Fiscal Backing, Inflation And US Business Cycles

>> John: So, let's get started, I'm glad everybody's here and anxious to hear of you from elsewhere but the title is Fiscal Backing Inflation and the US business cycles. We're happy to have Frank Smets talk to us, who's deeply engaged in the European Central Bank's work, the council, executive board and also a professor, which is always nice to have.

So, thank you so much for sharing your wisdom and your experience, Frank, go ahead.

>> Frank Smets: Thank you very much, John, it's, of course, a great pleasure to be here, it's actually very nice to see this conference room in real-life experience rather than on Zoom, so thank you very much for the invitation.

I should say I'm definitely not an expert and specialist on the US fiscal or monetary policy for that matter, and so you should take my views and analysis with a grain of salt. This is joint work with Raf Wouters, who is a longtime co-author and the usual disclaimer, holds his views expressed and my own and not necessarily those of the ECB or the European of the DORA system.

So, this is very much preliminary work, which kind of makes it very useful to get all your comments and suggestions, and you will see there's still a lot of work to do. So, that's sort of the outline of the talk and let me just jump immediately in sort of why Raf and I started thinking about this project.

It's really about the relative role of fiscal versus monetary policy in driving inflation, which is, of course a big debate all over the world in this country, but also in other advanced and emerging market countries. And of course, for a central bank to say that it's a little bit strange because we have inflation targeting regimes in most advanced economies.

And of course, they are, are typically described as monetary-led regimes where an independent central bank achieves an inflation target by setting interest rates in response to deviations of inflation from the target following the Taylor rule or some other policy rule. And fiscal policy is sort of working in the background to sort of back up the monetary policy, is not really focused on stabilization policy, is more focused on that sustainability and.

Now, during the low inflation period and the period in which interest rates were at the effect of lower bound, there were calls for fiscal policy to play a more active role in bringing inflation up to target. And this was based on sort of most of the time two arguments, first, that monetary policy was less effective at the lower bound, whereas fiscal policy, no, there's quite a bit of research showing that fiscal multipliers are higher when monetary policy is passive or fixed at low interest rates.

And on the other hand, whereas monetary policy didn't have much space to ease further or to respond further, fiscal policy did have space in a world where sort of r minus g was low or even negative, where interest rates were lower than the growth rate. And so, I think that basically was, roughly speaking, what many governments and central banks followed after the pandemic crisis.

So, both fiscal and monetary policy became very expensive, accommodatory, and of course, since then, we have high inflation, which has challenged, again, this sort of more fiscal-led policy mix. And of course, this has led to in this country and in other countries, about the role of expensive fiscal policy in driving inflation, and has also led to calls to sort of a return, a clear return to a monetary-led policy mix.

And again, that's definitely also the case in the Euro area, so that's sort of the context in which we started thinking about this. The other reason for doing this paper is that, in kind of my reading, and this is a very casual reading of the literature on the fiscal theory and the price level, I was always a bit, sort of frustrated by the fact that the discussion often was in terms of two extreme regimes.

Either you're in a monetary-led regime, so that would be like how I would interpret inflation targeting regimes, or you are in a fiscal-led regime, and of course, that comes from the Sandler work of Eric Leeper. In a monetary led regime, central banks applied the Taylor principle, fiscal authorities respond to any sort of debt sustainability issues that arise, and so monetary policy basically sets controls inflation.

Whereas in the fiscal-led regime, you have the opposite, no Taylor principle nor bad feedback, in that case, actually monetary policy is counterproductive, as Chris Sims and John Cochrane have analyzed in very much detail and fiscal policy controls inflation. So, if you think about the reality, probably, no we're somewhere in between, so a realistic model of monetary and fiscal policy interaction should probably allow for such an intermediate regime with partial fiscal backing.

And again, this is not a new idea, John has pushed this in RED 2022 paper and of course, now there's Bianchi Faccini and Melosi QJE paper that also goes in that direction. What I mean, that regime, in words, is that fiscal policy generally does commit to serve current debt by running future surpluses, but it may not take the full burden of adjustment, so that adjustment may not be sort of complete.

Whereas monetary policy is geared towards stabilizing inflation, like in the inflation targeting regimes, but it may have to take into account the inflationary consequences of that part of the debt that is unfunded. And so, that's basically the type of regime that we want to analyze, and again, we're not the first ones to do that, so

 

>> John: There's a question, why couldn't you have monetary policy separate, they're together here so much, right?

>> Frank Smets: No, no, they will be separate reaction functions, but of course, in order to have a stable equilibrium, they will, I mean, these will be like cooperative equilibrium in the sense that either you have.

Have a regime where the Taylor principle holds no feedback, or you have a regime where there's no Taylor principle nor that feedback. In both cases, you will have a stable inflation regime. And the authorities, they follow their own reaction functions, but kind of taking into account what the others do.

 

>> Speaker 3: And just to clarify, sorry, a realistic model of monetary and fiscal policy is an amended rank or you're a getting out of the mold?

>> Frank Smets: Sorry, I didn't.

>> Speaker 3: You're writing a realistic model of monetary and fiscal policy, you mean by that an amended, suitably amended rank model?

 

>> Frank Smets: Yeah, well, I'll get to that. I mean, okay, whether that's realistic-

>> Speaker 3: How do you take issue?

>> Frank Smets: Yeah, whether that's realistic obviously, what I mean here is that we have to think about these regimes with partial fiscal backing, rather than only think in terms of the extreme regimes.

And the different ways of doing that, I will propose one way, which is a bit different from the way literature has basically gone in terms of switching between regimes in the new Keynesian framework. Or it doesn't have to be new Keynesian framework, but then we'll get there. So, basically these are the three things we want to do in this paper and in the presentation.

First of all, develop such a model with an intermediate monetary fiscal regime with partial fiscal backing. There will be a parameter lambda, that captures the degree of fiscal backing. Actually, in this paper, we will assume in the baseline that this is a regime parameter which is constant over the whole 1965 to current period, which of course is something that for sure you can criticize and discuss.

And again, the literature has actually gone the other way, saying you have switches between these extreme regimes and has found evidence of that. To some extent, we're taking the other way, we said it's constant regime, but it's somewhere in between. But you could generalize it by having the lambda change over time, or b shock dependent.

Then we want to estimate basically a new Keynesian DSG model under that regime to basically answer three questions. First of all, what is the average degree of fiscal backing? So what is the lambda? Is it 0, 1, 0.5, what have you? Secondly, are the most important drivers of inflation, monetary of fiscal.

With that, I mean, are they driven under sort of the active monetary policy regime mostly or more on the active fiscal policy regime? And then thirdly, this lambda, of course, does affect the transmission of shocks to the economy. So what's under this estimated lambda? What is the effect on the propagation of business cycle shocks?

 

>> John: I know it's hard, which is why I wanna ask about the lambda varying through time, because as I think about why did 2008 not cause inflation and 2020 did, it seems you just read statements of public officials. 2008, we're gonna have stimulus today and debt repayment tomorrow, 2020, you read them and they say, what do you mean?

R is less than g, we never have to pay back debt. They got rid of all the pay fors and the Congress was kinda clear, we want this to cause inflation. And so we are going to run an unbacked fiscal expansion, which is kind of, when you want to run a Lucas Stokey state contingent default via inflation, set lambda equal to zero, and when you want to run a sort of standard fiscal policy and borrow and pay it back.

So I think of history as having a lot of lambda varying over time. But like you, I've never been able to figure out how to identify that by other than reading the newspaper and blessing them according to the results.

>> Frank Smets: Yeah, no, so actually identification will be a big issue.

I mean, for experience, the lambda is identified in the sense that we can, the data does have something to say, but of course it's conditional.

>> John: It's gonna be identified by, when I borrow a lot of money and I spend it and I don't get inflation, then lambda's, I forget with a large or small, it's gonna be either zero or one.

The problem is then if you keep a constant lambda, in another episode like 2020, with a lambda change, you're gonna say, that wasn't a fiscal shock, whereas in fact it might well have been a fiscal shock.

>> Frank Smets: Yeah, I mean, we'll get there, but we started exploring time variation and also shock dependence.

But so far, I mean, doesn't really jump out that you have big variation. But again, that's very preliminary.

>> John: We could jump out by simply saying, I wanna fit the data. So make the model fit the data perfectly by choosing lambda that works. And if you got a lot of inflation, that must have been small.

 

>> Frank Smets: No, okay, but that's how it works, but that's not what we find so far.

>> John: I'll shut up and let you get there.

>> Speaker 3: And not to jump ahead, I'll just say it and you'll defer it. The idea is, imagine that you have a player who plays the mixed strategy and mixes between two very different actions, top and bottom, and that's one player.

And there's another player who plays instead, a pure strategy that is a mix of the two because there exists a medium strategy that is neither extremist top nor extremist bottom. And so in games, it's very hard to tell.

>> Frank Smets: Yeah, may actually-

>> Speaker 3: But there are parametric restrictions or type of plays that you can't support in the long run, that's the idea, combination of longer restrictions versus parametric period restrictions on the model.

 

>> Frank Smets: Well, yeah, we'll be parametric. I mean, basically model and parametric restrictions. But it's true, maybe not very easy empirically, even with these parametric to distinguish between those two strategies. And actually, so most of lurch has done the first part and we're doing to some extent the second part, because we think that gives us in the future, more flexibility.

In the first step, we actually restrain ourselves, we want just have one regime, one lambda, and see what that gives. But then we can think about relaxing that and rather than have zero one, we can have the whole continuum. We'll take that estimated model just to look at the most recent period of inflation, see what, what does it say about the role of fiscal policy, monetary policy, in the high inflation episode of 21, 22, 23?

Okay, let me maybe not go through the literature. I mean, I think you've heard, given that John is here and many people have passed in this working group on these issues, the kind of literature, and you've heard many of the papers. And I mean, it is really what they are talking about, the mixture of the fiscal theory of the price level, and sort of the more standard new Keynesian Monetary-led analysis.

And of course, there's lots of empirical work also that has tried to get at that question, including very much trying to estimate. I mean, Eric Lieper, of course, was very, very early on thinking in terms of regime switching in these reaction functions. And then Francesco Bianco and various co-authors more recently.

As I said, we will take the view, let's not think in terms of extreme, let's just think about an average. Okay, so lemme just show you through very simple model economy. And again, the inspiration comes from the Bianchi Facini Melosi paper, how the methodology works. It's very simple.

So consider, and again, this Leeper already did this analysis in terms of what are the stable equilibria. So, consider an endowment economy with flexible prices and one period nominal government debt. Once you sort of linearize the equilibrium equations, you basically have sort of two equations that govern this economy.

One is the Fisher relationship, which is the top equation. And the second one is the intertemporal government budget constraint, which says that current debt-to-GDP ratio depends on the past, current debt-to-GDP ratio, the real interest rate, and then the primary surplus. And again, Pi t enters because of the nominal nature of government debt.

And then you have the two reaction functions. So monetary policy reaction function, which sets nominal interest rate in response to inflation and psi is greater than one. The Taylor principle applies when it's less than one. No real interest rates fall when inflation rises. And then you have a fiscal policy reaction function, where the primary surplus responds to the debt when the debt rises.

So delta b is supposed to be zero, greater than zero, the surplus rises. And then you have this one shock in this economy, which is this transfer shock, epsilon tau t. So if you combine equation one with three and two with four, you have this simple system of two first-order difference equations.

One sort of forward looking, one, kind of backward looking. So you kind of know that for stability, you wanna look for one aggregate value greater than one, one eigenvalue less than one. And so the seminal work of Eric in 1991, a long time ago, was to sort of show that depending on the policy parameters, the psi and the delta, you can have two very different stable equilibria.

No one equilibrium, so here I'm just showing impulse responses in that little economy to a 1% deficit shock. So that's on the left-hand side, you have the deficit to GDP ratio, and you have a 1% deficit shock. So this is the monetary-led regime, what Eric called active monetary policy, passive fiscal policy.

The Taylor principle holds, so psi is greater than one. And the fiscal surplus does respond to rises in government debt. So if in that economy you shock the primary surface, so you have an expansionary fiscal shock of 1%, nothing happens to inflation, which is the middle panel. And what happens to that is that it jumps up because the deficit rises, but then because of this reaction function, it will be followed by future surpluses.

And so that will come gradually down and then go back to its steady state decrease.

>> Speaker 4: Sorry, I don't see the axis. So basically, where does it end? I mean, I'm trying to-

>> Frank Smets: I don't see it myself. So it's, I think it's, is it 20 or 40?

I mean, I didn't sort of calibrate this simple economy to 16, so that would be 4 quarters.

>> Speaker 4: Pretty fast.

>> Frank Smets: Yeah, I mean, again, this is just to illustrate when we will estimate a model, and so that is supposed to then to be closer. So that's kind of the equilibrium that at least I have been looking at for the past 20, 25 years.

It's basically, central bank is in control. No, fiscal policy does all kinds of things, but it doesn't affect inflation. And that was also one of the reasons why I know in our models we thought, we can actually get rid of the government budget constraint, because with lump-sum taxes and forward-looking VCR, equivalence holds, so fiscal policy doesn't matter.

But there is this other.

>> John: Inflation isn't exactly zero?

>> Frank Smets: No, sorry, actually this is a land of 0.99. Yeah, I just wanted to show that you do get a little bit of action.

>> John: My programs work the same way here.

>> Frank Smets: Yes, it does work with one, too, but yeah, you know what I mean.

Now there's this other regime. And again here, so this is the fiscal-led regime. No, that's what the fiscal theory, the price level is all about. And so here I just calibrate the psi to be 0, so normal interest rates are zero, stay constant, and delta b also to be 0.

So fiscal policy does not respond to debt developments. And so in this case, no, we have the exact opposite. No, you still have the same deficit shock of 1%, but now the debt ratio doesn't respond, whereas inflation responds. So you have this peak, and again, it should be 1 and 0, but it's a little bit off because of the 0.01 rather than the 0.

So you have this immediate spike in inflation increase in the price level that devalues the government debt, so that in equilibrium, actually you don't see any increase in the market value of debt. And as a result, there's also no need for future surpluses to follow. So this is what Francesco Bianchi called an unfunded fiscal shock, no.

So the first one is a funded fiscal shock, a funded fiscal shock is a shock, is a deficit now, but there will be surpluses in the future to cover the debt that serve the debt that you have created. Funded shocks do not have an impact in this small, simple economy on inflation.

Unfunded shocks do lead to this inflation push, but do not lead to a rise in the debt ratio. Now, what Francesco and his co-authors has done, actually you can look at both shocks within one economy. Rather than think there's two separate one is this regime, the other one is fiscal led regime.

You can actually have one economy where you have analyzed both funded and unfunded shocks by modifying the policy reaction function, as is shown in this graph. So basically fiscal policy responds to only part of the debt, basically the funded part. So it's bt the debt minus the unfunded part of the debt, the bft- 1.

Whereas monetary policy responds as usual to inflation, but actually only it has this time varying inflation target by ft. So only to the extent that inflation is above or below that time varying inflation target. And how are these two new objects determined? Basically they are determined in a shadow economy.

One way of saying is the fiscal inflation target, or fiscal inflation is the inflation that you need in order to fund the unfunded fiscal debt. And so in that sense, the two are equilibrium. And in the model context, you will determine it within a shadow economy where only the unfunded shocks enter.

So if you do that. So now we have two shocks, you have a funded and an unfunded shock. And I mean the economy looks exactly like the previous economies, but now we have both shocks in the same economy. So you have a funded shock and the whole BFM QGE paper is to not do that in a larger estimated model and see how important are the unfunded fiscal shocks for persistent inflation.

Again, in this case, inflation is not persistent at all because it's one period debt and we assume the normal interest rate in the fiscal regime. Not to respond at all, but you can get different reaction functions depending on some other assumptions. Now what do we do now? So we basically use this methodology and we just say, well, you can also use this to look at intermediate regimes where fiscal shocks are partially funded.

So you use the same methodology, but now you say rather than having these two separate shocks, you have one shock that is partially funded, and the lambda here will give you the proportion that is funded. And one minus lambda is the unfunded part. The parameter lambda captures the degree to which the shock is funded.

If lambda is one, then you have here the blue line. So you're basically back in the monetary led regime. Fiscal shocks have no impact on inflation, but they do lead to higher debt. When lambda is zero, then you're here at the green line, which is difficult to see, but it's basically the line that is zero.

When you look at the right panel, the debt ratio, and has the highest inflation response in the middle ratio. But then you can look at lambda 0.5, for example, where half of the debt is funded and then in this simple economy, you basically split the funding, so to say.

So part of it will be funded by future surpluses. That's what you see on the left hand side, sort of the starred orange line. So there's some positive response of the surplus to the debt, but it's less than no when you have the fully funded regime and more than when you have no funding.

And similarly part of that will be solved by inflation. So that will jump up to 0.5. Again, if the lambda is 0.5, it will split these differences. And so that's what I now mean with this intermediate regime. Now we can say, okay, we have this increased flexibility. We can think, what's lambda?

 

>> John: Another way of putting it is you have a model with two shocks, but unfortunately you don't have a way of separately identifying the two shocks. So you identifying restriction is gonna be, well, they always move together in proportion with each other, right. So again, of course, I would love to get back to the two shocks, right.

Leaper, I don't know if you've you seen this recovery of 1933. Great new leaper paper. We're here to cheer leaper paper. But one possibility is different categories of expenditure. So he went and looked at what Roosevelt did in 1933, which is like pretty clearly stuff that we're doing for the National Recovery act is unfunded and stuff that's regulating military expenditures that's funded.

And just for your next paper, there's a possibility of saying that specific kinds of things that we're doing for stimulus because we want it to cause inflation, Covid relief spending that's unfunded, but infrastructure or military spending that we wanna pay off, that's funded. Possibility there.

>> Frank Smets: Yeah. No, so I should be very clear.

I make the opposite assumption here. No and see how far I go.

>> John: Yes.

>> Speaker 5: I have a question you may have answered this earlier. I taught till 12:20, so I got here late, worried about all the contingent and potential liabilities of the government. We have vast unfunded liabilities in Social Security and Medicare, for example.

In the US, states have vast unfunded liabilities. Other some school districts and cities do. Yeah. So how do you think, I suppose the congress passed a lot retirement age is raised to 72. Do you consider that a fiscal shock?

>> Frank Smets: Right so, I mean, so in the empirical application, I mean, we don't really take into account because in the end, the data that we use is the actual debt, the actual primary surpluses.

And so in principle, within the framework, of course, you could do the same thing you do, sort of you look at these new initiatives and you say, okay, that looks like it would be like a news fiscal shock. It kind of shows that there will be some spending in the future or some liability, which is not, which has to be funded some way.

And so, and then in the data, of course, if the fiscal year is right, then you should see it in inflation picking up. But.

>> Speaker 5: Going back to John's point about what's gonna cause those primary surpluses, big difference with their big hikes and business taxes and taxes on income than if there are reductions in the entitlement spending, for example, have very different impacts on the economy.

 

>> Frank Smets: Yeah.

>> Speaker 5: And so how is that working?

>> Frank Smets: So again, we will get there, but in the empirical application we'll make a distinction between Social Security transfers, government spending. So both consumption and investment and revenues.

>> Speaker 5: But treat it as the shorter run cash flows involved.

>> Frank Smets: Yeah, exactly.

 

>> John: You're not gonna do disincentive incentive effects, if anything. So that's mostly what you're worried about. We're just doing taxes and transfers.

>> Speaker 6: I wanna go back to something John said, but I have a slightly different take. I think. The model, the question is fundamentally under identified when you stick with the conventional time series statistics.

Now, John, he implicitly stepped away from that. He said, I read the newspapers and I see what the policymakers say they're doing. That's a source of identifying information that he's bringing to the table. And it seems to me that we ought to bring that kind of information to the table in a systematic way rather than the conventional approach, which is look at time series, see what fits the data.

We've made a bunch of assumptions, including parametric restrictions. Because I agree with where John was saying, but I wanna push, I think I'm pushing farther in his direction. I wanna systematically say, let's bring more evidence and data to the table, cuz otherwise I don't see how we get around this.

 

>> John: I wanna push even farther than you. The kinda questions that isn't asking today is the question off equilibrium threats, which is deep in he footnotes of all this sort of stuff.

>> Speaker 6: Yeah.

>> John: Never gonna be able to do time series tests of off equilibrium threats.

>> Speaker 6: Right, okay, so that's another reason to try to elicit people's beliefs, their expectations and so on.

So we're on the same page.

>> John: So why don't we go that direction? Cuz you started off this talk by implicitly saying, you can correct me if you think I got it wrong. Before the pandemic hit, professional opinion thought we were living in a fully backed world, full fiscal backing, traditional monetary regime.

Now, nobody thinks that. I don't think, at least with respect to the particular episode of the pandemic, it's kind of question of what the regime is. We're going forward, I don't know. But again, even your taking the model to the data in a way and you're estimating a constant Lambda, I don't think is consistent with the evolution of your own expert opinion over time.

 

>> Frank Smets: Yeah, no, no, exactly. No, exactly.

>> John: Just analyze economics papers together.

>> Frank Smets: No, that's fine. No, so, I mean, I think we understand what the issue is. I mean, I do think that, notice there's room for both types of works because we do need the empirical evidence.

And I think the kind of the narrative identification approaches that have become very important will be very useful there to see what. But we also want to understand then how we can model that. And this is where this type of work army, whether you like this type of model or not, this is another issue, is necessary.

Because then if we want to do policy analysis, we need to do kind of factuals. And for that we need to have a structural approach. So basically what I'm doing here is building more on the model work and say, actually you can sort of open up the lambda, you don't have to take a stand, it's fully.

And here I take a first step. I say let's just assume, which we do in much of our other estimates. We assume a constant monetary policy regime often when we estimate, a lot of literature does that. So in that sense, I mean, again, this is not a good reason, but-

 

>> Speaker 6: There's just one other kind of conceptual point worth making explicitly. As I understand it, everything here, we're in a rational expectations world. There's no room for disagreement of differences of opinion about what lambda is, which I understand getting away from that as a modeling approach is quite difficult.

But in practice, that's another kind of fundamental assumption that seems dubious in the current context.

>> Frank Smets: Yeah, no, I mean, I agree, and I think it's dubious whenever definitely there's a regime change. Or I mean, again, of course there is literature that tries to go that direction. I don't think you can do everything in one.

On paper, this is actually an AR paper which, anyway, that looks at sort of fiscal tier of the price level type of inner model, similar to the one that I will show with learning. Now again, that's not disagreement, it's just learning. And you do get some of the same effects, it gets more delayed.

It depends a bit on how you set up the learning trouble. So there's a lot of work to be done there.

>> Speaker 3: Frank, I thought a part of your answer to Steve's question would have been, it depends on how you interpret lambda. Because I could take a business cycle accounting exercise type of view and imagine that there are very many models of the primitive economies that boil down to equations that look like yours.

And the lambda is like a wedge in this accounting exercise. That is a stand in for class of models that are consistent with that reduced forms and classes models that aren't.

>> Frank Smets: Right.

>> Speaker 3: So is that the way you think about lambda?

>> Frank Smets: Yes, but of course, it doesn't mean that if the regime has changed over the time that you estimated, that may bias your estimate of the lambda.

But yeah, so it would be like an average estimated.

>> Speaker 3: An average or a wedge whose magnitude and sign is symptomatic as to whether a certain class of models applies to the episode that we are seeing.

>> Frank Smets: Right. So I will give you relative, if I get there, I will give you relatively precise answers to those three questions.

And then we can discuss whether the fact that I have not taken into count that these regimes have fluctuated over time, they bias that estimate in one direction or the other. So, I mean, I think that's the way to go. It's clear what the assumptions are. We will see what the outcome is, and let's then see whether you think there's reason not to believe some of that.

 

>> Speaker 3: The lambda, to conclude, is it parameter for you, or is it standing for a class of models that would boil down?

>> Frank Smets: No, it's a parameter that characterizes the average policy response to shocks in terms of how much, monetary-led. I mean, in the end it will show up in the interest rate responses and in the surplus responses to all kinds of shocks.

And they're different. In that sense, I'm not so sure this is not identified. I mean, Google said the pulse response are very different depending on the lambda, and this is normally how we kind of estimate models. But of course, it's conditional on the structure of the model, that's for sure.

Maybe if I can go through, because otherwise, I mean, it's fine, then you'll have to read the paper. Okay, so anyway, so this is basically how the methodology. Now, there's a second aspect which is a bit different from the existing work by Bianchi, Facinhe, and Melosi, that is, in their work, in their QGE paper, they only assume unfunded fiscal shocks.

So you have either all types of shocks that propagate under the monetary-led regime, like in the world that central banks think describes the world. And then you have some fiscal shocks that are unfunded and then are inflationary. And then of course, the central bank will have to do something with that.

But of course, in our economies, all shocks have fiscal implications, including monetary policy shocks. But But also productivity shocks, preference shocks, what have you markup shocks. And so what we do again is generalize this literature by saying you can look at how sort of these different lambda affects the propagation of each of those shocks.

And just to show you that in a sort of a simple model. So now I kind of make the model a little bit more complicated. So now we have sticky prices, so you will have a time varying real rate. So the first equation is the forward looking is curve.

The second one is a new Keynesian Phillips curve, some price stickiness here. And then we've also added, and again, John and others have done a lot of work on that, a long term nominal bond. So you have this new arbitrage condition and the definition of the return on the long term bond, which will depend on the price of the long term bond.

 

>> John: There's powerful identification of lambda, I'm surprised that company got away with lambda zero. And that is if you have the fiscal shock you showed there's a deficit and there's immediately inflation. So a strong correlation of deficits with inflation in the wrong direction goes the other way in the data.

And when the government raises no revenue from the increase in debt, whereas we know government raises a lot of revenue, when surpluses go up, debt goes down. Whereas in this model, when surpluses go up, that goes up. So I'm hoping, I'm anticipating you're gonna get powerful identification that says most of the stuff is in fact paid back.

 

>> Frank Smets: Right, exactly, but it's not just that. No, it's also how real rates respond to those shocks. Once you have a more realistic model with lots of friction, everything will now, actually, one of the things we are still struggling is exactly what are the key sort of correlations in the data.

That sort of determine the fiscal theory part? Because the part that you're talking about, that's easy. I mean, we've been estimating those models with those fiscal theory

>> John: I think long chapter in the fiscal theory, and this is why I thought about this, the chemo, and think about an AR1 surplus.

When you run a surplus, that raises all future surpluses and that raises the value of debt, whereas we know that when you raise surpluses, you lower the value of debt. Because you're paying down the debt, vice versa, deficits raise the value of debt. Pure AR1 or just one period thing, it would go the other way.

So I think that's a very important sign that most of the time deficits are repaid cuz you raise revenue from selling debt.

>> Frank Smets: Yeah, I mean, let me just illustrate that. So in this simple, again, this is not the estimated that comes, but in this simple nuke engine representative agent nuke engine model, just add price frictions to the previous setup.

And where, I mean, I didn't talk about that, but the reaction functions are now a little bit more complicated. There's some interest rate smoothing, there's some response of the deficit, for example, to the business cycle, to output. These are all real correlations in the data and real reaction functions.

So when you look at the same shock, this 1% deficit shock, now you see the primary surplus is the lower middle. And you can do, again, very lambda, keeping everything else constant and see how the economy responds. And you can already see where the lambdas need to be in order to have some rise in the debt ratio.

When you have a deficit, you have to sort of see what is no, how do you associate the inflation response with that deficit. If lambda is one, which is the blue one, then of course there's no inflation response at all, as in the previous case. There's also no output response, no real interest rate response as the lambda gets lower.

So there's less, or there's less backing of fiscal policy. What happened in this case, because the inflation, so you get inflation response in order to bring down the debt. Cuz of these frictions, this will also have a real economic effect. So output will actually also increase, so the fiscal multiplier increases in this model with partial fiscal backing, there's feedback of that on the deficit because higher output basically increases revenue.

So the deficit will be actually everything else less and that will also be a factor bringing down the debt. As you can see, as you go from blue to green, so you have all these mechanisms interacting. No, I mean, we have some estimates of what the impulse response parameters are of a deficit shock.

You can see which one, I mean, we could do, not the cristiano at all exercise, do impulse response matching. I mean, we won't do that, we'll just estimate the full model. But you can see how the data can actually tell you. Now, the thing is, this is a fiscal shock, but, and that's what the literature has not really focused on at all.

Also, other shocks, of course, have fiscal implications, and so this is a negative productivity shock. Think about the 70s, the slowdown of productivity growth under the monetary led regime. Again, that's the blue line, of course, that has a negative impact on output. So that's the lower blue line in the upper left panel, a positive impact on inflation.

Again, we have some sticky prices here. But that inflation response is relatively low. What does it do to fiscal policy? Well, lower output means lower revenue. So the get a deficit on fiscal and have a rise in debt. The rise in debt comes also from the fact that in response to the inflation in a monetary led regime real rates actually rise.

That increases the burden on that. So this is again the typical response that you will get in a monetary led regime. What happens if you have less fiscal backing because in response to this negative productivity shock basically no that rises. If you have, if that ratio is not backed then basically higher inflation.

So you go from the small inflation effects to higher inflation effects, that lowers actually the negative response on output. It will bring through some of these feedback effects but also through the direct price effect the debt ratio down. And so one interpretation of the 70s is this is fiscal policy.

No, it's like or is the outcome still of lack Tax fiscal policy in 60s and what have you. Another interpretation is that, no, this was actually the productivity slowdown, which undermined fiscal sustainability. And in a model where the fiscal backing is limited, this will actually give rise to higher inflation.

I have no priory, the two sound actually not unreasonable. And you can use an estimated model to see is it more productivity, lower productivity, or is it easier fiscal or is it easier fiscal responding to lower productivity?

>> Speaker 5: Which shock is this in your model?

>> Frank Smets: So this would be a productivity shock.

 

>> Speaker 5: None of them equation, could you just put the equations back up?

>> Frank Smets: So this is this epsilon Et.

>> Speaker 5: Epsilon, oops.

>> Frank Smets: The third equation.

>> John: Potential output.

>> Speaker 5: It's a potential output shock. Okay, good, which anchors the Phillips curve, okay?

>> Frank Smets: Right, so it's very much, yeah, negative productivity shock.

Now you can look at all the shocks in the economy. No, I mean the ones that the literature has looked at. John has looked at, Chris has looked at.

>> John: Phillips curve shock, you could just call it a Phillips curve shock if you wanted.

>> Frank Smets: Yeah, I mean, I like to call this a productivity shock because it actually doesn't give rise to a trade off.

If the central bank targets the output gap yt minus y star t. So what you call a Phillips curve shock would be actually a shock to that equation, which, see what I mean?

>> John: Where's your.

>> Frank Smets: I don't have a kind of a markup shock in the typical.

 

>> Speaker 6: You gotta get going.

>> John: Sorry.

>> Speaker 6: Please go ahead. Yeah, we'll talk about that later.

>> Frank Smets: Anyway, so you can look at other shocks, monetary policy shock. I mean, that's a well known stepping on the rake phenomenon. You will get in this, I mean, this is the model that people have looked at.

If you have partial fiscal backing and the monetary policy tightens, the central bank tightens monetary policy, then that may backfire. Why, because tightening actually does create debt, as you can see in the lower left panel. If that's not backed, it will give rise to inflation. And so rather than a fall inflation, you may get a rise in inflation in this case.

So that's the stepping on the rake that John and Chris Timms have. And again, you can look at all other shocks. So let me now talk about the estimation. So now, we basically put all types of other. And this will be based on my previous work with RAF, where we have sort of this mid sized new Keynesian DSG models, which we estimated on seven observables and seven shocks.

So these are monetary policy shock, government spending shock, productivity shock, two markup shocks, a preference shock. We add back in the fiscal block. We left that out because it actually didn't matter in our Ricardian framework. Now it will matter because we consider these equilibria with partial fiscal backing.

And so we put them back in. And again, for empirical purposes, we actually have three fiscal shocks now to taxes, transfers and government spending. And then the other thing we need to do again to keep track of this fiscal inflation target and the unfunded debt. You have this shadow economy where all the shocks affect the shadow economy with this parameter, one minus lambda.

 

>> Francesco: Frank, can I ask you a question?

>> Frank Smets: Yep, hi, Francesco.

>> Francesco: Hey, hi, good presentation so far. So I wanted to ask you if you had these shocks to the persistent components of spending or transfers, because in our work that's really what it plays a key role.

So if you look at the 60s and 70s, it's not so much about just temporary spending, it's just you have this increase in trend spending because you have all the welfare programs being created in the mid 60s with the great society initiatives. So of course you have way more flexibility in other dimensions, add this lambda to all the shocks.

We had flexibility in another dimension because we were allowing this lambda effectively to be time varying. One way to think about what we were doing is to have a time varying lambda. But I think that on top of that, it would be interesting to understand whether you allow for this persistent component in spending that arguably, if Asians start questioning how it's going to be financed, could give you this negative commitment between inflation and debt to GDP ratio.

 

>> Frank Smets: Yeah, so we don't have the kind of elaborate different structure because you have almost like three components, if I understood correctly, to these transfers. So we will just have one transfer shock. I mean, as you can see in the lower line here in this table, the estimated persistent, it's almost like a unit root.

So it is very, very persistent. And of course that just captures the fact if you look at the time series, I mean, it has been almost like trending up forever and particularly in the period that you talked about. So we do have that type of persistence. Interestingly, if you look at the three components, no transfers, government spending and revenues, taxes, the component that has the highest debt feedback is actually transfers also.

So that may be a bit different from your setup where you kind of explicitly take this part and assume there's no that feedback to that for the unfunded part. So whereas we don't kind of allow for this flexibility and we actually find that it's the transfers that responded more.

Also taxes does, but with a smaller coefficient, 0.03, and government spending almost 0. So government spending has its own sort of life. So this is basically to the first question.

>> Francesco: So can I give you one more comment? I mean this is a minor comment but then I think like you were thinking a little bit about the differences with what we did and what you did.

I think that what also this model forces is that suppose that you have this inflation like we think happened in the early 80s in which essentially what Reagan did is to shift the perception of what was funded and what was unfunded.

>> John: Its only really made some big cuts to spending but it definitely moved the perception about what was to be funded versus unfunded.

So this model I think would have a little bit of a hard time in capturing that dynamic because the only way you can change the unfunded component is that if you have spending cuts. As I was saying, I mean this is great and I'm a big fan of what you guys are doing but I think that's something that you might want.

To think about going forward.

>> Frank Smets: Yeah, no, I think you're right, actually, I won't talk about it, but in the paper. We have a first exercise where we actually tested this model where you have a constant lambda for all the shocks versus basically your model. Where all the shocks have an uncorrelated, funded, and unfunded component.

And we do find that empirically, and of course, we put some discipline so that actually the share is the same, no, not is the lambda, so to say the implicit lambda is similar. And what we find is we do find that you gain a little bit in terms of explanation, explanatory power by allowing for these uncorrelated, funded, and unfunded shocks.

But when we look at the actual correlation of the estimated shocks, the correlations are very high. So, it looks no, you probably need to have something even more complicated if you really want to, and maybe it's just about time variation in regimes.

>> Speaker 8: Yeah, since we're talking about your next suggestions for your next paper, I had a few that I thought were kinda interesting.

 

>> Frank Smets: Okay.

>> Speaker 8: So first was, have you tried to expand this to a Hank model? And following up on what Steve's doing, especially since in the US political system, it seems to be the transfers are going to one group and the taxes they haven't been able to. But they're trying to raise taxes on another group, which have very different saving and investment proclivities.

The second thing is, it may not happen quickly enough, but since you have lump sum everything here. What happens if you are simultaneously observing a negative productivity shock that was caused by big increases in tax rates, for example. Or the reverse of productivity boom that was unleashed by big reductions in tax rates, how do you disentangle that?

Third, eventually, the level of debt is gonna matter and take an extreme case, we'll hit a Sergeant Wallace upper bound. And the last thing is, in your period, one of the things that is most remarkable from a bigger picture is the globalization of financial markets. And the elasticity of supply of capital from the rest of the world to the United States has been far more elastic over a much longer period.

And much larger range than people were thinking about two or three decades ago. And so I'm wondering how any of that affects anything, I'm not suggesting you answer all those now, but those are things that immediately came to mind. I'm trying to map what you're doing to how I think about what's actually going on, the economy and policy.

 

>> Frank Smets: Right, yeah, no, I think these are all great, on post-Keynesian1, that's probably one of the first ones on our list.

>> Speaker 4: I had a question.

>> Frank Smets: Obviously, we have a very stark Ricardian model. It's no Keynesian, but lumps and transfers have no effect as soon as you include, no, it doesn't have to be a Hank model, probably.

I think Francesco actually had a tank model to take that into account, then you will get some demand, usual demand, inflation effects. And the question is, if we would include that, does that actually increase the lambda, no, or not.

>> John: On your framework?

>> Frank Smets: Right, yeah so that's, and we can easily combine shocks so if you want to see what the impact is of a combined shock.

Actually, you can look at periods when those shocks cluster and then see what the impulse responses say but they haven't done that.

>> Speaker 6: Technical question on this so, there must be some equations that don't have shocks or somehow else you got identification here, the likelihoods aren't all zero or.

 

>> Frank Smets: Sorry, okay, I don't think I have the, we basically have as many shocks as observables.

>> Speaker 6: How does that stop you from a perfect fit? You have as many shocks as observables and they just pick a shock in each period.

>> Frank Smets: Well, if, yeah, if you had the VAR, then obviously that non restricted, but there's lots of restrictions, no, there's a Phillips curve, there is curve, no, there's lots of.

 

>> Speaker 6: Other shocks, like uncorrelated over time or cross sectionally is that the identification? If I have the same number of shocks as I have equations, I just pick in every period the shock of that equation to fit that variable, and I fit all the variables perfectly.

>> Frank Smets: Yeah, but the structure, okay, this is where no, how do we identify the shocks, through the structure of the model?

No, so it's not that you can say, well, this shock explains that, no, because if things that then explains also other things. So there are identifying restrictions which are given by the model which are given by the model that allow you to.

>> Speaker 6: Okay, we'll follow up later.

 

>> Frank Smets: I think identification is a big issue, no, so it's not that I'm.

>> Speaker 6: Yes.

>> Frank Smets: But you can, again, given the structure of the model, you can actually test for identification, presumably.

>> Francesco: John, the likelihood is not going to be invariant, yes, I see John's point that exposed, you can rationalize everything with enough shocks.

But the likelihood is not going to be invariant to the fit of the model no. So I think here, part of the exercise are conditional on the defined restrictions of the model, you can still try to identify this lambda parameter, and I think that's a bit the natural exercise.

 

>> Frank Smets: Yeah, maybe just to show you, so I showed here the likelihood of the intermediate model. Which is the model with the lambda's estimate to 0.83, which basically means that the unfunded part is 0.17 percent on average over this period. And it's much closer now to the monetary led.

Actually, if you look at the likelihood difference, I switched the two numbers, so it's only eight points, which is, no, it's significant. Often people take seven here as significance, but it's not very different from monetary led, whereas when you look at the fiscal let, that is clearly rejected by the data.

Conditional again on the model and the identifying restrictions relative to the intermediate, because the difference is no more 80 or it's ten times as much. One thing that you also see as if you fix the lambda and you estimate the same model and you increase lambda, the kind of stickiness that you need in this economy to fit the data increases.

You have higher nominal stickiness, you have higher also real stickiness, you need bigger habits. You need larger investment costs, so the jumpy nature of the fiscal, the unbacked component, the fact that inflation actually does part of the work. And in this model also output is, needs to be moderate, if you want to have a lot of that, then you need to have more stickiness in order to fit.

 

>> Speaker 4: That doesn't make sense that it's a time invariance type of restriction, going back to this debate. So you have a saturated model, but there are the structural equations of the model are fairly linear. The timing variance of parameters is what buys you identification. So, the greater the lambda, which is time invariant, it's more sluggish.

The economy has to be, that makes perfect sense to me. And he's actually validating the identification.

>> Frank Smets: Maybe that's a good. Yeah, that's again something we can check. Yeah, lemme just maybe wrap up by saying, so we can do like a decomposition in the part of the inflation in this history that's sort of more fiscally led than monetary led.

And it kind of fits qualitatively with I think the work that Francesco has done, this QJ, but quantitatively it's much less important. So it's 60s, 70s there was fiscal inflation which is the orange part, and it started again contributing since the global financial crisis.

>> Speaker 8: Go back to that for a second.

I wanna absorb the picture better or maybe I can look at the slides later.

>> Frank Smets: Now what's different, again from Francesco's paper is that because we allow all shocks to contribute to fiscal inflation, what we find is that about half of the fiscal inflation comes from fiscal shocks whereas the other half comes from the supply shocks.

So there is this role for the other shocks and the endogenous fiscal implications of those shocks in driving inflation. So part of why you see higher inflation than 70s is because negative supply shocks actually lead to higher inflation because part of the fiscal implications are unbacked. Lemme skip that.

Lemme skip that. So you can look at any of the shocks in the estimated economy and sort of stare at them and think. More or less what I want to say, the message from these impulse responses, which again qualitatively are similar to the simple model, but quantitatively what we find is that the lack of fiscal backing.

So although it's relatively small, no 70%, it does materially affect the impulse responses of these public transfer shocks, these are the ones. Actually most of the effects that you get on the economy comes from the fiscal inflation responses and it also affects the supply shocks but not so much monetary policy or demand shocks.

 

>> Francesco: Frank, can I ask you, have you tried to do a counterfactual simulation in which you take your baseline model with the Lambda 0.33 and then you completely shut it down and you say it's all funded and then you show us what inflation would have been in the 70s?

It seems to me that you don't look at COVID but I guess maybe eventually you'll do that.

>> Frank Smets: Yeah, I think actually if I'm not mistaken, what you would have gotten is the blue part. No, sorry. So the blue part is actually the counterfactual of inflation. If there was full fiscal backing, so inflation would have been even lower since the global financial crisis.

And it would have also a bit lower in the 60s and 70s.

>> Francesco: Yes, thank you. Yeah, it's not exactly the same, but I agree with you that it's very, very similar, that you probably get very similar counterfactual results. So that's informative, thank you.

>> Speaker 5: Could you just go back to that plot of the surpluses?

Yeah, I thought the lambda meant that they funded and unfunded surpluses were always gonna move exactly together, yet here they're moving in opposite directions, I'm not understanding something. Bottom left 1975, how can funded be going down and unfunded be going up? I thought lambda meant they were moving always together in proportion.

 

>> Frank Smets: Yeah, they're cumulative, and of course, there again, there's various combinations of shocks that lead to, so you don't read through for one particular shock, it will always be the same effect. But then one positive shock that leads to fiscal inflation may be combined with a negative shock that leads to some fiscal disinflation, so there may be different quantities.

 

>> Speaker 5: Funded and unfunded shocks always move together, but the funded and unfunded deficits respond differently to other variables, is that right? The lambda meant that something always moved exactly together, so I'm just having trouble seeing why they're moving different ways.

>> John: So isn't it that the effect in a particular year that we have on here on the primary surplus, for example, or deficit decomposing that it affects shocks that may have occurred earlier.

That have accumulated to this in one direction, and the opposite shock that you're talking about, the other side of lambda might happen, etc, and they're being mixed together?

>> Frank Smets: Yeah, I mean-

>> John: That's what's going on.

>> Frank Smets: I mean, so, yeah, I assume, too, but we can do further decomposition than actually, I mean, but that, I think, is probably the case.

 

>> Klaus: Frank, can I ask a short question?

>> Frank Smets: Yeah.

>> Klaus: Klaus Maso here. Thank you, Frank. On this question, for the given lambda and the given size of a fiscal transfer shock, you would get the same type of inflation. And if so, of course, then the effect differs because higher debt level or higher duration of debt, you get a much bigger effect on relief, on reducing the debt level.

So do you take this into account when you show this decomposition that, say, in the 80s there was much lower debt. So a given lambda may have done much less in terms of reducing the debt level via inflation, whereas in the 2010s debt level were much higher?

>> Frank Smets: Yeah, no, we don't, so, again, this is also average.

So we have actually an average estimated maturity of debt, which is, I think, three years, which is much lower than the six years that you have now. But again, this is an average, I think it used to be much lower before, plus QE, of course, implicitly has reduced the maturity.

But it's true, if you would allow for time variation in the maturity, then given that this is a parameter, would be like a time variation in the impulse responses and also in the contributions, but we don't have that.

>> Klaus: Frank, but that can mean that if as duration has increased, so as the debt level has increased, that the fact that you can estimate a constant lambda may differ if you take this second round effect via the debt into account of higher fiscal inflation.

 

>> Frank Smets: Yeah. Why don't you think about.

>> John: I just wrap up.

>> Frank Smets: Okay, so this is the pandemic. So we basically estimated the model till like Q4, 2019 to Not have the pandemic shock, which is very specific shock and difficult to capture with sort of the historical shocks affect the estimation.

But then we kind of used the model to interpret what happened in the pandemic. And so the results you find here. So the inflation graph, which is the left upper panel, shows you no actual inflation. And the contribution, we kind of bundled the shocks in supply demand, monetary policy and fiscal shocks.

And you see the black one is the fiscal inflation contribution. So it was sort of significant of point of like two percentage points or more. But the peak of that effect was actually, according to the model, in 2021. So earlier than the peak that the actual peak in headline inflation, which took place in 2022, then the actual peak, which was in 2023.

And most of the peak in 2023, the model interprets as negative supply shock.

>> John: It's a negative supply shock that causes a fiscal response, that causes what I would call fiscal inflation. So it's not just nothing happened and the government went nuts.

>> Frank Smets: Okay, so we can do this decomposition, that's what you see in the lower, that's the fiscal inflation.

And you see that the contribution of the various shocks. So the biggest part is black part, which is the fiscal, but that comes earlier, whereas the peak of the blue part, this is the fiscal inflation effect of the negative supply shocks. That comes a bit later.

>> John: I think about Francesco's brilliant idea, which is rerun it with lambda equal one and show us inflation where there's kinda like no fiscal thing happening at all and see.

 

>> Frank Smets: For this, yeah, okay?

>> John: I'm sorry, I shouldn't be interrupting you.

>> Frank Smets: Yeah, no, no, no. We can easily do that. That's basically it. So if I can just sum up.

>> Speaker 6: 0.83.

>> Frank Smets: Sorry.

>> Speaker 6: 0.83.

>> Frank Smets: 0.83 is the average degree of fiscal vacuum. The average, I mean, I have to emphasize that.

The most important drivers of inflation are more monetary led. But there are these important periods in which fiscal deflation did contribute significantly. Sixties, seventies, and more recently, fiscal backing does affect the propagation of particularly expansionary fiscal and negative supply shocks. It creates fiscal space, stimulates output, and increases the inflationary effects of those shocks.

It seems to have, in our estimates, limited effects on the propagation of demand shocks, including monetary policy shocks. And then, okay, the post pandemic inflation peak in 2022 is mostly driven by negative supply shocks. But fiscal inflation, did offset the impact of negative demand developments in 2021.

>> Speaker 4: There's one question.

When you talk about propagation, you mean transmission amplification.

>> Frank Smets: Yeah.

>> Speaker 4: And can you tell the two, I mean, how much is, let's say a given productivity shock, negative productivity shock is fed into the economy. And then the effect with fiscal backing, the same shock is an additional blank effect on a number of variables.

Can I boil it down to.

>> Frank Smets: Yeah.

>> Speaker 4: A number, what would that be? I was curious.

>> Frank Smets: For the last period, you mean. I mean, that's basically, I think here.

>> Frank Smets: No, we don't do. I would have to calculate it. But no, a big part would be the black part.

 

>> Speaker 4: Yeah.

>> Frank Smets: Because actually the fiscal shocks, all the effects are fiscal inflation. So that's for sure. So if you didn't have that, then.

>> Speaker 4: I mean, even the transmission wouldn't happen.

>> Frank Smets: Yeah, okay.

>> Speaker 4: Yeah, okay.

>> Frank Smets: Yeah, okay? We talked lots of things to do. Has it changed over time?

Is it dependent on the type of shock? How robust are the results with respect to tank models? Actually is the degree here. Again, it's a linear framework.

>> Speaker 4: Yeah.

>> Frank Smets: So it's symmetric. I've always talked about that in terms of inflationary effects, but actually diverse also happens. It's symmetric.

Any political economy would tell you maybe it's more likely that there's less fiscal backing when there's expansionary fiscal effects then. So we could try to look at that and then this is all a positive exercise. So I think it's an interesting question, but it's actually the optimal degree of fiscal backing.

And that will depend on also the other shocks of the economy.

>> John: I would just say from my conclusion is that, you see in us fiscal history, you see most of the big changes that start a big fiscal issue occur either in really hard times or in booms, coz in hard times needs are exigent.

So a huge number of programs get instituted that you have a hard time titrating them back or eliminating. And booms, the politicians, maybe. Economists too, tend to extrapolate and everything seems affordable until it isn't. So I think there's a political economy side to this that is going on simultaneously with what you're observing.

It's kind of interesting. One of the things I hadn't actually expected, because in the past I never really looked very much at fiscal, is that if you look at the variance decomposition which I didn't show, of the primary balance. So what actually drives the primary balance?

>> Frank Smets: This is the fifth line.

I mean, it's not really fiscal shocks. No, I mean, there's some contribution, 17%. It's not monetary, obviously, but it's basically the supply and demand shocks, as you would expect. Most of the variation in the primary balance is a response to supply and demand. That screams at you in the graph.

Primary surplus tracks the unemployment rate beautifully. Right, and of course, that has implications, again, for the fiscal sustainability. And that's, I think, why you.

>> John: Frank, it would be nice to do it also across frequencies. So if you could do the same variance, the composition in the frequency domain.

And just show us what is the contribution of different shocks, let's say, the persistent component of primary surplus and deficits.

>> Frank Smets: I think that would be interesting to understand if it looks a bit different. The one year surplus is gonna respond to unemployment.

>> John: Yeah.

>> Frank Smets: But the 20 year surplus is gonna respond to debt.

That right? We hope. Yes.