discuss the implic after I reach some tentative conclusion, I discuss the implications for monetary policies. So now before I jump into a description of the main results based on that model, let me just show you some aspects of the data. So these data on wage inflation and the unemployment rate in the euro areas, again starting from 1970, the reason why I choose wage inflation and say not the weather or something else is because the model makes clear predictions regarding the relationship between wage inflation, not so much price inflation, that's one layer above, and wage inflation and the unemployment rate. Okay, so here you have in black wage inflation in the euro area, then employment rate in blue, and you can see a strong negative relationship between the two in the period that goes up to 1994, approximately, 93. After that, wage inflation very much stabilizes in the euro area, and the unemployment rate persists in that seeming random walk-like behavior. So that's an interesting observation, I think, because it has a bearing on what the sources of the unit root can be. So here is the same picture, but I have changed the sign of one of the variables, of wage inflation, and you can see how the two variables really track each other up to 93. In fact, I have performed a test for cointegration, and I have rejected the null of no cointegration for that early part of the sample. Here's the, these are the same evidence, but different perspective, so it is a Phillips-type draft with wage inflation on the vertical axis and the unemployment rate on the horizontal axis, and you can see this very strong negative relationship between the two variables, between 1970 and 1993, but then after that, there's what looks like a change in regime, and the Phillips curve, let's go it that way, becomes flat, okay? And you can see contrary to what Charles was mentioning earlier, you can see that it's not only because we're at very low inflation rates, because when the unemployment rate goes down during this later period, inflation is not going up, as you can see here, okay? Now, is the Phillips curve completely flat in the more recent period? Let's zoom in on that period, and here is what we have, it's not completely flat. There is still a negative relationship between wage inflation and the unemployment rate, it's just that it's much weaker, okay? In the paper, this is formally tested and so on, I won't bother you with the numbers. Now, so what I do next is to, again, to set up a model is based on some, as I said, an aversion of the New Keynesian model that I developed a few years ago, and we have a version with Franks Metz and Rob Vauters, which we have estimated for the US, and it's a model, again, with monopolistic competition in goods and labor markets, nominal rigidities in the form of staggered wage and price setting in La Calva, just a representative household with a large number of members. There is heterogeneity among the members of the household in the sense that they have different occupations, different disutility from work and so on, and the model allows for three different possible statuses for a single individual, can be an employed person, an unemployed person, or just a non-participant, like we see in the real world. Now, in the model, and this is critical for what follows, wages are set unilaterally by unions, and each union represents a type of labor and occupation, okay, and there is a continuum of such occupations. Now, so unemployment in the model actually shows up, you know, can be represented by a diagram like this, so there is a labor supply schedule, okay, so for each level of employment, say, and this labor supply schedule gives you the reservation wage for the marginal worker, okay? So if the real wage is given by this, you know, the labor supply gives you the number of individuals who would want to participate in the labor market, what we could call the labor force. The unemployment rate adjusts the difference between the labor force and employment, which is determined by the labor demand, and then there is a key concept, which is the wage markup, which I denote by this mu w, the wage markup is just the gap or the difference between the real wage in locks here and the reservation wage of the marginal worker, okay? Now, a key result in this framework, which should be, no, clear to just by looking at this picture, which I call the fundamental relation, is a simple linear relation between the wage, the average wage markup in the economy and the unemployment rate, okay, which you can see here. Now, in the standard New Keynesian model, wage setting involves some exogenous, not what I call exogenous natural wage markup, that is unions have a desired wage markup, okay? And they set wages so that the expected average wage markup over the duration of the contract equals that desired wage markup. That desired wage markup is a function of the wage elasticity of labor demand, and you can think of this as a proxy for the market power that unions have, okay? And that is taken as exogenous in the model. Now, in the equilibrium, the average wage markup in the economy and hence the unemployment rate deviates from the desired wage markup because wages are sticky, wages are not adjusted continuously, okay? And that's the source of unemployment fluctuations. But that behavior by each union individually is consistent with optimization by the desire to maximize the utility of the representative household, given what other unions do and given the behavior of the economy. Now, this type of wage setting gives rise to a wage equation, a wage inflation equation, I should say that looks like this, okay? So wage inflation is related to expected wage inflation and it's inversely related to the unemployment gap where the unemployment gap is defined as the gap between unemployment and the natural rate of unemployment. Now, what is the natural rate of unemployment in this framework? The natural rate of unemployment is the rate of unemployment that you would observe if wages were fully flexible. That is, if the wage markup was equal to the desired markup at all times, and it's given by this expression, okay? Now, so that's one type of wage setting. The alternative wage setting arrangement that I analyze, and that's, I guess, the novelty of the paper is one that is inspired by the insider-outsider models of one-sharp summers, Lindbeck and Snower, and others, which I just incorporate into this more modern macro framework. So here, the wage setting rule is different. So each union sets the wage of its workers according to a rule that can be expressed like this in words, you know, you set the wage so that the expected employment over the duration of the contract equals current employment, okay? So essentially, you don't care about the unemployed. You don't care about maximization of utility of the underlying households. You just care about maximizing the wage of your current members who are those who are employed subject to the constraint that, at least in expectation, they remain employed. So that gives rise to an equation and a wage inflation equation that looks like this. So again, wage inflation depends on expected wage inflation because wage setting decisions are forward-looking in this model, but it also depends in a nice way on the change in employment and is the log of employment. So in the growth rate of employment, okay? Now, this is critical. The difference between the two formulation, the two wage inflation equations is very important in terms of implications because here, you know, the deviation of unemployment relative to the natural benchmark will have an influence on wage inflation and it will be an stabilizing influence. Whereas in this case, you know, the only thing that matters is the change in the employment rate, not the level of employment relative to any benchmark, okay? So the economy may remain permanently at the level of employment, which is inefficiently low, without that, you know, leading to changes in wages that would bring them back to the efficient level, say, okay? So to close the model, I introduce a simple monetary policy rule which some authors like Orphanides, Frank's mates and so on have suggested approximates while the ECB policy in recent years and the only, you know, twist that I introduce is that I allow for changes in the inflation target. Those may have been relevant in the early part of the sample, obviously not so much in the more recent period, okay? So here is the first hypothesis, the natural rate hypothesis. Well, what is the source of the unit root in the unemployment rate according to this hypothesis? It's a unit root in the desired wage markup, okay? So we may think of changes in institutions or changes in demographics, things that we've done really model explicitly that change permanently the bargaining power of workers or wage headers of unions, okay? That, oops, sorry, that generates itself, it generates a random walk behavior in the natural rate of unemployment and of course under the conventional wage setting arrangement that random walk behavior or that non-stationarity is inherited by the actual unemployment rate, okay? Now, what is the, now under this assumption, I can back out, okay? I will skip some of this. Now I put this model to a number of tests and we essentially conclude that this is not the explanation for euro area unemployment. So let me show you some of these tests. So first, under the assumption that the natural rate of unemployment follows a random walk, I can back it out as the long run component of the observed unemployment rate. So here you see in blue, sorry in black, what is the estimate of the natural rate of unemployment for the euro area? And what you see in red is the unemployment gap, the gap between the actual unemployment and the natural rate of unemployment. And clearly this there, and what you see in gray, the shaded areas are the CEPR dated recessions. So what we see is that much of the increase in unemployment under this hypothesis, much of the increase in unemployment during recessions is the result not of an increase in the unemployment gap. In fact, the unemployment gap goes down in many cases, but an increase in the natural rate of unemployment, an increase in the bargaining power of workers, which is hard to believe. Now, one can, again, under these hypotheses, one can back out the unemployment gap and see what is the predicted behavior of wage inflation generated by that unemployment gap using the wage inflation equation that I showed you earlier. So let me go to this. So this is an extended version of that wage inflation equation in the sense that I allow for indexation to past price inflation, okay? So what you see in blue here is actual wage inflation, okay? What you see in red is the wage inflation generated by the model allowing for indexation to price inflation. The correlation is very low, 0.24. But in fact, the positive correlation is the result of the mechanical, is the result of indexation and the fact that wage inflation and price inflation are correlated. If I remove the indexation term, what I have is this is the predicted wage inflation. Again, you should ignore the level, the fact that the level is low. The correlation is actually negative, minus 0.2 with actual wage inflation, okay? So I conclude that this hypothesis doesn't provide a good explanation of the high persistence of unemployment in the euro area. Now let me turn to the second hypothesis, the long run trade-off hypothesis. Now the New Keynesian model actually predicts a long run trade-off between inflation and unemployment, okay? Now it turns out to be a very small trade-off if you calibrate the model with any reasonable parameter values, okay? But the idea is the following, okay? Here, under this hypothesis, the ultimate source of the unit root in unemployment would be a unit root in the inflation target of the central bank, okay? So suppose that the inflation target of the central bank follows a random walk that would make wage inflation non-stationary, and again, given this long run trade-off implied by the Phillips curve, that would make the unemployment rate non-stationary. In fact, here is the long run relationship between the unemployment rate and wage inflation implied by the New Keynesian Phillips curve. Again, if I look at the data, if I calibrate the model using, you know, any range set of reasonable parameter values, I get very, that this long run trade-off is very small, and I cannot, it cannot explain the increase in way, the increase in the unemployment rate that we observed in the 70s and 80s and early 90s, okay? So let me show you some simulations. Again, I'm skipping on, so here's the key simulation. So in blue, you have the actual unemployment rate in the euro area. In red is the unemployment rate predicted by the model. When I feed into the model, the, these shocks to the inflation target that are consistent with the long run behavior of inflation in the euro area. So first, the model fails to capture, you know, the upward trend in the unemployment rate during the disinflation period. Again, because the trade-off is very, very small. It's very tiny, okay? In other words, the Phillips curve implied by the model is almost vertical, whereas in the data, we don't observe at all a vertical Phillips curve. And also the size of the fluctuations in the unemployment rate are completely at odds with what we observe in the data. So conclusion discarded. And I'm left with a third hypothesis, the hysteresis hypothesis. So this hypothesis is based on the assumption that wage setting is carried out not with an exogenous desired wage markup in mind by unions, but through these, you know, under these insider-outsider arrangement in which wage setters or unions care only about those who are currently employed. Now, the implication of the model are very different. First, employment is non-stationary. And the unemployment rate is non-stationary. And this is a result of any shocks, even in response to transitory demand shocks or transitory monetary shocks that those variables will be non-stationary, okay? And that's what Blanchard and Summers refer to as the hysteresis phenomenon in their original paper. Okay, so let me show you some simulations. Okay, so here you see, this is a response of the unemployment rate to a transitory adverse demand shock. And you see how the unemployment rate increases permanently, output decreases permanently. And the effect on wage inflation and price inflation is really tiny. If you look at the units here, this is, it's almost nonexistent. Okay, and again, because wage inflation and hence price inflation depends only on the change in employment, not so much on the level relative to a natural rate. So let me show you some predictions or the model's predictions regarding wage inflation. So here you see the blue line is actual, the red line is predicted. So the model fits reasonably well, the behavior of wage inflation. Now again, this is allowing for wage indexation. What you see at the bottom is the role played by changes in employment in determining wage inflation. So here we see more action that in the case of the natural rate hypothesis. And if I focus in the more recent period, we see that the correlations between predicted and actual are higher. So 0.68 when allowing for indexation to price inflation, 0.52 when not allowing for that or just focusing on the employment change component. Now notice that the model cannot explain some episodes. For instance, the 2009, I think it's 2009, 2010 episode of the missing this inflation. The model calls for a negative wage inflation but the data don't deliver that. We have a strong stability of wage inflation but other than that, the model performs relatively well. So let me just, I have just, if I can take one minute. Again, the previous analysis suggests that there are alternative possible sources of that unit routine in the euro area on employment rate. The one that seems more possible is the hysteresis hypothesis. And again, these permanent changes under these insider, outsider model, these permanent changes in unemployment rate may be the result of any shock, not only a demand shock. So in some ongoing work in progress, I have looked more formally at the implications for monetary policy. In particular, I have derived the optimal monetary policy in a version of the New Keynesian model that allows for these hysteresis effects. So let me just conclude by showing you two slides that show the responses of the economy to supply shock first, the technology shock and then to a demand shock under the optimal policy which I have derived and contrast it with the responses implied by the simple rule that I used earlier that is meant to describe what how the ECB and many other central banks carry out monetary policy. So this is an adverse technology shock. The adverse technology shock under the simple rule that's the blue line, leads to a permanent increase in unemployment and a permanent decrease in output well beyond what the negative technology shock calls for, well beyond what is efficient. Now in red, you have the response under the optimal monetary policy. So the unemployment rate remains almost constant, not completely constant, but almost constant and the decline in output is much smaller. There is a permanent decline in output which is warranted by the permanent decrease in productivity, but the decline is much smaller. Of course, this comes at a cost and the cost is higher price inflation and higher wage inflation, but the difference relative to the simple rule case, it's relatively small and it would seem to be perfectly acceptable given the differences in the consequences for unemployment. And the final slide I want to show you, it's the same exercise, optimal policy versus simple rule, but now in response to a demand shock. Now in response to demand shock, it is optimal as you can see to fully stabilize unemployment, to fully stabilize output. And this is consistent with full stabilization of price inflation, full stabilization of wage inflation. In other words, in this model, not surprisingly demand shocks do not generate a trade-off and here the optimal policy, it's one of full stabilization of all the relevant variables. Now what happens when the central bank follows the simple rule that I introduced earlier? Now the simple rule doesn't fully stabilize unemployment, but now the consequence is that the unemployment rate increases and it increases permanently and output decreases and decreases permanently. And there's a slight decline in price inflation and a slight decline in wage inflation. Now in the standard model, I conclude with this idea, in the standard model with an exogenous wage markups, the deviations are following the simple rule that I introduced versus the optimal policy in response to demand shocks are very small. There will be some deflation, there will be some small increase in unemployment, but all these variables will go back to their initial levels immediately. In this case, the effects of not following a very strong counter-cyclical policy from the very beginning are permanent, okay? And that's the main difference. So let me stop here and apologize. You made the point very clear, okay? I'm very glad to be here. Thank you for inviting me. And this is indeed a very challenging paper on a challenging topic that we all realize is absolutely central. So the starting point is that the Euro unemployment rate behaves very differently than that in the US. In the United States, there's substantial volatility with a consistent reversion toward the mean. The average unemployment rate of the US in the last 50 years is 5.9. Clearly, there are all sorts of years going back when it was 5.4, exactly what it is today. In the Euro area, we have in contrast a unemployment rate that wanders around, that can't reject a unit route, that has more persistence than in the US and raises questions about what is causing this upward drift. My discussion raises more questions than answers. I'm going to question the unit route characterization that it does not apply to the entire period. I'm going to call attention to similarities between the inflation process in the US and the Euro area. I'm gonna suggest three or four reasons why it is more fruitful to study the change of the price level, that is the inflation process instead of the changes and wages that are emphasized in the paper. I'm gonna give you a brief update on my longstanding model of US inflation. I'm gonna see how close we can come to using that sort of model, very similar to Larry Ball's, to characterize Euro area inflation. And at the very end, I'll have a couple of things to say about Geordi's three models, just very briefly at the end. So here is exactly the first graph that Geordi started with. Blue is the Euro area inflation unemployment rate. Red is the United States, you see the mean reversion. This is current up to the fourth quarter of 2014. And this is table one in the paper. It's a little bit hard to see from this distance, but this is a reproduction of table one. The test is the significance with which you can reject a unit route. The two statistics on the left are for Europe, insignificant rejection of the unit route, whereas on the right you have the US, significant rejection of the unit route. Well, I took a closer look at the two unemployment rates and I said, okay, well, obviously the Euro had this huge increase in unemployment in the 1970s, so let's cut that out. And if we just look at the US and Euro unemployment rate since 1990, what we notice of course is an outstanding overwhelming source of difference and that is the mean is different. The mean European unemployment rate over the period since 1990 is 3.5 percentage points higher than the US. But it didn't look like the other kinds of super differences were there. So what I said to myself was, let's see if I can just run a simple regression. Let me see if I can explain European unemployment by American unemployment. I'll stick in a constant of three and a half percent and then I'm gonna run a regression in which European unemployment is on the left and on the right is going to be US unemployment, four quarter moving average to get this persistence and I'm gonna put in the fourth lag and the 12th lag of US four quarter moving average and there's the actual and predicted. So this is my evidence that the difference between Euro and US unemployment has been exaggerated. This is with the constant forced to be three and a half percent. This is with the constant estimated freely. We have exaggerated the extent of the difference. The overwhelming question is, why is the European unemployment rate been so much higher over the last 20 years? If you look at the unit root tests again, all you have to do is exclude the first 10 years. If you do the whole test again starting in 1980, you have a very strong rejection of the unit root for Europe. In fact, even stronger rejection than you do for the US. Now let's turn to the reason why we want to study price changes and not wage changes. First of all, central banks have an inflation target. I don't know of a single central bank that has a wage change target. As you'll notice in Geordi's slides, another problem is that wage data are more variable, have more volatility and are harder to pin down than inflation data. Next problem is that wage changes have no implication for price changes until they're mediated through productivity growth. So we have to look at the change in unit labor costs which in Geordi's notation is the wage inflation minus abuse theta here for the growth rate of productivity. But even then, inflation does not equal the change in unit labor costs all the time always because if inflation doesn't equal the change in unit labor costs, it means there's a change in labor share of national income and indeed that happened in Europe and that is a very important fact that should guide us in looking for answers to some of these puzzles. Here if you just accumulate Europe's trend unit labor cost minus Europe's PCE inflation starting in 1970, you see a sustained upward movement for the first 10 years, then a plateau and then you see a sustained downward movement which has received a lot of comment. Now can you apply the same model of say wage markup setting in this environment in which I would say unions are being very aggressive in the 1970s and labor has lost some of its market power in the last 20 years. How different is US inflation from European inflation? Well here's the PCE headline inflation rate for the US versus the Euro. Could you really tell the difference if I didn't have labels on these graphs? They are so similar it's uncanny and in fact if you look at the last 20 years they absolutely trace each other. Now this is headline inflation so it's influenced by oil prices. Look at the up and down of the inflation rate in 2008, 2009 in response to the marked fluctuations in oil prices. You can't talk about inflation without having some allowance for supply shocks. In contrast you compare wage changes in Europe with wage changes in the US they look very different unlike the similarity of the inflation process. Now I wanna call your attention to that red hump in the late 1990s in US wage changes. Now that was a period when the United States went through a very different event than Europe apparently and that was the dot com productivity revival. I mentioned before you just cannot make implications about inflation from wage changes without looking at the behavior of productivity. So here's an HP filter of productivity growth in the Euro area versus the US. Of course the scale is different but you'll notice that there is this big hump in US productivity growth in the 1990s that does not exist in Europe. Europe had faster productivity growth during the whole post war period of catching up until 1995. Since 1995 Europe has had consistently slower productivity growth almost down to zero in the last five years. When you take out the productivity growth and you look at unit labor costs in the Euro area versus the US except for that first 10 years they look much more similar and that's because we have made this important productivity correction. Now it's time to look at the US inflation unemployment process. Here I've changed colors. Blue is the US unemployment rate. Orange is the US inflation rate. And my approach to this process in a model that I labeled 35 years ago the triangle model of US inflation. US inflation depends on a heavy foundation of inertia that's the bottom of the triangle. One side of the triangle is demand in the form of the unemployment gap. The other side of the triangle is supply in the form of oil shocks, price controls, import prices and productivity trends. So just to see how this works look at the first decade, the 1960s. This starts in 1962. We had the blue line comes down. We had the Vietnam War boom. Very low unemployment by historical standards and low and behold inflation speeds up gradually. Unemployment goes first. Inflation follows. Inflation moves very slowly because of the inertia. Then we have the 1970s. The causation is totally reversed. We have the supply shocks driving everything. Oil prices, the end of price controls in 1974 causes a spike in the orange line. Unemployment follows a year later. Same thing happens at the end of the 1970s. Spike and the inflation rate do mainly to oil prices. And then we had the great disinflation led off by a spike in the unemployment rate in 1981 and 1982. Now, no one's gonna be able to read this but this is the latest reading on my inflation equation for the US. It consists of up to six years of lagged inflation rates indicating the importance of persistence. The unemployment gap and the NARU are estimated simultaneously. There are four different types of supply shocks. Food and energy prices, non-oil import prices, changes in the productivity trend and the Nixon price controls. Now, estimation stops in 2006 because here's an important lesson. I haven't heard a word about this yet today. Any Phillips curve estimation is heavily dependent on a lag dependent variable, lag wages or lag prices. Any Phillips curve inflation equation has a high R squared and not look at goodness to fit. You have to simulate it out of sample and generate the lag variables endogenously. And when you do, you have a test of whether this equation is gonna drift away from the facts or doesn't. And here's 33 quarters of simulation of that equation with the red line is actual, the black line is simulated. This is an equation that still tracks the behavior of the US inflation rate very well. So let's take a simplified version and apply it to Europe. Here we have now just three lags of three past years of inflation, the unemployment gap estimated simultaneously with the Nehru and I didn't have European data for the food and energy effect. So I just stuck the US food and energy variable in the European equation and it does just fine. All of those variables are significant at the 1% level and you'll notice a unemployment effect on inflation that's quite a bit smaller than Larry Ball's and more in the ballpark of Olivier's of around minus 0.2, minus 0.25. Here's the Nehru that comes out of this for Europe. I think it's a little bit low because it suggests that the actual unemployment gap has been positive for Europe during the whole last 20 years. And if that were true, we would expect inflation to have slowed down more than it did. But it is possible to pull a Nehru for Europe out of this and how does it do in that crucial test of simulations? Now I'm starting in 1987, so I don't have as much data. I'm gonna take a shorter simulation period of four years and we're gonna say with no information on lagged inflation, how does the equation do over the last four years? And the answer is it's got drift. It predicts too little inflation, too much negative inflation over the last four years. So then I thought, well, this is a paper about hysteresis. Let's take hysteresis seriously. Let's add in to that very simple European Phillips Curve equation, the change in unemployment. Well, when we add in that extra line, we see that the change in unemployment has the correct sign. It's not significant. I'm very skeptical of this because I think that hysteresis is very important in Europe. But the one thing that the benefit you get by putting in lagged, the change in unemployment is that it does improve the simulations. And so this European equation is spot on in 2014 in predicting how much inflation there was in Europe. So let's just conclude with some comments on the three models. The natural rate model generates increased unemployment through an exogenous shock to the wage markup. It operates just like an oil shock and the timing relationships in those theoretical simulation graphs are just right. You have an initial shock, in this case, to wages. It gradually pushes up inflation. And then unemployment follows, and a reduction in output. I just wonder, however, is a wage markup shock a plausible event in data covering the entire euro area when wage bargaining, particularly before 1999, was carried out at the national level. I just wonder whether that leap is plausible. In principle, however, the wage markup hypothesis does have some promise to helping us understand the process by which the European labor share increased back in the 1970s. The long run trade off model has a rather strange idea that the central bank can pinpoint the price target precisely. That's the opposite of timing in the real world. If you want to choose a lower price target, the way you do it is you raise interest rates, as in the voker disinflation, unemployment rises. And only then does inflation respond to the higher unemployment. So in my view, that second model of Jordi's has the timing backwards by having the inflation rate instead of the interest rate as the instrument of the central bank. And we see here, again, that's the inflation rate, that the inflation rate only fell in the early 1980s after a big jackup of interest rates and high unemployment. The histories, this model, I just question whether it is right to apply it to employment instead of unemployment. We had stable wage changes together with very different behavior of employment changes over the period he studies. So my conclusion is we got three big puzzles. We haven't settled any of them. Puzzle number one, why was the unemployment rate in Europe so low before 1975? I think this was a period of rebuilding rapid productivity growth, continuous excess demand, and a flow of an excess supply of workers from the farm to the city. Why did the unemployment rate go up so much from 75 to 85? I think you had the perfect storm of oil shocks, wage markup shocks, and wage indexation that all fed into inflation and caused the necessity of disinflation. And finally, why is European unemployment so high today? I'll go back to Blanchard and Summers in 1986 and the section here about hysteresis. I don't see how you can make much progress without recognizing that the high unemployment countries in Europe are continuing to have wage stickiness and downward wage rigidity. Thank you.