Let's go for the last session of the conference, the fourth session, which deals with monetary fiscal interactions. In the context of a monetary union, we have two very interesting contributions here. So the first one is going to be presented by Hushin B, from the Federal Reserve Bank of Kansas City, who is going to present the paper asset purchases in a monetary union with default and liquidity risks, which is joined work with Andrew Forester and Nora Trump. So Hushin, the floor is yours, you have 25 minutes. Great, thank you so much for having the paper in this wonderful conference. So this paper is, as I said, joined with Andrew and Nora, and we talk about asset purchase in the monetary union model with both default and the liquidity risk. So usual disclaimer applied here. So this paper is motivated very much by the policy discussions and the policy actions taken at ECB. As the members of the executive board have been discussing, the financial market fragmentation can impale the transmission mechanism of monetary policy. And this is particularly relevant for the euro area, when you have different countries, have different fundamentals and different institutions. So ECB has asset purchase programs to address the market fragmentation driven by different type of risk, default risk, liquidity risk, for instance, OMT rolled out during the height of the debt crisis, and TPI rolled out last year as the ECB raised interest rate. So the question we are going to focus in this paper is specifically how do default risk, when it interacts with the liquidity risk, impact the economy, and how used for asset purchase to counter them. So to answer that question, we're going to build a two-country monetary union model features both type of risk. And we're going to specifically look at one type of transmission at the moment is that when you have deteriorations in the macro fundamentals, that's going to drive up the default risk, and then that can speed over to have a liquidity risk through the financial market conditions. So what do we find is that through the lens of this model, we find that both type of risk can dampen the economic condition following the increase in government debt. But the magnifying effect from the liquidity risk is far more consequential, and therefore making the asset purchase market more effective in the presence of a liquidity risk. So let me dive into details with the model. It's a two-country model. In the home country, the government says tax and government expenditures, and they can issue debt. Now there is default risk in the sense that the government could default. And the default probability, so you can think about there is two regions, default or no default. And then the default probability follows the indulgence regime switching process here in the sense that the default probability is not exogenous. It depends on the state of the economy, depends on the debt of GDP ratio. The higher the debt is, the higher the likelihood of default is. And then there is financial intermediary, which will follow the Gutter and Karate setup. The household will deposit at the banks, and then the financial intermediaries will collect the deposit to buy the debt from home government as well as the firms. There is a liquidity risk in these channels that the tightness of the credit constraint can vary with default probability. I'm going to explain more as I dive into the details. At the moment, the foreign country is abstract from the segmented financial market. So there is no financial intermediaries as a standard model that the household will directly invest in the private firms and also directly hold the government bound. There is a union-wide monetary policy. There is Taylor rule. And the monetary policy could also purchase the government bound. And it's going to follow some type of rule as the financial conditions tightened that's going to trigger the asset purchase in this framework. So this is another way to visualize how the model looks at the moment. In the home countries, you have a household, flow the deposit to the banks, and the banks will purchase private debt as well as public debt. In the foreign sectors, it's simpler, and the household directly invests and also hold the government bound. There is capital flow between the two countries. So there is a common deposit rate in this monetary union. Now, let me start with the home government. The government collected tax, lump sum tax, as well as distortion tax, income tax, and the consumption tax to finance government spending. They also issued long-term government bound. So the Kappa B here is a decay. You can think about this coupon that's decaying over time to capture is a long-term government debt. And here we are going to assume that lump sum tax is going to respond to the change of the government debt. This is a simplified assumption that just to say we're going to allow the least distortion tax to respond to the debt dynamics. We could use the similar rules, distortion tax, it does not change the result much. Importantly, the government can default on the bonds and by taking a haircut. So there are two regimes here. They can default, take a haircut of a delta B or no default. And the default probability follows here is we take a logistic function and you can think of some kind of function form of the debt-over-GDP ratio and as well as macro conditions of the economy. So let me visualize that here. So the blue line shows in the baseline case as debt-over-GDP ratio goes up, the default probability goes up. And to the red line means that the deterioration of the macro fundamentals could shift your default probabilities. Therefore, the same level of debt that in more deterioration, the macro fundamentals could face higher default probabilities. So we don't explicitly model the decisions of when they default, but you can interpret this. The similar dynamics could arise in the model that you take those strategic decisions on board. This is simply to capture that the default probability is not exogenous. It depends on the fundamentals in some kind of systematic way. And the banks who hold those bonds understand that. And for other firms here, the wholesale firms, they issue a long term private bond to finance private investment. So this is not the friction in the model is that in a standard model, the household would be directly invest in the firms. Here, the firms have to issue a share of their, have to issue bond, which is on the right-hand side here, showing the net flow of long-term bond. Gonna have to issue this bond to finance eta i share of the investment. And they use the investment, the capital as well as the label to produce. That's standard. And we also have a home investment producer here. They assemble investment with the adjustment cost. And in the simulation, I'm gonna use that in the sense, if you consider there is a demand shock, how that demand shock could shift. Characterize that as a deterioration in the macro fundamentals, how that's gonna give rise to the default probability. The household here, they deposit in the domestic financial intermediaries. They also hold the one-period cross-region asset so that you have a union-wide deposit rate that is the same across two countries. And then we have the financial intermediaries. So first, they face a balance sheet constraint in the sense that at every period they're gonna collect the deposit, DT, from the household. And then they're gonna purchase government and private debt, BT and FT. And at their market value. And then they can also accumulate the net worth. So the net worth is gonna depend on the realized return on holding those assets. So when the government is gonna default and take a haircut, that's gonna reflect in the net worth of the bank. And that's gonna have implication for the bank dynamics here.  And if there is no survival rate, then what's gonna happen is that they're gonna accumulate enough net worth, they don't need to rely on the deposit. So we follow the literature that, assuming those firms, those banks, have a survival rate of a sigma. And therefore, with a one-minute sigma, they may exit from the banking sector and take the net worth with them. And we also assume there is an incentive constraint here, in the sense that the banks can divert a e to the v share of the asset. Therefore, that gives rise to the financial frictions here in those models. But because they can divert a share of the asset, so they have an incentive constraint, the value has to be higher than whatever the asset they can divert, otherwise the household will not deposit at the banks. And here we are gonna have introduced a liquidity channel. So the e to the v is a share of the asset they can divert. It's gonna vary with the default risk. And the higher the default risk, the e to the v is gonna go up. It's the highest share of the asset they're gonna divert. The binding constraint is becoming small binding. So the intuition here is that if you think of extreme case, that the incentive constraint is only occasionally binding.  Therefore, the constraint would be becoming binding, from not binding to becoming binding. So here we're not explicitly modeling the occasioning binding constraint. We introduce these liquidity channels to capture the dynamics in essence. So here at the bottom, we have the first order condition for the bonds. So for instance, the lambda v here measures the, is like a random multiplier associated with the incentive constraint. And the return on asset, the difference between the return on the asset and the deposit rate is the excess return. So if the constraint is not binding, this would be standard. There is no excess return. In this model, with the financial friction, the lambda v is positive. And therefore, the excess return is gonna depend on the, how tight your incentive constraint is. The tighter the constraint is, the bank is gonna ask for higher excess return for that asset. And those are adjusted for the leverage and adjusted discount factor from the bank's perspective. Okay, for the foreign economy, we abstract from the segmented financial market for now. There is no banks. So therefore, there is no default and liquidity risk as well. Households hold the gamut bonds, hold their own gamut bonds, and invest in private firms directly. The monetary policy at the union wide in the background, there is a standard Taylor rule. They follow the deviation for the inflation and output. That is weighted across the union. Importantly, we introduce unconventional policy of asset purchase, that the B, CB. So this is showing that at each period, that the monetary policy, the central bank, can go in the market to purchase the government debt. And the T here is whatever is either deferred asset as what happens now or the profit you make. And that, it's at the union level. And we assume that asset purchase is triggered by follow some kind of rule here that it depends on the excess return. So because excess return measures the financial constraint or how tight the financial market is, conditions is, the higher that spread, then the larger the asset purchase is. So it will capture that in the frame mechanism in the rule of perspective. So that is basically our model. And then now, oh, one more thing here. The solution, so because we have two regions here, you have a default, it's gonna take a haircut, the government, and then there is no, when there's no default, the haircut is zero. And there is some kind of probability, the transition between the two regions. And we also have a liquid channels, as I just explained, data V also depends on your default probability. So we solve this, we cannot solve the model by linearization, so instead we use the method by developed by Andrew and his co-authors. So those specific method would be geared towards solving those regime switch model that allowed the endogenous regime switch in the sense that the transition probability is not exogenous. All right, let me go to the result here. So the question we're interested is, how do default risk when interact with the liquid risk impact economy? And how does each channel contribute that impact? And also how effective asset purchase? So we're gonna start with a simpler case to say there is increase in the debt, therefore the default probability goes up and explain the transmission mechanism. And then I'm gonna show you a case that is kind of saying, oh, there is an active demand shock that leads to increased government debt. So it's one step further, but the underlying transmission mechanism flow through the same way as a simpler case here. So in a simpler case here, let's just think that there is a case of government debt increase by close to about 14%. And in this case, when debt increase, the government bond price declines. Now you have a higher supply, the government bond price declines. And then from bank's perspective, that tightens the balance budget, the constraint, therefore the private bond price also has declined. Basically they would have to sell the private bond to absorb the high government debt. And in this case you have the net worth is lower from the lower asset prices and the leverage is higher. And it's also drive up the excess return on the government bond. So basically we is in the higher leverage, we is in the lower net worth. What happens is a bank would ask for a high excess return on the asset in this titling financial conditions. And of course there are two extra channels that strengthening that dynamics here, one is default probability, which shows that at the bottom right here, as the debt goes up, the default probability goes up. So when the default probability goes up, the banks expect that they may take a haircut in the future that can further contributed titling conditions here. And also there is extra liquidity risk here, the channel, when the default probability goes up, the eta V also goes up. So the constraint that banks facing are even tighter because of the default probability. So there is a baseline in fact, there is default channels and then there is liquidity channels. And I'm gonna decompose that in a minute. If I do that, let me show you the impact on the real side. So the blue line shows a home economy and the dash is showing the foreign countries here. Because the banks has in the titling financial conditions, they sell the private bond actually, then the investment declines, take a pretty sharp declines here, 7%. And that leads to a low output and also because from the household perspective that they have a lower deposit in the banks and that their consumption could increase temporarily. But over time, because the lower output, the consumption also turns negative. Importantly, inflation for the home country in this case is increased because with titling financial conditions, it will raise the financing cost for the firms and that's inflationary. From the foreign countries, on the other hand, because there is a capital outflow from the home country to the foreign countries, therefore the investment is actually increased in the foreign countries and output goes up, consumption goes up. And that also has inflation goes up because that's more like a demand-driven. So even though the inflation increase in both countries, the underlying reason is different. One is from the supply side and one is from the demand side. Now let me decompose how the impact on the financial sectors, what is contributing to the default risk or what is to the liquidity risk here. So we hear that the blue line here shows the difference between the basement case, which is what I just showed you, against the case, there is no default risk, there is no liquidity risk. So you wanna think the blue line is basically, what is the default channel and the liquidity channel together contributed to the overall impact? And you can see here that in this case, the both channels lead to higher debt and the lower government prices and also they have a much lower net worth, therefore investment is lower, output is lower, excess return is higher, as the blue line shows here and inflation is also higher. Now interestingly that the red line is showing what is contributed by the default risk per se. And so you wanna think about the red line is the difference between the case, you have the default risk channel but they don't have the liquidity channel. And against the case, there is no default, no liquidity. So that is just the red line just saying, if you only have a default, you don't want to trigger the E that channels, what is the impact from that per se? And you see that it's qualitatively similar but quantitatively is much smaller that the debt is higher but the government bond price did decline but to much less extent and the net worth is declined but also to much less extent. So this is really highlighted that even though both channels could dampen the economic conditions but the really big impact is coming from the liquid channels from the banking sector. Okay, so then what we do here is that we say, now we introduce asset purchase in the presence of a two type of risk and we say how much the asset purchase could contribute like depends on which channels you have. Again, the blue lines you wanna think about how much a big impact the asset purchase could have if you have both channels in presence versus the red line here is showing you only have a default channels. So again, the asset purchase showed in the middle column here that the magnitude is would be different because it depends on the excess return on the government bond. And as I show you here that when you have both channels the excess return is much stronger when you have both channels. Therefore, the asset purchase quantity is a bit different. And so you see that with both channel play the asset purchase could really benefit could improve the output of our economy as net worth is higher. It's that of course it's boosting the government bond price. Therefore, it's improved the balance sheet for the banks that they did not have to sell as much private bond. It increased it's relative to the baseline case. It contains the scope. The investment has to decline and also contain the scope the output has to decline. And on the other hand when you only have a default risk of channel here the asset purchase is it triggers a smaller and that impact is smaller but it's really because the impact from the liquidity risk is much stronger than the default risk per se in this model. Okay, so before I go to the next exercise let me quickly summarize here is that as I said both default and the liquidity risk can dampen economic conditions here when you have increased government debt you have a high default risk but the impact from liquidity risk is far more consequential therefore the asset purchase becomes more effective in this case. Now we want to consider a negative demand shock to the home country. So you think here we can see the negative investment efficiency shock but it could be other shocks that just lead to deteriorations in the economic conditions and then therefore the government debt is increased and the default probability goes up it also shift the distribution that therefore that even for the same level of debt your default probability could be higher. So both channels is going to increase the default probability and also could have the tightening liquidity channels if that is present. Okay, so let me quickly go through this. You know it's a quantitative could be different but the qualitative is really assuming as what I just showed you. Right, you have when this is again the difference between the blue line is showing when you have both channels in presence you know how much both channels going to contribute to the economy versus you don't have either channel and the debt is going to be higher government debt price is lower and investment is lower versus you have only have default channels that is much more content the scope. And again asset purchase similar as a simpler case that the asset purchase is more powerful he has much big impact when you have both channels in place. So let me conclude. So at the moment what we have is we're showing that when you're having a case that the default risk leads to a liquidity risk and we show the magnifying effect from this liquidity risk really appears to be far more consequential and therefore asset purchase it seems more effective. So next step what we would like to do is that introduce the financial intermediary to the foreign country block. Therefore we could explore more about the cross countries be over through the financial channel at the moment that we only have the trade channels. And you potentially could ask a question is that what if you have a union water liquidity shock how that affect countries with a weak macro fundamentals. So with that. Thank you. Thank you very much. We've seen also for adjusting so well to the time slot. So the discussion is going to be provided by Anna Rogantini Pico from the ECB. Anna you have 15 minutes. Thanks a lot for letting me participate in this great conference and discussing weeks in papers. So let me start first putting the paper into the Euro area context. Prompted by crisis of various nature the ECB has put in place a variety of policy tools involving sovereign bond purchases. In 2012 at the peak of the sovereign debt crisis it announced the outright monetary transaction in 2020 to address the pandemic emergency the pandemic emergency purchase program was set up announced and implemented right away. And just a year ago in 2022 the transmission protection instrument was announced to address fragmentation risks and help the transmission of monetary policy. Well some of these policy tools have been activated like the PEP others have only been announced and this has been enough to calm things down like the OMT for example but in all cases the big challenge for policymakers is really to understand how two risks the sovereign risk and the liquidity risks which are at play together how they interact and they reinforce each other. And when we have a better understanding of this of course how this asset purchase is done by central bank can facilitate a smooth transmission of monetary policy when the two risks are at play. So this paper really is an extremely timely contribution to the policy debate on how to think about sovereign and liquidity risk and their interaction. So the paper in a nutshell so the big contribution is to jointly model the fault and liquidity risk in a two country monetary union set up and in particular the fault risk is endogenous in the interim regime switching process that depends on debt to GDP and on macro fundamentals. And the second important ingredient is liquidity risk and that stems from financial market segmentation meaning that households can't directly buy bonds but they have to do that via intermediaries which are constrained. And so that generates friction with this amplification channel. So once the model is set up with these features then what Hook's seen has shown us is a quantitative assessment of the relative importance of these two channels in response to an exogenous rise in government debt. And in particular the direct effect of sovereign risk turns out to be moderate but what is really quantitatively more significant is the amplification coming from liquidity risk channel. So given these two channels at play if we want to evaluate the effects of sovereign debt purchases done by the central bank because the stronger amplification comes from the liquidity risk then it turns out that the asset purchases are most effective in dampening precisely this channel. And so they're more stabilizing when there is liquidity risk which amplifies sovereign risk. Government purchases would be effective also in absent of this amplification effect but the effect would be less strong. So the plan of the discussion is first to zoom in the main ingredients, the sovereign risk and liquidity risk and then thinking about whether this is really a model for OMT or TPI which direction of propagation which should think about and explore and thirdly on the spillover effects across countries. Okay, let me start from Indogenous Default Risk. This happens in the home country. Remember this is a two country setup but sovereign risk only happens in home country. And so there is a haircut that the GDP, when the GDP ratio goes above a given threshold, BSTAR. And it's Indogenous because there is a probability that the GDP is bigger than its threshold which is dependent on two things. One is macro shocks. And the other is debt to GDP ratio. The second ingredient that is important is this liquidity risk channel and this is modeled adding a friction a la guerre d'encarradie and more recently Sims and Wu. And here, so financial markets are fragmented because as I was saying, households can't directly purchase bonds but they have to do it via intermediaries. But these intermediaries face an agency problem in the sense that they could run away with their assets. So there must be an incentive constraints for them not to do this. And so that's the incentive constraints. The value of the intermediary has to be non smaller than a given share of the assets that they hold. And this is both private assets and sovereign bonds. And what is important is this ETA, this share that can be thought of as credit tightness. And what is important for the amplification channel is that this ETA is gonna be a function of the default probability. So this is what connects the sovereign risk to credit market tightness. And so in particular, if this parameter phi is zero there is no amplification effect coming. So the default risk is not gonna make financial markets tighter. But if this channel is at play, then an increase in the default probability is gonna tighten the constraint that the financial intermediaries face. All right, so then the, well, this liquidity risk channel amplifies sovereign default risk at Bocola 2016. So now to my first comment, is this a model for specifically OMT or TPI? So here I reported the description of TPI in the ACB statement. And it says that the Euro system will be able to make secondary market purchases of securities issued in jurisdictions experiencing a deterioration in financial condition, not warranted by country-specific fundamentals. So we all know how hard it is to really identify the cause of the deterioration in financial condition in practice. But this can be done in a model. That's I think why we have models for like to fix ideas and think more about how we can decompose the two. And so I was thinking about the amplification channel that is activated in response to micro shocks or fiscal shocks. So at the moment, what you've shown us is an exogenous increase in debt to GDP. It would be this S, T minus one here in the, which is gonna increase the probability of default and so tighten the financial markets. But this, like the model at the moment is kind of silent about what drives this exogenous increase in debt to GDP. It could be driven by fundamentals, worsening, but it could also driven by beliefs that just move. And here I'm thinking about, I don't know, the Calvo model or more specifically to apply to the Euro area, Corsetti and the dollar 2016. So I was wondering whether if we wanna think of your model as a model for TPI where the central bank can intervene only if this increase in the excess return is not warranted by country-specific fundamentals but it might be belief-driven, well, can really the two drivers of this increase in debt to GDP be disentangled. And even if we think about OMT, the mere announcement of OMT was sufficient to actually rule out this belief-driven fluctuation. So I think if you want to target your model more specifically to some tools that the ECB has or central banks have, it will be nice to think more about the drivers of this increase in debt to GDP. My second comment is on the propagation of the shock. So at the moment, you've mainly focused on the amplification going from sovereign risk via this liquidity risk channel through to a tightening in credit markets. But of course it depends a bit on what crisis you have in mind when you model. But I think your model allows you to also think about the opposite direction of amplification. Everything is already there. And if you think of the past crisis, well, we had credit crunches which actually triggered sovereign debt crisis. So if I think of the ingredients that you already have, this would mean an increase, like a credit tightening that triggers a contraction in the economy. Because you have endogenous default risk, this would lead to a drop in debt to GDP ratio. And so it would trigger an increase in default risk. And so you would have this feedback loop. But the trigger would start in the financial market and move to the sovereign market than the other way around. And I think because you have these both channels and both directions of propagation, I think it would be nice to look at both directions and not only one arrow, let's say. And finally, my third comment is on how you could leverage more the two countries setup. But I saw from your conclusions like that you're already thinking about this, so I'm very glad. So at the moment, all this amplification effect going from sovereign risk to credit markets, we would have it also in a close economy setup so you don't really need a two country model. But I do think that having a two country model is valuable, especially if we wanna think of the Euro area and the ECB policy tools. And so at the moment, the two countries are connected via imports. So consumption and investment baskets are made of domestic and imported goods. And there is a one period nominal bond which is traded across countries. So this allows you to look at the spillovers of an increase in the home country default risk to the foreign country. But let's now think about the crisis that the Euro area had been through. And if we think of the sovereign debt crisis, there was a huge exposure via the banking sector from one country to the other. I'm thinking here of German banks, for example, being exposed to a Greek sovereign bonds. And so I think in your setup, it would be really nice if you could model these spillovers more directly, having a segmented market also in the foreign country and having intermediaries in the foreign country directly being exposed to home sovereign bonds. Now you can only look at the macro consequences, but you don't have this direct spillover via the financial markets. And here what I'm thinking about would be having, like model intermediaries also in the foreign country as be subject to these incentive constraints and having them holding not only foreign country bonds but also home country bonds. So in conclusion, I think it's a very nice framework that connects sovereign risk to credit tightness and allows you to study the propagation of shocks of different nature. And in particular, it's a model that features endogenous sovereign risk and liquidity risk channels that amplifies sovereign risk. And there's a very nice technical contribution as well because it's challenging to solve these regime switching models and you do with the machinery of Andrew, I guess. So my comment is maybe one big comment is like, now you've built this very nice model that you can use as a laboratory to think a bit more precisely about which crisis you wanna model and as a consequence of which shock. And in particular, I would try to really think whether the increase in data GP is driven by macro fundamentals of by shifts in beliefs because then the policy tool that can be activated can either be activated or not. So it would be nice to see what are the differences. And then I would think more whether the crisis originates in the sovereign debt market or in the private credit market because you can get amplification in both directions. And finally, I would, because we are thinking about the Euro area, I would try to think harder about the spillovers from one country to the other also connecting the financial sector more. Thanks a lot. Thank you. Thank you very much, Anna. I would suggest now opening the floor for questions and then probably Heshin, you may want to address also some of the comments made by Mariana to whether we further points and questions. So Klaus, Leo, Sujit. Yeah, thank you. Thank you for the great presentations and discussion. I would like to take a step back, thinking about the overall framework or setting. I mean, your model nicely shows that if there is a fundamental shock, the problem results from the fact that banks hold government bonds. A lot of government bonds, I would suppose, and that these government bonds are not in investment funds or directly held by households. So that means now there's a reason for the center bank to intervene. Now, if there was better regulation which would reduce the amount of bonds, banks are allowed to hold from their domestic sovereign to reduce the doom-loop risk potential, that would be less of a need for QE or TPI or OMT to step in into such situations. Now, can one think that banks and regulators are not ignoring the signal sent by, say, TPI? Could it be that banks say, oh, there is somebody who will step in as you describe in your model, even in a fundamental shock because it spills over into a liquidity shock, and say, okay, I have less need to de-risk my balance sheet. I have less need as a bank or as a regulator to tell the banks that it's perhaps not good to have too many sovereign bonds of their own domestic sovereign on the balance sheet. And if these incentives are created by the center bank, I would wonder how far we are away from this wonderful paper by Fari and Tiro, 2012, which was called Collective Model Hazard and Bank Bailout or something like this, or is it not exactly what the center bank may induce what Fari and Tiro have written 10 years ago? Thanks. Let me first say, I find this paper really very, very interesting and helpful also for us to understand better what could be done. And this amplification channel, I find it simply convincing. If it's there, if you not have only default risk, but liquidity risk, Klaus explained, maybe we could discuss why we have reached this point, but if this is strong in the financial system, it makes intuitive sense that central bank purchases will be more effective in mitigating risk. Now, my question is the following. Let's assume for a second, there is not this amplifying liquidity risk channel, just default risk. I mean, how do we have to model to design central bank purchases of debt? So not unintentionally, we may make default even, even more likely. And there are, you know, there are very simple points. For example, as the bonds bought by the central bank senior or perceived as being senior, this can make a residual debt held by private investors more risky. This by simply through a poor design could destabilize the system. In a monetary union, there are these important aspects of risk sharing versus non-risk sharing. Do we create free writing incentives to default on taxpayers from other countries or not? So all these things, I think for this, you need to have a different setup, but they would matter, so to speak, to understand how we address the underlying problem. And then on top of this comes a channel which you so nicely describe. Oh, sorry, Sujit, you may want to address these points, Hushin, and then we take a second round of questions. Sure. Yeah, thank you. Let me start with Leo's question. So yeah, that's an important question, is that how does asset purchase will change the bank's incentive in terms of, you know, it's related to cross-question about, you know, whether they should even purchase or having those risky government bonds? It's a little bit out of the scope of this paper because we are taking as, you know, the default, of course, the probability is endogenous, but we don't model that incentive, right? In the sense is to really address your questions, you have to model when we'd like the default. And in reality, of course, there is a willingness or to pay back like that. There's also political factors there. And I'm very sympathetic to your point, but there's a little bit out of the scope of this question and we acknowledge that. And going back to the first question is that the regulation. So that's gonna be like, ultimately say what's the optimal determination? Like who should hold those, taking, let's assume that the government debt, those coming debt is risky, who should hold those debt, right? So it's against a little bit out of the scope of this model because, you know, like, regardless, you can think about the framework, right? Not just all banks holding it. Like a household could hold in some of the bonds, but then you need to introduce some kind of friction in the sense that, you know, when they intermediate in those bond market, they maybe have some not as efficient as a bank. So therefore, there's some adjustment cost. That can be done. But again, when those households they have, has a haircut, there is consequence as well, right? So in terms that the model perspective, that's not gonna change a whole lot of who's holding that. But I think it is important question is that, ultimately, who should hold those risky debt? If you are thinking that it is risky and there's no, maybe the best answer is to make it less risky, but that's of course, it's another questions for itself. Going back to Anna's point, I think I very much agree with all your discussion. Thank you again for those comments. And probably as you can see that the paper is somewhat not entirely complete, that we build this infrastructure, right? That can do more. At the moment, we really focus on how the default risk is gonna channel to the liquidity risk and then the response from the central bank. But that's why I was saying the end is that we could have the foreign economy also have the banking sector and then really build that the interaction between the financial friction, financial sectors and to address that, you know, you could say how the liquidity risk affected the default and how to leverage these two countries set up at the moment is a little bit, I mean, I have to say that the fact that you have two countries, right? So when the domestic financial condition tightens, you have capital outflow. So there is some level of those impact that kind of further constrained the domestic if you think about the compared to the closed economy, but for sure it's not fully leveraged the framework. And that's something we tend to do as an extra step. So we have three minutes for three questions starting from the right, so you get a bit more than two from the left. So please try to be concise. Thanks very much. It's a similar to a starting point of Klaus, but what if you just tightened liquidity regulation in the model, would that not reduce the need to have asset purchasing purchases? Thanks. Yeah, and I would like to follow up a bit on the comments by Anna. And I'm wondering whether the relative importance of the default risk relatively to the liquidity risk could be affected in a situation where we have a sudden stop that suddenly increases the default risk of a country for a given level of debt? Yeah, also leveraging on Anna's discussion. To what extent does the introduction of asset purchases reduce the probability of switching to the, if you want, bad equilibrium? Because in a sense what you show us is you need very aggressive asset purchases to intervene once a shock occurs. But in a sense, what Anna also mentioned, the specificity of OMT and TPI is it's introduced and in a sense it provides an insurance and if it's credible, it may never need to be activated. And so to what extent can you capture some of this by, for example, reducing the adverse liquidity effects of a shock occurring because something is in place, but it may not need to be used. The second comment relates more to the instrument choice of the central bank, because given that liquidity risk is so prominent, you could think of liquidity providing facilities like the FATS BTFP, no way. You lend against collateral without haircuts at power value and so in that sense you would shield at least the banking sector and that relates maybe to comments by others. It depends a lot whether in your model you have one type of financial intermediary and let's call it a bank, but if you have non-banks, then of course, you would have a difference between asset purchases and liquidity providing operations. So as you know, I'm a great fan of this research of yours. A question that perhaps you will want to consider at some point if you have not done it already is how precious it is to have in the financial system an asset that can truly be regarded as safe and compare the overall performance of the model with such a financial system with one in which sovereign debt is indeed full of default risk. Great, thank you so much for all the questions and it definitely provides a lot of food for thought and the way further explore those framework. So there seems to be some questions. So let me start with a sudden stop. Yes, so I think the relative like smaller impact for default risk in this model is that it's already assuming in a sense if the banking constraint is already binding the extra impact from that potential haircut is small but you absolutely right if you have occasionally binding consent from financial intermediaries you as you know, it's captured by the ETAV, right? So you want to think that ETAV, why is it so powerful is because it captures how you could making the constraint much binding therefore that impact we really try to highlight that is why the impact is so big but if, but once the constraint is binding the extra impact from the potential haircut is fairly small. So that's kind of what we show in the model and then for the vitreous point of asset, yeah so if we're gonna have like cross country asset holding like the banks could hold in German bonds then we could have that, we could address that that we could compare how, for a baseline case how that impact and then to Christopher's points about the announcement effect, yes to address that we would really need to take a word and we're saying that you would have like some belief driven not a fundamental driven, right? You have some, even there is no deteriorations in the necessary in the macro conditions or but there is some beliefs about driven so therefore the announcement could have a big impact on it. We could probably think about that some of that a news shock, you know like okay you have announced something's gonna happen will it potentially happen in the future and to see how those news effect affect the dynamics. We have not done that yet but that's a good point and the liquidity providing, yes that would be I guess I don't know whether in this framework necessarily gonna impact is gonna be different even though you know so BTFP you have collateral you know you can basically get the money from the Fed using the collateral as without a haircut. Instead of saying you're gonna purchase the asset that's gonna boost the asset price therefore you are in the bank in a better position with the asset quantitatively I'm not sure whether it's gonna be different but that's certainly something we could try to explore in a sense different programs how that affect the impact. And the tightening the different liquidity constraint or you know like different regulations in the banks that would be so the incentive constraint in the banks some people would interpret that as a bank regulations. So you could think about it you could probably have something similar to say okay what if you're gonna penalize the asset that has haircut versus in terms of the regulation versus if you have a safe asset you don't penalize that that's something we could explore as well. Thank you so much. Thank you, thank you very much. We've seen enough for a very, very good presentation and discussion. So next on the list is Francesco Bianci from Johns Hopkins University who is going to present the paper fiscal influences on inflation in OECD countries 2020, 2022 which is joint work with Robert Barrow. So Francesco, what is yours? First of all, thank you for having me and given that I'm the last speaker of the day let me take this opportunity to thank the organizers for this great conference. So this is a joint work with Robert Barrow and what we are interested in doing in this paper is to understand the cross-sectional inflation episodes in the post COVID period through the lens of the fiscal tier of price level. So this is mostly Robert speaking the first two bullet points. So this theory has been around since the early 90s and like Robert is saying here it wasn't taken seriously by mainstream macroeconomists for a while mostly because there was a little bit of the understanding or at least the notion that inflation was mostly under the control of the monetary authority and it is probably close to the truth for the period from 1980s to 2020. So somebody might argue that maybe the 70s can be interpreted as fiscal inflation but in recent years central bankers economists really thought about inflation as the result of monetary policy action. However the post pandemic inflation associated with this large increase in deficits led some macroeconomists to look a bit more closely at the fiscal tier of price level and one of them is Robert and that's how we got to work together. So in particular what we're going to do in this paper is to think about the cross-sectional evidence on 37 OECD countries over the period of 2020, 2022. So really in the aftermath of the pandemic and we are going to, as I was mentioning in the beginning do this through the lens of the fiscal tier of price level but I would say in the bare-bone version of the fiscal tier of price level. So you will see in a moment we basically try to be as model free as possible and really think about a frictionless environment with no nominal rigidities. And the idea is that this allows us to get to the essence of the fiscal tier of price level while in some of my previous work you need to buy perhaps other assumptions with respect to nominal rigidities or other kind of frictions. So in a nutshell you can think about the fiscal tier of price level has stemming from these government inter-temporal budget constraints that is effectively an accounting identity in itself. The fiscal tier of price level thinks in a different way how this accounting identity can hold. And so on the left hand side you have the market value of that in real terms. And this has to be equal to the present discounted value of future primary surpluses. So these movements in primary surpluses can potentially lead to movements in prices and in richer versions with maturity structure can lead to movements in expected inflation. Okay, so as I was saying, so in this paper we try to make a series of simplifying assumptions to get to a very simple econometric exercise. What I would like to emphasize is that there are a series of simplifying assumptions but qualitatively you're not losing anything from making these simplifying assumptions. They simply allow you to look at the data in a much simpler way than you would be able to do otherwise. So what are these simplifying assumptions? So the first one is that we suppose that there are M periods, think about the post-pandemic episode during which governments spend significantly more than what they would have done otherwise. So think about a pre-pandemic trend that would tell you how much governments typically spend so we can measure the excess spending as a result of the increase in spending observed pre and post COVID. Then we assume, and we had I think a long discussion about this yesterday, we assume that the growth rate of the economy is equal to the real interest rate. Again, here what you need is that this is not particularly important for what we are doing. So as long as they are similar, you will get a similar approximation. We are going to assume that in response to this increase in spending, there is the possibility of a temporary increase in inflation over the target, the last capital T periods. And here capital T also coincides with the maturity of a standing debt. And then finally, we assume a particular maturity structure for which nominal payments grow with the economy, with nominal GDP. So if you make the simplifying assumptions, then the nice result is that you get a very simple functional form in which on the left-hand side you have the increase in inflation with respect to the pre-pandemic experience. On the right-hand side, you have a fairly intimidating term that is the increase in spending divided by the real value of the debt-to-GDP ratio and the average maturity structure of outstanding debt. So it doesn't take, I guess, much to think why the first term is there, why the increase in spending is there. It is sometimes a bit less intuitive to understand why the real value of debt or the maturity structure should be there. And I'm going to talk about that in a moment. But so notice that there's this coefficient eta. So in the extreme version of the fiscal price level, this coefficient would be equal to one. In the extreme version of record and equivalence, this coefficient would be zero because any change in spending today is expected to be undone by future changes. So what we're interested in is trying to understand what is in the data, at least with respect to the post-pandemic experience, this coefficient eta. So as I was mentioning in the beginning, for a long time the inflation was really perceived as under the control of the monetary authority. Another way to say this is that perhaps during regular times, inflation is not so much related to fluctuations in the present discounted value of spending. And so you might think that what happened with the pandemic is that we had a sort of emergency budget for which there was the understanding that we were not going to increase taxes following these large fiscal stimulus. And so this is related to some older literature by Lucas and Stocchi in particular with respect to wartime financing. But more recently, Sergeant and his co-authors have a paper in which they draw the parallel between the post-war war experience and the post-pandemic experience. They basically do a series of, they draw a series of parallels between what happens following a war and what happens following the pandemic. And more modestly, I also done work on this topic, showing again that you can think about the post-pandemic inflation as the manifestation of an emergency budget or what we call it in our work is an unfunded fiscal shock. But long story short, while during regular times, you might think that inflation is perhaps coming from business cycle dynamics or other events. So there might be some key moments in which inflation might actually be really related to expectations about how the government is going to finance a large increase in spending. Okay, so as I was saying, let me explain for a moment why we have the different terms. Okay, so the first term is the size of the fiscal stimulus itself. And that's exactly what you would expect beyond the fiscal price level. So this idea that if you have a larger fiscal stimulus and possibly some nominal rigidity, that might eventually lead to inflation. So what makes this functional form a little bit different from this basic Keynesian thinking is the role of the other two terms. So the first one is the amount of outstanding debt. So if you remember, this term enters in the denominator. So what that means is that for a given fiscal stimulus, the larger the amount of outstanding debt, the lower the increase in inflation. So why is that the case? Well, because if you think about inflation as a form of financing, the larger the amount of debt that is currently outstanding, the same amount of inflation is going to generate more revenues because you are essentially inflating away, roughly speaking, a larger portion of accumulated debt. And before the maturity structure, the maturity structure here plays two roles. The first one is that if you have an outstanding maturity structure, you can smooth out the increase in inflation because by smoothing out the increase in inflation, long-term nominal interest rates go up and these devalues the current amount of outstanding debt. And more in general, the longer the maturity structure, the stronger these revaluation effects. And so unlike what you would expect from the simple Keynesian intuition, these two terms play an important role in our empirical results. Okay, so the other important event that on top of COVID, on top of the fiscal stimulus that occurred over the relevant sample is the Russian aggression of Ukraine. So we control, we try different things. We try to measure the distance from the border with Russia or Ukraine. We try to control for the trade relations between these countries. But it turns out that the one that seems to work the best, and I guess that's a fact of life, is the simplest thing. So to simply have a dummy variable for the countries that are on the border with Ukraine or Russia. So in our empirical analysis, I'm going to show you two sets of results. One is let's say the basic specification based on the relation that I show you. And another one is a relation in which we add, it's a regression in which we add a dummy variable if the countries under examination are on the border with Russia or Ukraine. Okay, so the countries that we are looking at are the 37 OECD countries except for Turkey that as you probably know, has been all over the place even before COVID and arguably for reasons that are not really related to the pandemic. So this gives us 20 countries outside the Eurozone and 17 countries in the Eurozone. So for the Eurozone, I'm going to show you two sets of results. In the first set of results, we are going to treat these 17 countries as a unique economy consistent with the fact that they have one single currency, but also consistent with the fact that they are fairly integrated with each other. And then I'm going to show you another set of results in which we also control for the amount of spending that occurred in the different countries. We are going to look at both headline inflation and core inflation. And as I was saying, we are going to look at with and without these Ukraine-Russia border. And we are going to look at what is interesting for us, what is interesting for us is the estimated coefficient eta. You can think as the share of spending that is financed by the surprise in inflation. Okay, so this is our core results. As I was telling you, the advantage of doing a little bit of work ex ante through this series of approximations is that then the econometrics is very easy. So that's a little bit different. As I was saying from other things I've done in the past in which you take the model at face value, but then the econometrics become a little bit more complicated. So here essentially what we are doing, we are regressing the change in inflation, post and pre-COVID, on the size of the fiscal stimulus rescaled by the amount of outstanding debt and the maturity structure and the average maturity for each country. In the first two columns, you have headline inflation. In the third and fourth, you have core inflation. In column two and column four, we control for the border with Ukraine. So as you can tell, these coefficients are all strongly statistically significant. Etta, that is in the second row, let's focus in the interest of time on the case with which we control for the Russian border. You can see that the coefficient is statistically significant and around 0.4. It gets a little bit closer to 0.5 when you look at core inflation. And interestingly, also the border dummy is a strongly statistically significant. And if you look at the R-square in column two and column four, you find an R-square that approaches 80%. So that means that a fairly large fraction of this cross-sectional variation can be explained by the combination between the fiscal stimulus and the Ukraine-Russia conflict. As you can see, the coefficient on our composite government variable, government spending variable doesn't change. Significantly, with and without the border, especially if you focus on core inflation, what it does is really is able to explain why a couple of countries that are on the border with Russia or Ukraine experience significantly more inflation than what can be justified just by looking at their spending. So this is essentially what I just said. So, as I was saying, we look at both the euro area and the US and for the euro area, what we find is that both measures of inflation and spending are slightly below the United States. Interestingly, both economic areas are very much in line with the rest of the world but in the middle of the pack, so to speak. So there are no outliers in any direction. And when you plot the relation between our composite government spending variable and the change in inflation, you get this very nice relation that doesn't show any particular outliers. Again, controlling for the border with Russia or Ukraine. So you see that all countries line up on the diagonal. You see it in the middle euro and the euro area and the US are really like in the middle, both in terms of spending and inflation experience. So if you do, as I was saying, we can also do this for core CPI and the results are essentially identical at least visually. So as I mentioned to you, we treat the euro area as a unique, oh, sorry, I was jumping ahead. So as I was mentioning to you, the components of our government spending variable all have a theoretical interpretation. So there is a reason why they are in there. So something that we try to do is to assess if any of these components is disposable. So in other words, we took our same model and we restrict, let's say, the maturity structure to be equal to the average or the amount of debt to be equal to the average or the amount of spending to be equal to the average across countries. So as you can imagine, it doesn't take much to guess that restricting the amount of spending is strongly rejected by the data. But what it was interesting for us, and to some extent also a little bit surprising, is that even if you try to restrict the amount of debt or the maturity structure to be equal to the sample average, the model is strongly rejected by the data. So what it means is that if you do some kind of model comparison, you would always put something like at least the 99% weight on our baseline model in which government spending is rescaled by maturity and outstanding debt versus the alternative. And if you consider the model in which you simply do not control for any of these two variables, the model doesn't work that well. And we believe this is actually interesting because again, you can think about a new Keynesian story, a Keynesian story in which more spending leads to more inflation, but then that doesn't seem to be working that well. In the sense if you consider a regression in which you regress the change in inflation on the amount of spending across countries, you actually don't get any meaningful results. Okay, so as I was saying, I jumped a little bit ahead. For the eurozone, we also try to see whether the amount of spending in the individual countries was an important determinant of inflation. So we did this in multiple ways, but let me just tell you the one that made the cut for the paper. So we have our baseline regression, but now with a very simple variation. So instead of having one economic area for the whole euro area, we consider all single countries individually. And for these countries, we have the amount of spending for the whole euro area. And then, and you see this in the third row, sorry, I was going to point to it, you see this in the third row, for these countries in the euro area, we also control for the difference between the country level spending and the euro area average. So that's the third row in this graph. So again, in the interest of time, let's just focus on column two and column four. You can see that if we look at headline inflation is mildly statistically significant. If we look at core inflation, that arguably is the cleanest measure when it comes to this idea of spending leading to higher inflation. The reason why I think it's cleaner is because it removes energy prices effectively. You see that the country level amount of spending is not statistically significant. So this is actually important because it's basically saying that for the euro area countries, the amount of inflation that you experience is largely determined by the euro area level of spending. And this is in fact consistent with the idea that the fiscal theory of price level should apply to the whole euro area and not just to single countries. But again, it wasn't obvious to us. And mostly because the euro area is not like the United States in which there is a very well-defined fiscal authority and a very well-defined monetary authority. So we thought that that was interesting. And again, as before, for the euro area controlling for the border with Russia or Ukraine is actually important. Okay, so if you wanna visualize this, thank you. If you wanna visualize this, so here the orange, gold line is our baseline. So what is implied by the aggregate level of spending? And so if you just control for the country level of spending, you get the blue line that in the case of core inflation is essentially horizontal. Okay, it means that it doesn't really contribute to explain much of the variation in the euro area levels of inflation. So I'm actually essentially done. So I'm a little bit ahead of time but nobody ever complained, especially not for the last speaker of the day. So what we did in this paper is to think about the fiscal stimulus implemented in response to the COVID pandemic and try to think about the inflationary consequences of these fiscal stimulus through the lens of the fiscal price level. As I was saying, we made a series of simplified assumptions that again, I wanna stress out that they don't change anything qualitatively, they just give you a very neat empirical relation that you can easily test in the data. And we applied it to OECD countries. So we are currently collecting more data to see if we can apply the same exercise to more countries. And what we find is that in fact, there is a strong relation between the amount of spending, once corrected for the outstanding debt and the maturity structure and the inflation that these countries experience. The other particularly interesting results given that I'm at the ECB is that for the 17 Eurozone countries, it seems that what really matters is the amount of spending for the whole Euro area. What we find is that the coefficient for this amount of spending is statistically significant. It's around 40, 50%. So there are two ways to interpret this. The first one is that the remaining part is going to be financed by future increases in taxes. The alternative interpretation is that part of the financing came from a rebound of the real economy, possibly triggered by the increase in spending. Thank you. Thank you very much, Francesco. So the discussion is Luis Garricano from the LSE. Luis, you have 15 minutes. I joined Francesco in thanking Stefania and Natasha and Jacopo and the Mostoners and Bastos and Leopold and Nico for the organization. It was a great time, a great conference. Thank you very much. So very fascinating exercise and interesting paper. I really enjoyed working through it. Let me just start with the most obvious, but just it needs to be said, which is that the fiscal fear of the price level doesn't say that fiscal deficits lead to inflation. So it's something that people tend to think and they talk about Japan, et cetera. It's not about that and that's not indeed what the paper claims that the paper does. That's a very good job, but I just start with this so that it's clear what the theory says is that fiscal deficits that are unfunded or there is an expectation around unfunded will not, will lead to inflation. The ones that are not funded by spending cuts and taxes are lower interest rates. So economic history says that the sergeant's been doing a lot of work on that or tells us that open happens in wars. It also, John Cochrane shows in his book that in normal times we do see that surpluses usually happen as a corresponds to deficits in normal times. So this distinction between normal times and special times is one that Barbara and Bianco and Bianchi and Francesco leveraged here and they say, look, inflation and fiscal deficits might not be much related to normal economic times but could be closely collected in unusual events which makes a lot of sense. There's a current QJA paper by Marco Bassetto and David Miller which has these two regimes and M regime and F regime and basically the arguing, look in the M regime you're far from the constraint from the moment where people start to panic. So basically whatever happens with government deficits not going to have any fiscal consequences whereas in moments where you are close to that to that moment when the curve starts shooting up there is going to be information sensitiveness. People are going to be talking about it. They're going to be doing Google searches. They show there are increased Google searches and the risk is going to be that these deficits will show up in indeed in price raises. So here what we have is not, I mean basically the model would give you with complete flexible prices, the one of shock in the price. Although as I had to read it was the use, the expression it was using yesterday with me was like what we thought was not inflation shock but a price shock. So it's very much what it appears in the theory. In this particular version of the theory in order to account for the fact that inflation staggered over several years you could think of sticky prices. You could think of, okay, well, we could just think of one period which is the three years of inflation. Here what happens is there is long-term debt so even with flexible prices you're going to have higher inflation devaluing today's debt, tomorrow's debt and little by little I'll show you that later. So they get a very simple equation and you can think of it as, if you think of just the OLS as just basically measuring the rise in the price level divided by the initial surplus shock is going to give you the fraction of the debt that is not paid by the subsequent surpluses. So it's a nice use of the fiscal theory to understand this important empirical question. I think it's the right framework because we're talking exactly about this first order prediction of the theory. The findings are consistent with the significant impact of the COVID shock and indeed as you saw the numbers are 40 to 50% unbacked. So the model just, I will not go through equations. I think if I just could tell you what the basic ideas are. You have basically an equilibrium condition. I'm not going to enter into this division. John Cochran heard the pilot constraint. You know, he hates that, but this is to the eye of the beholder here. We think of an equilibrium condition. The net present value of the government real primary surplus must be enough to finance this stock of private debt. So in the right, you have real surpluses. In the left, you have it. I mean, the P is you could put the P in the right to make it nominal. So with no government revenue increase, they're going to just simplify by looking at G then assume G equals to R and work through in the value of the debt.  So you just work through that. Simplified Taylor expanded, get rid of the terms that get small and you get this pretty equation, which is the one at the bottom, which says that the sum of the primary deficits over GDP divided by the initial stock of debt is going to be related to excessive inflation. The paper has this kind of extra twist, which is because debt has this maturity structure, the fiscal shock is not going to give you one of jump, but it's going to give you jumps over time. So you're gonna have this, the notation is from John Cochran's book. You're gonna have this at every maturity, you're going to have some drop in the price of the bond that is given by how much the price level is jumping up. So how is that inflation arrived? Well, the monetary authorities accommodating or generating the chosen time path level of inflation. So they're going to take it to the data. This is the formula, the inflation rate reacts to a community search. I think everybody sees that from the formula. There's a slope that measures the amount of unfunded debt and probably it should be part of the model from the start, if possible. So there's the hypothesis which you can test that this time is different. You could have the h equals zero and then everything is as usual or you could have a positive eta which tells you we're in a war pandemic situation. The inflation increases larger, the bigger baseline of debt GDP. Francisco pointed this out, I'll talk briefly in my comments. And the debt maturity, this is more straightforward so I wouldn't discuss that. Debt maturity is going to mean that the higher debt maturity with a little increase in inflation, you're going to soak up more of the debt, get rid of more of the debt with less inflation. So that's actually giving you lower inflation rates with the same G. So the empirical strategy, the authors called old school econometrics which I like because I'm old school. So they just have the inflation differential regress. I mean, you could just see the paper as, hey, what's the correlation between two things and to what extent the excess government spent to GDP correlates with those inflations across those OCD countries. So three comments, the supply shock interpretation, the initial debt in the numerator and the euro zone. I will talk a little bit about the monetary fiscal interactions in the monetary union, the fiscal implications and so on. So on the supply shock interpretation, the authors argue that what you need for identification across country variation can be treated as exogenous. So the question whether this could be also consistent with inflation coming with the supply shock and think of Olivier's example yesterday from an energy price. So you have an energy price increase, higher energy prices, what are we going to do? I mean, we could just say, okay, we're going to get the price level back to where it was. So that means everything else has to have lower prices. The central bank says, well, there's sticky prices. So that's just too hard. So it chooses a higher overall price level and then the supply shock spreads. There's nothing nefarious, just that the bank is not targeting price levels. It's targeting inflation and once things have happened, well, bygones are bygones and so on. So is this really, really that different? Okay, so think through it. So the key claim, I think, and I put this on the table for Francesco and you all to discuss, but it seems to me that the point estimate that 40, 50% of the extra spending was financed through inflation. That seems to be still true. I mean, what's going to happen is you're going to have this. Precisely because the bank is just doing his job and saying, okay, well, this stuff happened, but inflation is just whatever it is. We're looking forward and not backwards. Then this result is still going to be true. So I think that it doesn't really matter, but I raise this issue. Second, the denominator, they also say, look, this is less intuitive, Francesco, explain it, I think very clearly. So I don't want to say much about it. The result follows simply from, if you have a lot of debt with, I think Francesco said it better than I'm going to say it. So if you have a lot of debt, just a tiny bit of extra inflation is going to wipe out sufficient debt to pay for all that extra G, basically. Third, the Eurozone and the European story, there is wide variation across countries in inflation rates. Part of it is the Baltics and the Korean crisis getting different, but it's clear. So these kind of supply and political issues in part, but it's also clear as Francesco showed you that the overall level matters. And I wanted to spend a couple of minutes talking about what are the fiscal theory implications in terms of the Eurozone or the fiscal monetary implications or at least to open some questions for discussion. So I'm working on this book with John and with Klaus on my right. We are still kind of working through it. I think it's in a relatively advanced stage, but there's still work to do. And basically what we are starting from is something that you probably saw in my question yesterday and some of the interventions by other people in the panel, which is this sense, this bizarre sense, that Europe is getting more intergovernmental.  But think about from the expenditure side, people are talking about the need for a public, for a budget, for some public goods funded from the center, from the revenue side, we're talking about on resources. Well, the on resource discussion is going nowhere. The parliament tried to get these on resources on the table and the countries are totally against. The public goods, finance public goods, we tried that with the next gen. I mean, it was the next round, it was getting smaller at the end. There are no public goods with next gen, all the money checks for the countries. So the idea is, I mean, to some extent, what we are seeing is like, okay, there's only one European institution, which is this one where we are sitting right now, the European Central Bank. And it's kind of by necessity, by obligation, I'm saying by choice, it's just basically taking out all these other functions, this lender of last resort, lender of first resort, lender of second resort, all the other resorts, both in the interbank market and in the lending to governments in the past, in the recent past. And also with some of these instruments that we were discussing, like TPI, what you see is that there is an extent to which, and I don't want to exaggerate this, to which this insurance is creating the following type of moral hazard. Countries and European council as a whole don't need to do things because, hey, we already have common debt, which is reserves and the ECB doing its job. So think of the ESM ratification by Italy. Italy refuses to ratify the ESM. Will it refuse if the ESM was behind? I mean, the ECB was not behind. I mean, the ESM is a good thing for Italy, but they prefer to just kind of avoid cafe-credible threat and avoid this. Banking union, basically the banking union was dropped exactly, the banking union roadmap was dropped at the same time as the TPI announcement. So there is here a problem, which is like in the sovereign exposures problem keeps being there. So we are discussing the extent to which the institutions governing the error change over time as the ECB took all these other functions and the fiscal rules became less and less credible. There is now, we believe, a bit of a fragility with these very large sovereign fundings and this long-term situation with this in the long-term that the ECB has this gigantic balance sheet. I don't think there is a very clear sense that this is going to be reduced. You could say, oh, well, Japan has the same situation. So who cares? I think there are difference here as we discussed in terms that we need incentives for the construction of Europe that now don't seem to exist. And we believe that institutional changes are absolutely urgent to ensure that the Euro area is prepared for future adversaries. And right now, I honestly, like I've been on the inside and some of you know what I've been doing politics for a while. I'm now back to academia, but from the inside, you don't see any movements on any of these topics. Going back to the paper, pathbreaking work taking fiscal theory to data, a really nice parsimonious explanation and very important implications for policies. So congratulations to Francesco and I have 45 seconds left. So I think ours. Thank you. Thank you so much, Luis and Francesco. Let's do the same as before. Let's open the floor for some questions. Etore Lucho. First of all, just a quick reaction to Luis. If DCB is a central bank without a state, the problem is not with DCB. The problem is with the lack of the state. But so regarding this very interesting paper, you rightly move from this state contingent nature of public finance and you rightly assume an ETA above zero under exceptional circumstances, such as a pandemic or a war. At the same time, state contingency also means that fiscal policy can respond differently to different shocks. Now, I know that the US is pretty different from the Euro area, but here in the Euro area, we had two fundamentally different states of the economy during the period that you are considering 2020-22. We had in 2020-21 a phase that basically was of divine coincidence, but then in 2022, in the presence of a strong external supply shock, we had a monetary policy tightening coupled with a new generation of fiscal measures, you know, unconventional fiscal policies. So actually, if you look at the COVID-related measures already in 2022 on the aggregate, there was a rolling back of these measures. What kicked in were these new measures such as, you know, gas and electricity price breaks, energy, VAT cuts, which were deliberately, by very construction, designed to lower inflation, and in the short run, they succeeded. Although, of course, in the longer run, the jury's out whether this is mere inflation smoothing or really can have an effect. But so my point is that state dependency may matter not only for ETA, but also for the type and the composition of fiscal policies, more traditional measures, you know, with aggregate demand effects or unconventional fiscal policies. So does this matter should be taken into account? This is my question. Yeah. To question one very specific one, brother, the very specific question is linked to the revenue component of the reaction because as Luis was showing in one of his slides, it's assumes that revenue do not play a role and you have just expenditure in your estimate. Still, I guess country may have differed in the extent to which they acted on the revenue side. So I'm wondering why you are not taking into account perhaps because it's difficult to discriminate between the overall response of revenue and discretionary revenue measure, the discussion that we had also yesterday. So that is the specific question. The broad question, again, suggested, I mean, by listening to the discussion by Luis, is about the Euro area. I mean, and the fact that you showed that in the case of the Euro area, the effect is not differentiated. Now, in the pandemic, we also had the fact that the increase in deficit was all financed or overfinance in some cases by purchases of bonds by the ECB. Okay, I don't think this is capturing in your very simple specification, but I wonder whether you could elaborate whether this may have a bearing on your result. Yeah, first, well, thanks, Francesco, for this very, very interesting work. And I have a question about interpretation, but I think it's important. You find a positive value of ETA and throughout you have emphasized how this is consistent with the fiscal theory of the price level. But at least from a theoretical point of view, I view it consistent also with a word where the central bank is active. It tries to stabilize inflation, even not fully. As for instance, we have seen yesterday in the paper by Christian. We can even have a central bank that keeps the real interest rate constant, but generates inflation. And, but this is not related to the fiscal theory of the price level. So I would like to hear your thoughts about this. Thank you, Davide. Yes, Klaus, please. Very short question. Many of you know in the ECB that I'm a big fan of the work of Francesco. And I find it really interesting, this emergency case, which you know with Robert Barrow discusses that there is an emergency and then it doesn't depend whether you have a high or a low debt level to start with almost everybody uses some inflation. And even those with a very low debt level much higher inflation to get the same relief. And how does this Francesco contrast with the other work you're doing where say the fiscal limit paper you presented at Jackson Hole, where I always got the impression whether the fiscal theory kicks in with the deficits creating inflation is always when you are at the limit. When the fiscal authority has so much debt and so high taxes that they cannot further increase taxes credibly after a shock. So if that is to say outside a broad emergency like a war or a pandemic, then it would more depend on this country specific kind of constraints on future fiscal policy. How do you see that? If I may add my own five cents following up the comments by Davide and Lutro. I mean, I guess that in the Euro area we can distinguish two different periods after the COVID. The initial one was one with a very large fiscal response by national authorities by all the governments of the Euro that however came with falling inflation and falling inflation expectations. Don't forget that. I mean, at the beginning of our challenge was to reflect the economy because the shock was initially strongly disinflationary also with a negative impact on long-term inflation expectations. So I'm not sure that of course this is very informal, but I'm not sure that the mechanics of the fiscal theory of the price level applied to this very initial stage. The second stage was one of sustained inflation which can be argued that is lasting until now. But here, as far as I remember the fiscal theory of the price level tells you something about the connection between fiscal policy and deficits and the price level, not about inflation. In order to generate sustained high inflation you probably need sustained surprises on the fiscal variables because in expectation even in a non-recardian fiscal theory price level regime expected inflation is still controlled by the central bank. So in your view, how we should think about the fiscal theory in order to account for these two different stages in the crisis here in the Euro area. So with this, I'll give the floor to Francesco and we may pick up second. Okay, so let me first thank Luis for the great discussion also for broadening a little bit the perspective like mentioning his work. So let me start from the end. I always find it easy because I remember the question very well. So yeah, the very first version of the fiscal theory of price level was about price level determination. Then since then, and John's book I think summarizes this very well things have evolved quite a bit. So the first thing that was done is, well, if you have a maturity structure what stabilize that is also expected inflation because it gives you revaluation effects. Then people started working on non-minor agilities and I did a lot of work with that and there you have that even without a maturity structure inflation has its own persistence and so there is this interplay between the non-minor agilities and the fiscal theory of price level but even without going there and Robert prefers not to go there because he's not big fan of non-minor agilities you can really think that if there is a maturity structure there is an interest of policymakers to reflate the economy like very much like you were mentioning because that devalues the value of outstanding debt. So Klaus made a great point. So here it's a bit subtle the role of debt because it has two roles for conditional on a certain amount of unfunded spending, larger debt, lower inflation. There is a different question is like how likely are you to engage in unfunded spending and that might be the other way around if you already have a large amount of debt you might be more tempted to go with an unfunded level of spending. Now the reality of this and you know this is something I learned by working on US data the reality of this is that typically high fiscal inflation is associated with low debt. It's almost like the high inflation and low debt are just the other two sides of the coin in a sense if a country is allowed to drive up his debt to GDP ratio without massive inflation is because for one reason or the other maybe because it's part of a currency union there is the expectation that somehow we'll be able to sustain it, okay? But yeah, but if you are like, okay we are in a dire situation and we are more likely in engaging in unfunded debt because in a fund spending because we have already a large stock of debt that's definitely consistent. I think COVID is a little bit of a particular case in which no matter what your starting position was there was some justification in using unfunded spending also in light of the fact that monetary policy was constrained by the lower interest rate environment. So that would have made another good point. So I discussed a Chris paper so I know it very well. Like I think like in all models I think you need to buy something. So in increased work with the Marios and Chen you need to buy a boundary rationality of a particular form. You need to buy the fact that nobody internalizes the long-term low motion of the debt to GDP ratio, okay? So Lucio, yeah, so we don't talk about we talk about revenues in the paper. We basically say that revenues did not change much and mostly the large variation in primary services was mostly coming from spending at least for the window or time that we look at. Now we know that given that because of tax brackets some people have moved up in the tax brackets and so that has generated a mild increase in revenues just coming from the higher inflation. But again, if you think about the fiscal stimulus for us in the data it seems to be the cross variation seems mostly coming from different levels of spending. With respect to the ECB buying government bonds well, if you think that eventually these bonds will have to return to the market is still an increase in outstanding debt. Unless you think that the ECB is literally going to eventually monetize it but then that's inflationary in itself. I totally agree that it's important to think about that's a address point it's important to think about how exactly you implement spending. As I was saying, we take a very kind of high level approach here, then of course for policy purposes for policy advice, yes, it's also important to understand how you spend the money and it's possible that the error term that we don't have a 100% R square so it's possible that what explains that error term is well, no all spending is the same. I think I'm done. I mean, I don't think I had to add much to what Luis said I think these were more like kind of constructive comments there's nothing, that particular disagree with and I agree that John really hates that this government budget constraint thing email us saying that we shouldn't use it. We had at least one remaining question by Ramon. Ramon, please. I just have a final question it's almost more for Luis. Whether you think that now that it's more this intergovernmental mood, we are very lucky because if they had postponed 10, 15 more years the peer partner report, we will not be here. That's a philosophical question. I guess it goes with the, so my reflections went with the title of session so I hope this goes as well.  I mean, the rule based trade order, right? The Washington consensus, that's the 90s. We have some good rules and we try all to behave well. The euro is a child of this consensus, right? This free capital mobility is a rule. It's an independent central bank. We are going to tie our hands. We're going to not do bad things on budgets. It's kind of a son or a daughter of Lucas, Toki, Prescott, et cetera, et cetera, et cetera, right? So am I, it's now 30 years since I took my first microclass in Chicago. But all that is kind of the rule based world order and intellectual construct behind the Washington consensus is kind of being kind of questioned everywhere. And in some sense, the European Union, the limitation of state aids, the limitation on what the governments can do to help their companies. All of those things, we have a single market. We are all fulfilling the rules. Outside of Europe are being put in question. And in some sense, it's inevitable that inside of Europe, all of those institutions are kind of, I don't know, I mean, in some sense, I mean, think of the single market and state aid rules. They are being obviously in question. And yes, I would think the very report wouldn't happen today. I would agree with that.


In this video, we provide the solution to question number four for the practice exam number one for math 1060. And we're asked to find the equation of the circle whose center is at four comma negative six at whose radius is equal to seven. So we need to know the general formula for the equation of a circle. It'll always look like x minus h squared plus y minus k squared. And this is equal to r squared. So let's understand the formula here. H and k are the coordinates of the center of the circle, h being the x-coordinate and k being the y-coordinate. This point is provided to us. So h is four and k is negative six. Do notice that these are negative signs here, negative h and negative k. So you'll see the opposite sign of what you see in the point above. So you're gonna look like x minus four because you see a positive four right here. And then you're gonna get y plus six squared because you see a negative six right there. Get the opposite sign. And then on the right hand side, you're gonna square the length of the radius that's provided to us, which is a seven. So if we square that, we'll end up with 49. So the correct answer would be x minus four quantity squared plus y plus six quantity squared. And this is equal to 49. And so we select choice B as the correct answer.


The number one trick all Narcissists use This is the narcissist's primary objective It is the most important thing for them When they are dealing with you and they will go above and beyond to achieve this It is a cunning scheme which is intended to deceive you. It's intended to outwit you by creating an illusion By creating a deceptive appearance or impression by planting a false idea or belief and This trick is designed to keep you under their influence and control It's designed to give them power over you By stripping away power that is rightfully yours But to do this They have to get you to hand over your power to them They have to make you believe that you are not deserving of your power They have to make you believe that you are not worthy and they do that by creating self-doubt By making you lack confidence in yourself and your abilities This is the number one trick all narcissists use They have to do it It's the only way that they can keep you as their source of supply Because otherwise You would realize that they're not bringing anything to the table They're not doing anything for you So to balance it out And to make you think that it's a fair exchange They have to make you think that you're not doing much for them They have to make you doubt yourself and they do this By targeting yourself with and self-esteem Minimizing your accomplishments Minimizing the value of anything you're doing for them And comparing you to other people This is how they lock you under their control This is how they keep you as their personal workhorse While you're not expecting anything in return from them because you are led to believe that you're not doing enough You're led to believe that you need to do more for them Before you can expect anything in return They make you believe that there's something wrong with you There's something wrong with what you're doing and they do that By never revealing their appreciation By never showing you their gratitude Even if they secretly admire your efforts, they cannot let you see it Because then they would be letting you preside over them They would be giving you the authority Which wouldn't be of any use to them because they're weak They're not really about anything So the game is to make you doubt yourself So that you don't come to the conclusion that they ain't about shit But now that you have this information There is a way out of the maze And that is through recognizing your worth Recognizing all of the work that you've put in Recognizing everything that you have accomplished if you look back and evaluate everything that you have done You will see that you have done a lot more for them than they have done for you You're more of an asset to them Than they are to you They need you more than you need them, but they can't let you know that Because then that would put them at a disadvantage It would make you look at them and then you would realize that they're not doing anything for you So why would you keep them around?  They've distorted your beliefs about yourself They've made you less confident Narcissists want to be around powerful and successful people. They admire people like that But they don't want you to use that same power on them Because then you could tear them to smithereens So instead they have to domesticate you they have to tame you to their liking Where they don't ever have to praise or compliment you While still receiving all of the benefits and conveniences That you have to offer Thank you for watching. I hope this video resonates with you Please like comment share and subscribe if you would like to donate My PayPal link is in a video description Coaching inquiries You can email me at coaching an arch-survivor at the crew UK. Thank you for watching and I'll talk to you soon