 Hello. Welcome to the afternoon session, the last session of this conference. My name is Gabriel Perez-Kiros and I work for the Bank of Spain. And then the first speaker that we are going to have, the keynote speaker, is going to be Jennifer Castle from Oxford University. Okay, thank you very much and let me thank the organisers for this very kind invitation and for some really fascinating talks over the past two days which have been really enjoyable. So this paper is on forecasting UK inflation. So a couple of disclaimers or apologies. First, I'm afraid it's frequentist, so that may come as a shock. Secondly, I'm afraid it's only point forecasts, so again, apologies for that. But, and thirdly, I'm afraid it's based on UK data, and of course I'm in a room full of Europeans here, but hopefully you'll see that the methodology can apply more generally. So let me start by just motivating the question. As I'm sure has been the case in Europe as well, there's been a big shock to UK inflation. We've got CPI inflation in the top panel there and CPI food inflation, and over 2022 we've had this massive rise in inflation, both in food and energy. In the UK, energy prices at the consumer level are regulated, but you can see the huge jumps over 2022. And so the interesting question is really how these big shocks to food and energy are feeding through to inflation. So the aim of this paper is to understand how the costs of energy feed through to both inflation and the broader economy. And we're going to try and produce some projections of UK inflation based on various energy scenarios. And the methods that we're going to use are to look at very long run time series of data. And the reason for doing so, I'm going to look at about 160 years of data. And the advantage of doing that is that we've got shocks like this in the past. We've had wars in the past. We've had pandemics in the past. We've had huge inflation spikes in the past. So using a long run time series of data enables us to identify the model. So I'm going to build four different models. And these are all going to be conditional models. I'm going to build models of wages, prices, unemployment and productivity. And the reason these are all separately built is that we've got quite a lot of nonlinearity feeding through. And you'll see why it's very difficult to build the whole system. But we test for super-exogeneity for each of the equations. And then we can actually put all of those equations together into a system at the end. So as I've just emphasized, the big advantage of using this long run time series of data is that we've got this past variation that we can use. But of course there's a drawback. This is going to be annual data. And that's not very helpful when one wants to forecast inflation in the current climate. And so what we're going to do is use more rapid, high-frequency data to update our forecast based on this annual projections that we're going to produce. So let me show you some of the data that we're going to model. Here we've got UK wages and prices over this 160-year period. So UK wages have risen 700-fold, prices 100-fold. So there's a huge amount of variation in the data, and that really helps with identification. And look at wages and prices, wage and price inflation. We've had periods where inflation have hit over 20% before. So that's very useful when we're looking at inflation running upwards of 10% in the current climate. As well as that, one of the key aspects over this very long time series is just how remarkably constant the cointegrating relation has been. So this is UK real wages in the red line, and the dashed blue line is UK productivity. Just look at how close they move together. That's going to provide our cointegration over this long-run time series. But I'll also note, look at the flatlining post-financial crisis. This is a real issue in the UK about the flatlining of productivity. And another interesting aspect has been what's happened to the energy use. So this is energy consumption over this long time series. So total fuel consumption is the red line, and initially it was almost all coal consumption. But then we started to diversify into gas and oil and since renewables, and now actually coal consumption is near zero. But you can see that there's been a flatlining of total fuel consumption, and that's due to big efficiencies since the 1960s. So this is the kind of data that we're going to use, the variation in that to identify contributing factors to inflation. So this is a brief route map of what I'll talk about. I'll build the conditional models of wage inflation, unemployment, productivity, and price inflation initially. And then I'll show how we combine those conditional models. But then if we want to do some forecasting, I'm going to base these forecasts on some assumptions. So we'll make some scenario projections based on higher frequency data. And then I'll give you some forecasts for 2023 and 2024 before concluding. So what's the modelling approach behind this? Well, as you've seen from this data, there's clearly non-constancy of change. This data is really highly volatile. So we're going to use a general to specific strategy, allowing for brake detection over the entire period, and allowing for non-linearities. So we're allowing for structural brakes, non-linearities, and unknown sets of variables, explanatory variables. So we're going to start by building a general unrestricted model for each of these conditional models. We'll include intercepts, lags of the dependent variables, and a huge range of conditioning variables that are all motivated by theory and past evidence. Then we'll include polynomials for possible non-linearities. And you'll see that we'll map to, say, smooth transition models using those non-linearities. We include step, impulse, and trend indicator saturation. So this allows us to detect for outliers and location shifts and trend brakes over the entire period. And then we're going to do selection, model selection. We'll retain the regressors and select for the non-linearities and the impulses at a very tight significance level. So we really have a prior that these shouldn't enter unless they're really there, if they're very significant. So we select at 0.1%. Then once we've picked up any brakes and outliers, we'll select over the regressors at a 1% significance level. And then we undertake further transformations for cointegration to include the long-run information. And then finally, we do super-exoginality testing, given the conditional single-equation conditional models. And we find that the resulting equations are congruent encompassing models. So we're content to proceed with these single-equation models. So if it's straight after lunch and you're all a bit tired and you'd like to switch off, let me give you the brief summary. This is what the four models look like. And then I'll go into some detail. But if you get this slide, then you can have a short dose. So the wage inflation model, the real wage inflation is driven by productivity and the markup, along with a really important non-linearity, which is a wage price spiral, and an additional non-linearity coming through an unemployment relation. So there's a lot of non-linearity in the wage inflation, which is really going to drive the inflation forecast. Unemployment is a remarkably simple model. Unemployment over this 160-year period is explained by real borrowing costs over revenues, which we proxy by output growth. And it fits remarkably well over this period, including the COVID period. Productivity, we model production functions. So we have labor productivity driven by capital per worker and energy per unit of capital. And we use trend breaks to capture the changes in technology. And then finally, our price inflation model depends on both short and long-term interest rates, broad money growth, commodity prices, which is really important in the current climate, world inflation and unit labor costs. So they're the four models that I'll build, and then I'll show how we combine them. So let's start with the model of real wage growth. So this model looks very complicated. I'll take you through it step by step. But the first thing to explain is we're modeling the real wage growth. That's the dependent variable here. And the first thing I want to convince you of is that it's a well-specified model. So in the top panels here, we've got the model fit and the indicator adjustment. So these are the breaks that the model picks up. We've got the scaled residuals and forecast errors, residual density and residual auto correlation function. This, for such a long time series of data, is a very nicely specified model. So we're happy that it's congruent. So what is actually going on in the model? Well, the first thing that's going on is we've got a short run impact of changes in productivity on real wages. And that's roughly about 0.5. So there's a fairly rapid incorporation of productivity increases into real wages. But notice that this is symmetric. There's no nonlinearity in that. So it also reflects the dampening of real wages due to the productivity slowdown in 2008. As well as the productivity growth, we've got this strong equilibrium correction mechanism. And you saw that in the data of real wages and productivity trending very closely together. So we've got a long run feedback to real unit labor costs of about 20%. So that's a half-life of just under four years, which is a fairly rapid incorporation. Now this coefficient is really important. This is a non-linear term reflecting a wage price spiral. So let me show you what this thing looks like. We've got, we saturated the model with polynomials and we found evidence that the Taylor expansion was a close approximation for our smooth transition model. And so we've got a smooth transition, a logistic smooth transition function in annualized squared inflation. So that's the transition variable. We select the threshold and the speed of transition by grid search and the actual data is using observed data. So the function here is this smooth transition function here. So what's going on? It's actually adjusted by a minus one. So down at the bottom here at zero inflation, this is minus one. At that point, there's very little reaction of real wages to price inflation. So workers are inattentive. They have no idea that inflation, while inflation is very low, so they ignore it and they don't make any wage demands on it. But as inflation rises, as you can see as we get up to about 10%, workers are really attentive. They realize their real wages are being eroded and so they're pushing for nominal wage rises to match price inflation. And up at this zero on the F function, that's 100% pass through. That means workers are demanding 100% compensation for the rise in inflation. So if inflation is exceeding about six to eight percent, then we should start to see wage price spirals and of course inflation at the moment in the UK is up at eight point seven percent and there's clear evidence of these second round effects through wage price spirals coming through. Now the next thing in the model is a non-linear unemployment term. So we've got unemployment. It's just demeaned over this 160-year period unemployment's roughly five percent. But the quadratic term comes in as well. So initially, well let me show you what that function looks like. So this is a non-linear unemployment function initially as the unemployment rate rises, the impact on real wages falls. That's the standard relationship that you would expect. But once unemployment hits about eight percent, now the impact on real wages actually starts to rise again. So initially we have this loss of workers bargaining power but then we get this movement along the marginal product curve which raises the real wages of those still employed both from more capital per worker and from the employed being more productive. And so actually we get this upturn in the impact on real wages. That goes to show unemployment is certainly involuntary in this world. Okay, what else do we have in the model? We've got three step shifts all around the first Second World War and these are step shifts that cannot be explained by any of the variables in the model. Okay, so these are step indicators been picked up by searching over the entire sample and they are not explained by the other variables in the model including productivity. And the sort of most realistic explanation of what's going on here is that there's been an increase in female labour force participation from the Second World War and a rapid upskilling of labour and so we get this upward shift and it's a really big upward shift. So pre-Second World War real wage growth was about 0.8% after the Second World War it jumps to 1.7% so a really big shift from the Second World War effect which needs to be modeled. Finally, we've got a step shift in 2012 this reverses unfortunately the growth that we saw post-Second World War growth shifts down by about 2% per annum and again none of the variables in the model can explain this step shift and it really is fundamental to being able to forecast over the following period. So then you might say well hang on you've got all these indicators these step shifts in the model and you're not really telling me where they're coming from the difficulty with step indicator saturation is that it's a-theoretic. We don't have a strong economic argument because we're searching for these step shifts on a data-based method and actually one way to think about this is that you can identify these step shifts or outliers, these impulses due to economic variables. So one argument might be well of course over this long time period the UK had a lot of incomes policies prices and wage controls and so can we think of the indicators as essentially picking up price and wage controls? Anyway we test for that and we find evidence that actually we can't explain the data from wage and price controls so we reject that interpretation. Then the next question is can we are we okay to model this as a conditional model because of course we've got contemporaneous variables on the right hand side and so we need to ensure we've got super exogeneity. So under the null hypothesis the parameters in that conditional model that I just showed you must be invariant to the shifts in the marginal models of any included regressors. Notice that we've got indicators step shifts already in the conditional model so you might say hang on how can you test for super exogeneity given that you've already got these step shifts. Well it's quite important to note that actually the test for super exogeneity is not impugned by the presence of common shifts in both the conditional and the marginal models. So if you've got common shifts in both the conditional and the marginal model they will stay in there and then you test for the significance of any shifts in the marginal model over and above those common shifts. And so we do that we run a var with two lags in output per worker price inflation and the unemployment rate retaining all regressors and again selecting the outliers and step shifts at a tight significance level we find 10 impulses and 7 step indicators found and then we put those into the conditional model and test for their significance and we conclude that it's valid to condition on the contemporaneous regressors in other words we have super exogeneity. So I hope you're confident that that's a good model for real wage growth. These are the forecasts and I show you these so I call them forecasts they're not really forecast they're sort of in sample model fit as it were using known regressors but the interesting thing is over the COVID pandemic crash and recovery actually the model does extremely well. So that's one model let me move on to the unemployment rate model and this is a really simple model we model unemployment as saying employment is going to increase if it's profitable to higher people and we proxy that as revenue minus costs so what are revenues well we proxy changes in revenues as changes in GDP and we've seen evidence of that through the cointegrating relation that essentially that relationship holds in terms of the costs well capital costs depend on real borrowing costs so we just look at the long-term interest rate minus inflation so combined that gives us a measure called the profits proxy and you can see in the data here that's the blue line it actually closely maps to the unemployment rate so we build a model of the unemployment rate this is the unemployment rate on lags of itself and the profits proxy we don't include non-linear terms here there's not strong evidence of non-linearity but of course we do include structural breaks and outliers and we pick those up using saturation techniques then we transform to a dynamic model in differences and we get a long run relation here of the unemployment rate essentially if the long-term interest rate equals the real growth rate then the profits proxy would be zero and equilibrium unemployment would be about 5% and that essentially matches what we see unemployment to be over this last 160 years so earlier in sample periods saw really huge key changes if you think about what's happened over 160 years we've had two world wars we've had the introduction of unemployment benefits huge industrial changes all of these things have gone on and yet this model only picks up one difference and two impulse indicators just one explanatory variable and yet this model fits very well so I think this is quite a remarkable model to try and convince you that the model fits well we've got the data the change in the unemployment rate and model fits in the blue line in the top panel there the scaled residuals, the one step ahead forecasts including COVID period residual density autocorrelalogram and the intercept adjustment you can see we just need four outliers to be corrected there so that's the second model the third model is the production function so we're going to augment the production function with energy data that's a key component of the UK data and as you can see here we've got the red line is total fuel consumption and that's consists of an energy mix that's been changing over time but also the actual total fuel consumption's flattened off since the 1960s as well and that reflects increased efficiency you can see the uptick in renewables here, the green line which is only just starting to outweigh all of the other fuels but what's quite remarkable over this long time period is that we've seen a 90% fall in the ratio of energy used to capital stock look at that huge increase in efficiency over time so that's energy per unit capital stock has really dramatically declined so how do we model this well we're going to use exactly the same methodology that I've used for the previous two models we build a dynamic model of output based on capital, labor and energy we use impulse, step and trend saturation and now notice that we're doing trend saturation as well so this allows for a broken trend in every period and that's going to be picking up changes in technology we test for homogeneity and we can impose that restriction so we end up with an equilibrium correction model of productivity, output per worker or the change in output per worker as a function of capital per worker and energy per unit of capital and that gives us a long run relation here at the bottom with the indicators capturing changes in total factor productivity again we have to test for super-exogeneity can I convince you that it's okay to model this as a single equation model so we test for the invariance of the coefficients so we model energy per unit of capital as a function of output per worker capital per worker and the lags of energy per capital select the step and trend saturation at a tight significance level and then put those into the conditional model and we find evidence of super-exogeneity so again we can use this as a single equation model we can then solve out for the long run to obtain a production function and that's our production function here sensible coefficient on labor you might think hang on that's a very high coefficient on energy compared to capital stock and I would agree I'd take the joint combination of capital and energy together but you know one can justify the coefficient on energy because essentially energy use really was crucial to the development and does the model fit well again let me convince you this is the model fit and residuals, residual density and autocorrelogram and the intercept adjustment notice we need again very few intercept adjustments so outliers but we do have one in the very last observation 2021 that's Covid going on here and notice the advantage of using saturation techniques because we can pick up outliers at the very beginning and end of the sample as well so other break detection techniques would have struggled to pick up this very last outlier and then finally the fourth model a model of price inflation so again the same methodology we're going to have a dynamic model of the GDP deflator applying saturation and selection and the variables we're going to have in our model are excess demand for output money, national debt, unemployment exchange rate, unit labor costs, interest rates, wages, world and energy prices so everything that you think matters for inflation should be in there we come up with our price inflation model note that actually it doesn't go right back to 1860 unfortunately we're still working on that because the second world war period really did have some quite big shocks to inflation that we're modeling but let me explain what's going on in the model this is the model fit and residuals residual density and autocorrelogram and actually the model fits very well so what's going on well we've got some inflation inertia so lagged inflation plays a role on the monetary side we've got the growth rate of broad money matters the change in the short term interest rate matters and the short long spread matters as well then we've got commodity price inflation that's enters in there you'll note that actually that's a tiny coefficient and in fact it's insignificant despite that we're going to keep it in because we're going to have a huge change in commodity prices to forecast and you'll see that despite the tiny coefficient on it it's actually going to play a big role in inflation forecasting as well as that we've got changes in unit labor costs and now you can start to see I've made an argument for this big nonlinearity in the real wage equation that's going to feed through unit labor costs here so the nonlinearity from that model will feed into the price inflation model then we have world inflation that also matters and we have again we've aggregated the outliers and step shifts into an index of retained indicator variables and that's mostly covering wars and previous crises then there's this interesting step shift this is we've called it the China effect so there's a step shift in 1993 and we think that represents the downward pressure in the UK from Chinese prices so let's combine those four models that was a very brief tour of four econometric models but here I've summarized them in these four equations here so notice that we modeled real wage growth but now I've just matched that nominal wage growth and this F tilde is that wage price spiral the nonlinearity that matters there everything that's exogenous is collected in these capital D terms so in those four equations there are a lot of variables in the models that were relevant and they're all picked up by these capital D terms other than what I've called endogenous variables in other words the variables from the four equation system so I'm actually going to make a simplifying assumption I'm going to close off that second nonlinearity which was the nonlinearity in unemployment if you recall the nonlinearity kicks in when unemployment rate goes above about 8% and in the UK we're well away from that at the moment so we don't need to worry about that second nonlinearity instead we need to worry more about the wage price spiral so we'll close that off and then we can just do substitution to solve out for price inflation as a function of all of the exogenous variables in those four models and we can take the coefficients from the estimated models to back out the actual parameters for this solved out price inflation model so we're going to need to make some assumptions on what the wage price spiral nonlinearity is going to be doing so I'll consider two cases to start with the first is when workers demand 100% in compensation for inflation so in other words they want nominal wages to match the price inflation the second is we'll look at when workers demand 50% of inflation as compensation so that's when F tilde is minus a half so we can then back out the parameter estimates for this solved out price inflation model and then substitute in all of the other drivers that we had the exogenous variables and this is our final conditional model for price inflation so let me talk you through what matters here so increases in the growth of broad money, energy prices, world prices the markup and the long term interest rate are all going to raise inflation and increases in capital energy in the short term interest rate all reduce inflation and so if for example if you were thinking back to 2022 when we had this energy shock if we had a reduction in energy availability of say 10% it's going to reduce output by 2.8% as you can see from production function and that would exacerbate inflation by 2% through the price inflation curve so what are the implications for current inflation well rapidly rising price inflation can stem from commodity price inflation as we've seen in there a tight labour market driving very low unemployment levels means that that second non-linearity is not going to kick in but low productivity from the recession is likely to dampen the effect of real wage growth but unfortunately the second round effects via the wage price spiral are really very significant and they can exacerbate the inflationary pressures and that's going to dominate the lack of productivity effect okay so that's the model that we're going to be looking at and I'm going to go back to the general model and so I want to forecast 2023 and 2024 but I've got more up-to-date information than just the annual data looking backwards so I'm going to come up with some assumptions for what I'll call scenario projections for inflation now when we started doing this we looked back in 2022 and really we just made some predictions and we got in a prediction for energy price inflation that's the delta P0 here of 150% so we thought energy prices would rise by 150% over 2022 it actually turned out that they rose by 170% so that wasn't a bad prediction but pretty sizable increase in energy prices so they were just based on judgment but we can do a bit better than that we can formalize the scenario sort of maybe you can call them initial conditions and to do that we'll use a technical card T so this was a method we developed in the M4 forecasting competition which is essentially a univariate statistical forecasting model and the idea of card T is that we estimate three univariate statistical forecasting models we start off by looking at a damped trend based on first differences of moving large values but we add in seasonality the second model is an autoregressive model with seasonality but we force a unit root if we're close to that and the third model is we estimate a trend halved integrated moving average model and those three models we then just take the average of those just a simple arithmetic mean and then we treat those forecasts of that average as if they were observed so we treat them as if they're part of the data rather than and then we estimate a richer autoregressive model over that forecasting period and then the fitted values from that model become our final forecast undoing any transformations that we did in the process so that's the method that we'll use to get some scenario projections for these conditioning variables so let's look at broad money we're going to need a projection of broad money over this period and this is actually very straightforward as a simple extrapolation so we're going to put in forecast of about 3% for 2023 and 2024 what about well prices well not much is going on well prices either so we put in projections of 1% and 3.5% and what about commodity prices we put in predictions of minus 34% for commodity prices long term interest rate we put in about 3.6% capital per worker unfortunately we do not have high frequency data for capital per worker so simple extrapolations of about 1.2% and energy per unit of capital is falling so that's going to be running at about minus 8% so all of those we're going to put into our assumptions and you can see these are the assumptions we've now included as the baseline assumptions for our inflation projections for 2023 and 2024 so from those we can now produce our inflation forecasts so what are our inflation well I guess these should be now cast made in 2023 given that our scenario projections were based in March 2023 so if we assume full pass-throughs that is the wage price spiral has a full impact so workers put in 100% demand for the price inflation that they've seen in that scenario we predict inflation to run at 10% and you can see the composition of that effect the rise in short-term interest rate has this very significant downward pull on price inflation but actually is counteracted by the long-term interest rate so that 10% seems actually not far from what it looks like we might be at if we had less pass-through so if the wage price spiral didn't fully kick in and workers obtained say only 50% of the inflation into their wages we would predict inflation of about 5.4% over 2023 so you can see what effect the wage price spiral has that's a really dramatic shift from 10% down to 5.4% depending on this non-linearity that's kicking in so these are the forecast for annual inflation over this period if we have full pass-through 2022 would have been about 12.5% 10% and then next in 2024 down at 7.4% much lower if the government can prevent the wage price spiral from kicking off which there's little evidence that it can do so we can actually do a bit better than that let's go back to 2022 and see how well we did and use that to try and figure out exactly how much pass-through of the wage price spiral there is so in 2022 our scenario was that there was an equally weighted rise of 50% increase in oil and 250% increase in natural gas that's what drove the 150% increase in commodity prices and you can see the commodity prices is this blue bar with a 6 on so that 6% of inflation was driven by commodity prices in 2022 out of the 12.5% so half of the rise in inflation was predicted to come through commodity price inflation short-term interest rates would need to rise to 5% to offset the direct contributions of those energy price rises and we can see the direction of which short-term interest rates are moving in now actual inflation reached 11.1% but if we look at the annualized inflation rate over 2022 it was 9% so from that actual out turn 9% we can actually reverse engineer exactly what the degree of pass-through was given known values so we can use the standardized values for 2022 for commodity prices world prices at 8.3% short-term interest rate of course short-term interest rate was rising over this time but over the year it averaged 2% long-term interest rate at 2.5% broad money growth at about 6% and given those if inflation was 9% we would have seen a pass-through of about 0.8% in other words 80% of the rising prices were demanded for in rising wages so using that estimate of 0.8% we can then look at the impact of inflation based on our scenario assumptions that we had so for an 80% pass-through we predict inflation will be 7.5% in 2023 and 5.6% in 2024 so the Bank of England are forecasting inflation of 8.3% in 2023 quarter 2 so an annualized forecast of 7.7% so we're very close to their prediction for 2023 however we're not as optimistic as they are for 2024 we're significantly higher 5.6% relative to their prediction of 3.3% so it does suggest that this degree of pass-through really, thanks, really matters it hinges on the non-linearity of the wage price spiral and there's quite a bit of evidence coming out certainly in the UK at the moment that actually wage price spirals are really starting to be embedded within the system so let me conclude there's been a recent rise in UK price inflation it was unanticipated but it certainly wasn't new by historical data and so the history can shed light on the current inflationary climate and therefore using this long run time series of data which has a lot of variation in inflation in the time period can help us to identify the explanatory factors and non-linearities so that wage price spiral would be impossible to identify if we didn't have the 1920s and 30s in our data set we also need to model structural breaks and distributional shifts and saturation techniques were really crucial to getting congruent models for these periods the conditional empirical models jointly model the dynamics location shifts, relevant variables and non-linearities here's the rub and this is where I think you're going to attack me on so the methodology doesn't produce uncertainty bands or distributional forecasts and the uncertainty that we get stems not only from model uncertainty because we've done a lot of selection and parameter estimation uncertainty but also the uncertainty from those scenario assumptions that I started with as well and so I guess my question to you today would be very helpful to have some feedback is how do you think we can embed all of those measures of uncertainty when thinking about our point forecast here but it's important to use automatic tests for super exogeneity that justifies our single equation modeling but then we combine those models to get out system forecast but you see we can't do a system model directly off because the wage price spiral in the real wage equation includes contemporaneous price inflation in a non-linear functional form so it's very hard to think about how one can do at the outset a system model so I think this is a way to justify actually getting a system by doing it in a series of single equation models finally price and wage equations combined with non-linearities can give us projections for the contributions to inflation so it's quite useful to see what the breakdown is where are the impacts coming from so despite the fact that commodity price inflation actually had a very small coefficient on price inflation model actually the sheer magnitude of the jumping commodity prices meant that it contributed half of the rise in inflation in 2022 and energy costs along with unit labor costs really do seem to be fundamental to explaining past inflation episodes and therefore are very useful for thinking about current inflationary episodes so thank you perfect timing any questions from the floor thanks thanks for the very nice presentation I guess I have two comments of really questions the first one is perhaps I missed that in the model but I was wondering if there is any role of expected inflation so inflation expectations because that's typically what workers really try to renegotiate the salaries on and then perhaps related to that I guess one could argue that if you don't increase labor costs then you kind of trigger strikes and if you live in London you see that every day every other day and so that essentially is a labor supply shock so I was wondering you know if you had a thought on the interplay between these two things increasing labor costs or vis-à-vis labor supply shocks thanks thanks a lot Jenny for this presentation so except if I missed it which may be the case you did not mention the great moderation effect right that is a fact that starting from you see what I mean Gabriel we don't have any reduction in cycles it's something that we have in most countries but it doesn't seem that you have this for the UK and the second point you did not mention something that happened in June 2016 that is a Brexit so I was wondering to what extent the Brexit can have any structural effect on exchange rate, productivity inflation and stuff like that and if you come for this in your forecast I would like to ask about the question for inflation you have also money in there do you also consider the higher order of money effect on inflation so you can trigger some spirals with this and may it be a way to model the effects of like asset purchase programs and lots of expansion of the balance sheets sorry, me first quickly it's very short your equations are a bit in the spirit of this old layered NITIL checkmen approach right and they had the price wedge as an important determinant of a price wedge spiral in there so the difference between the GDP deflator and the HIC or the CPI so I wondered about that so very nice talk, thank you I was wondering on the price equation so something that I have experienced is that when you include inflation expectations which I was missing in the equations you capture some of the nonlinearities are directly going into the inflation expectations because they are fast, I don't know here on the yearly but the capture of all the nonlinearities that you might find in the wages or in the unemployment as you were mentioning so why you didn't include inflation expectations thank you for the nice presentation about the way you present the econometric results regression results, I like very much that you also put the diagnostics there below so you know what the fit is but the R squared is almost consistently about 0.98 0.97 and that feels sort of like you think such a great fit for the single equation models and then as a time series regression person you think well maybe there's some sort of like problem with non-stationarity and I don't think that that is really the case I think it is much more because you do all the saturations that you have all these big outliers that are taking out and they of course explain a lot of the variation so you should not present the R squared without the outliers and breaks instead of the residual sum of squares or the total sum of squares that you basically account the total sum of squares with the outliers and stuff and I think more realistic I have a question myself something that worries me a little bit is the fact that fitting in sample do not mean necessarily predictive power and then I would like to suppose that there is a dummy now that is playing something that is not included in the past but you don't know if it's happening right now then perhaps something of like estimating this thing in kind of like the sample experiment saying like see with your model up to what point you will have been able to forecast future inflation and so predictive power of the sample not just fitting in sample and then just doing one exercise of the sample there are no more questions just that thank you very much for those excellent questions I hope I'll be able to address them all so let me start off with inflation expectations because there are two questions about why inflation expectations were not included so the pragmatic answer unfortunately is that we just don't have the data on it going back to 1860 and obviously it would be wonderful to include inflation expectations but over this long time period we we just don't have the data I'm less worried about not including inflation expectations because I think over 160 years it's very hard to think about how inflation expectations would have essentially been a constant effect over there I think it would have had a very variable effect over time and actually I think a lot of what the model can pick up is things that can capture inflation expectations without directly including them but I completely take the point that that is a drawback of looking at these long time series models and I think the answer would be to say let's think of it as just one model in a suite of models of which many include inflation expectations so a bit of a get out but that's my answer on inflation expectations in terms of the question about the strikes and whether we should interpret labour cost versus labour supply shocks again yes that's a very relevant point and if you look over this long run time series of data the number of periods in which there were really significant strikes in the UK versus periods in which there were significant labour cost effects and we don't disentangle the two now one might be able to argue that actually the impulse indicators could pick up the strike effect separately from the price from the labour cost effect but I'm not sure that it's actually doing that one way to test that would be to take the dates of all the strikes over the 160 year period and see how they map to the impulse indicators that we pick up but in many of the cases very few impulse indicators were picked up so I'm not sure that actually we need that but I think the point is a really good one and I think we probably need to drill down to just the real wage equation in order to try and disentangle the effect of the sort of supply side versus the cost side issue but very good point thank you very much I'll follow up on that one so the next questions are about the great moderation and the 2016 Brexit shock so the whole benefit of the impulse saturation methodology is that we can be agnostic about when shocks occur it's just whether they occur in the data so we don't impose the idea that there is a Brexit shock and in fact you'll see in the data we do not pick up a shift for Brexit and I think that's because Brexit is a massive shock to the UK economy that's undoubtable but it didn't occur in a one-off shift in fact I think it's a gradual process that's changing the entire structure of the economy and I think that's much harder to pick up so one way we could think about picking up that kind of shock is by slowly evolving shocks over time so we might think of slowly evolving trend changes that occur from the point of the Brexit referendum but actually have only started to be implemented once Brexit was actually implemented and who knows how Brexit is eventually going to be implemented so I think that's something that one probably needs to wait some time in order to disentangle the great moderation we don't pick up any big shifts and so that suggests that the great moderation those are just a reduction in volatility over time one thing you might say well we need to be modelling time-varying volatility over this period as well the diagnostics for the models suggest that our model is well behaved regardless we don't need to model time-varying volatility over this period so maybe the great moderation wasn't such a big shock in the the opposite of a shock in the UK to what one might anticipate in terms of the higher order effects of money we have a test for non-linearity so which essentially which essentially creates polynomials of all the principal components of all the regressors in the model and then we take the polynomials of these principal components the nice thing about that is that they're all orthogonal and then we test for the higher order polynomials and for the price equation actually we didn't find any evidence that they mattered and therefore we didn't go down the route of non-linear modelling and hence including polynomials of say broad money because we didn't find evidence of the non-linearity through the price equation all of the non-linearity was coming through real wages there but we did test for it but I think over this very long time series the impact of broad money is actually if you think about how central banks have been setting monetary policy over this really long time period it's very hard to see how broad money has had this constant effect over time the price wedge that was a really good point we don't have CPI data going back to 1860 unfortunately it would be lovely to include that but that's why we model the GDP deflator rather than the CPI we just don't have the data but if anyone is working on historical data and can get that for us that would be wonderful and something very important to test so again I think the argument is this just has to be one of a suite of models where one could use more recent data to look at issues like the price wedge there the R-squared really good point so I must admit I've been taught never to look at R-squared but you are right it's not an issue of non-stationarity we are essentially modelling a lot with impulses and the steps and I think you're right it's very important to exclude those particularly when you're looking at forecast confidence intervals as well because we don't want to essentially under predict the degree of certainty that we have over the forecast period by the fact that we've fitted a model fairly well by capturing the impulses and steps and so you can actually back out both the equation standard error with and without the impulses and do a comparison because if you're doing all of the work through the impulses and steps you'd worry about the model so very good point and I will correct that in future papers and then finally the predictive power out of sample yes so one of the constraints of the model that we have is of course it's based on contemporaneous data so all of our conditional models have contemporaneous variables in the conditioning model and so if we wanted to look at truly ex ante predictive power we would then need to model all of our conditioning variables as well and there's evidence that actually the more there's a forecast taxonomy that we have when we have exogenous variables that also need to be forecast that introduces a whole new layer of forecasting mistakes that one can make and so I guess that's the concern by trying to model these contemporaneous regressors in a forecasting context but that would be the true test of the model constancy indeed so I agree so I hope I've answered everyone's questions Profit margin is now very crucial issue for the Euro system there is a box also in the latest BMP report so we like to hear from you how you calculate profit margins for instance the most traditional banks use the simplistic rule the deviation from GDP at basic prices minus unit labour cost or profit which is the ratio from operational surplus over GDP thank you Yes again I'm afraid it is an issue of data constraints over this long time series because we need data in 1860 so it is purely just the markup of GDP over unit labour costs that's all, sorry