 Thank you very much for those very kind words and I should only share with the ECB the importance of climate change as a policy challenge, which we have to face. And I feel like to some extent I've already had a good discussion of the paper about to present, but I'm going to go forward anyway. I think there's probably lots of commonality and let me see at the outset that I'm really pleased to see the ECB posing this challenge of how we bridge together science and practice, which I believe to be a tremendously important past to be done and look for ways for doing that better. I think it's just, and I think climate change is certainly a good example of where we need to do precisely this. Part of what I'm going to talk about is based on joint work with, with Buzz Brock and Mike Barnett, and some of what will be, they're not responsible, however, for all this stuff I'll be talking about here. They're probably like to distance themselves from someone I suppose, but anyway. Anyway, this is my, I think how, how do you think about uncertainty and how we can poke with uncertainty in ways that are really grassless nature. And that's what I want to wrestle with today, and talk about what I see as the challenges. So let me first. Hayek wrote this very interesting essay as part of his Nobel address. Usually one year, if you get the Nobel Prize, you're supposed to write this address about why you won the prize was kind of boards, boards, most of the people writing essays and so Hayek really took on this task about limits for understanding There's lots of high as XA that I would probably, that I disagree with that about quantitative modeling and the like, but there's this one passage in here that in some sense keeps me up at night. It's just kind of a warning that even if true scientists should recognize limits of studying human behavior as long as the public has expectations. There will be people out there. I'm not saying not the ECB, but there will be people out there that pretend or believe they can do more to meet popular demand than what is really in their power. And this is what we want to guard against. This is how we want to use, we want to recognize the limits of our understanding while not using that as an excuse for an action. And so how do we do this in sensible and smart ways? And this really I view as a challenge and how do we avoid the concerns expressed by Hayek? So when you confront policy uncertainty, there's this tension. On the one hand, this is limited understanding of the mechanisms by which policy can influence economic outcomes. On the other hand, there's this demand for precise answers by the public or government or policymakers who have to communicate with the public. So how do we address that tension? How do we think and in a way that's constructive? So in the specific case of climate economics, let me just sketch out three different sources of uncertainty. And I'll be filling in some gaps on each one of these. The first is climate sensitivity. And the simplest way to pose this is what are the temperature responses to changes in emissions? So we'll admit CO2 in the atmosphere today. There's temperature responses tomorrow and the future multiple decades and way far out. What are those? And what are those magnitudes? Next, beyond temperature changes, what are the environmental tipping points? Potentially dramatic consequences might be triggered after crossing some temperature anomaly threshold. How do we cope with those? Third, there's kind of damages. We're going to damage, as we damage the environment, we can limit economic opportunities. There'll also be forms of adaptation and how do we try to address those issues as well? So much of the existing quantitative research in climate economics to date has targeted the so-called social cost of carbon, which is arguably somewhat more connected to fiscal policy. And so my first discussions about illustrating how to uncertainty makes you think about policy in different ways. I'm going to be focusing on the social cost of carbon calculation. Then I'll return to discussions about central bank policy. So one approach to doing this that's been advocated in by the National Academy of Sciences, Engineering, and Medicine, and by lots of researchers is to say, well, look, this is an interdisciplinary problem. We need inputs from multiple sources of expertise. And this study that I'm referring to refers to this so-called modular approach to the social cost of carbon. And they break these things down into four different modules. One is the social economic module. It's involved in trying to figure out projections of emissions of CO2. The next one is the climate module. This is the one where we're going to emit CO2 in the atmosphere. What impact is that going to have on the overall climate system? The damage module. So number two involves climate scientists. The damage module. And now we want to start talking about the economy's potential responses to these changes in the Earth system. And the final one is the so-called discounting model. And in the simplest form, although I'm going to be pushing well beyond this, there's a kind of a think about there being a time series of future damages. So we're going to damage the economy today, tomorrow, a decade, many decades out many years. How do we collapse? Think of that as a social adverse cash flow. And evaluate that social adverse cash flow and reduce it down to a kind of a single present value. And that's what that gives us rise to a type of notion of the social cost of carbon. Now, shortly, I'm going to be pushing back or at least talking about this much about going beyond this modular approach, which I think is going to be tremendously important. But let me just put this approach out there. This kind of, I think, is a framework that lots of people engage in this measurement and you're kind of working with them. So let me just talk about some of the evidence that comes out of, say, climate science. So climate models are highly complex. They have ambitions in terms of both over space or over geography as well as time. They have potentially interesting nonlinearities and alike. And so do model comparisons across climate models is potentially quite challenging to do. But about one way that has proved useful is to look at so-called policy experiments. You run through these models, inputs of gigatons of carbon and then trace through their implications for changes in temperature. And then we see what the different models tell us and then we can make various different comparisons. So here I'm pulling off some models that have been compared with the climate science literature. There's a very interesting paper by Ricky and Caldero and many others that engage in these type of comparisons. And what we're doing here is some models are featuring the mapping from emissions to carbon in the atmosphere. Other ones are featuring things like carbon in the atmosphere into temperature changes. In some sense, we have combined those type of predictions. And that leads us, in the case of this tabulation, at least to a total of 144 different model combinations. And so what I reported here are the impulse responses, if you like, to trying to trace through temperature changes in response to some exogenous input of carbon into the atmosphere. Some exogenous emission of carbon. And you'll see the models, the basic pattern is about the same across models. There's this kind of peak of fact, roughly speaking, over a decade. And then things flatten out. Now, if I were to explain what's long-term to economists and what's long-term for a geoscientist, scientists are very, very different. So I think about 100 years is being long-term for them. That's like we're just getting going. So indeed, there are more trend dynamics that play out over long, more longer time horizons. But over 100 years, this is the pattern off of these different responses. And you'll see in the blue line the mean response. Then I'm also going to give you the 25th and the 75th percentiles. And finally, the shaded region gives you the upper and lower obliques here. So the eventual impact of this emissions, there's a substantial amount of input of variation going all the way from the one degrees to just under three degrees in terms of their own. So this is one source of uncertainty. So now I'm going to put on the table just a sarcastic model of damages. And this is a highly stylized one. I'm not connecting this to any very explicit data because it's a little bit kind of too general of a level, but it captures the type of damage functions that are sometimes used by environmental economists. So I think of this as tracing through proportional reductions in economic output. And there's lots of disagreement or variance or uncertainty about what those effects might be. And there's even uncertainty about the timing of when they might get triggered. So what I'm showing you here, some people talk about temperature anomaly of 1.5 is being critical. So here what happens is you've got fairly modest impacts on damages and then beyond 1.5. There's a chance things could get much more severe. And this region here is kind of showing you the different ranges of possibilities that might occur. Once we go beyond that anomaly. Now, we really don't know. There's been discussions of the threshold of 1.5. There's other discussions that have been too. So another possibility is that, well, it's really two degrees across the threshold. And then from that point on, things become much more serious, substantial and severe. So this has to do with this kind of tipping point uncertainty, if you will. You know, at what point in time do it really tip the overall environment and therefore impacting economic opportunities. So what I want you to imagine here, and this is just a highly stylized calculation illustrator important point is imagine that we can't really appeal to historical data to get, to find two predictions about when these thresholds exactly where these thresholds sit and like. But one can easily imagine that once we start experiencing the damages, we figure things out. So I'm going to write down some social decision problems where I'm going to take a stark simplification by well, let's suppose that there's uncertain when the threshold, where that threshold is between 1 and 2 degrees. But then once you cross it, you figure out how much that curvature is the damage function becomes revealed. Of course, you'd want to watch Richard dynamic model of learning, but the idea is here is that once we start damaging the environment in more severe ways. Things will become all the more clear to us about the nature of the nature of the damages. There'll be uncertainty that gets resolved. And a lot of other treatments and within the social cost of carbon literature have no dynamic structures to the calculations. So here I want to put in the table. Well, we're going to learn about stuff. Maybe we eventually learn it's very, very steep. But by that point in time, it may be very costly to act. So, you know, some people say, well, let's just wait till we figure things out. Well, that, that waiting may be very, very costly. And so, so, so it sort of straight up between acting now versus waiting until you know more. And, you know, and these pictures are to try to illustrate the aspects of that trade off. So let me get back to this modular approach as we start putting uncertainty on the table. We start thinking about connections between these modules. Remember what they are. There's the social economic climate damages and discounting. Now, there's been lots of uses of so-called emission scenarios that are specified exogenous. And then we're uncertain about which ones are, which ones are, are, are going to play out. What are you, and based on part, and that's what's captured by those, those figures that, you know, the plausibility of those scenarios is going to dependent part on the damages which we wish or which could reveal as we push along those scenarios. If I'm on a high emission scenario, and I'm surprised by how much damage is being done, then most likely there'll be some type of adaptive policy change, maybe, maybe suboptimal or the like, but it's hard to imagine there wouldn't be at least some type of policy reactions to it. So we really, you really have, it really doesn't make a whole lot of sense to be thinking about these emissions inputs coming from the social economic component independently of what damages we might emerge once we put uncertainty on the table. So that's one source of this connection between these modules. That's important to think about simultaneously. There's also with environmental economics literature, lots of discussions about discounting. Often what's done is you take a constant discount rate, you do some external sensitivity. But one of the lessons we've learned from asset pricing from, from valuations, these lessons, you know, came first for doing investment theory and private evaluations, but they carry over also to social value. So one of the things that's really important is that discounting should in effect be stochastic. That is, you should, how much you discount things should depend in part of what gets realized in the future, and that again gets back to how severe the damages are to the underlying environment. And so you really want to, so so much more coherent approach is this probabilistic approach. This is kind of what drives a lot of driven claims for I think they're really carries over social valuation as well. And that's what you're going to make and depend on the types of macro about how the macro uncertainty plays out. So again, there's this interaction between this discounting module and what, and what you're thinking, and the nature of the economic damages being done, the potential damage is being done. And so there's, so these modules, even though they have this appeal of making interdisciplinary research easy or easier. There's important interactions across these, which, which, which really make you have to start thinking about these things simultaneously, once you want to treat uncertainty explicitly. So, I want to think about, for me, there's two interesting type of uncertainty trade offs I want to turn the table here. And, you know, I'm interested in building mathematical models on informed by expert judgment and empirical evidence, but we want to use those models smartly, intelligently, and in wise ways. And so we saw that these type of discussions get in some sense confused when people talk about these some models even in the recent pandemics models can produce things like best guesses. They can also produce potential bad outcomes. How much attention do we pay to the best guesses versus the bad outcomes. Now that's a policy decision. It's not a scientific one, but it's very important sort of policy making once you take it on certainly into account. The other one is, what should we do now versus waiting for better information to become available. So you have some people naively argues that's why there's uncertainty, which is wait, wait until I figure things out. But the problem is, and Frank mentioned this in the outset, that could be a tremendously costly to society for doing that. So how do we frame that trade work right out between how much we act now and how much we wait until that new information comes in. These are the type of this is where I think the tools of decision decision theory and are certainly can come and play in very, very important ways. So, when I think about decision theory and uncertainty, I like to take a very broad perspective on it and there's ways to formalize this. I draw through three distinctions that I find useful coming out of decision theory. Some of this is out of my own work, some of this comes from statistics control theory and the like. So what we usually take up teach in economics classes is about risk. This is cases where you have unknown outcomes with known probabilities. There's so-called rational expectations models in macroeconomics and stochastic general equilibrium theories all about risk. We feed in these shocks people and people, maybe econometricians don't know but the people inside the models are behaving as if they don't know probabilities but not outcomes. So we talk about risk aversion risk prices risk compensations. I think that under this heading of risk. Next one's ambiguity that multiple models on the table I showed you 144 different climate model configurations. How, how much do we wait each of those different outcomes. We wait an equal age we wait them differently, differentially. So, statistics in some sense has been all about this, this question for, you know, for many decades now. But this, but remains an important source of uncertainty that goes beyond risk, how, how much competence we place in the different models, how do we wait them. There's, there's this whole theory of so-called subjective probability going back to Dfinetti just savage it's very elegant, but even they argue that when you kind of fill in the holes of ambiguity with subjective probabilities you can only do that very crudely. So how do we do, how do we confront that type of uncertainty. And the third one might be the most important one is probably the hardest one to wrestle with is mis-specification. A model we write down in macroeconomics and economics more generally and other scientific disciplines are, in some sense, mis-specified. We build models that are tractable we build models that are transparent they give us insights. We know that at some level they have to be flawed. So how do we know, given the flaws are sometimes in unknown ways, how, how do we use these models smartly. And when we know that we recognize that mis-specification. So all these are in hopes of building better ways to do on certainly quantification designed specifically for dynamic models used for policy. So, you know, we're talking in the formalism, the mathematics and like, let me just kind of talk you through how these methods can work. How do we navigate uncertainty. So we want to use models sensibly. We don't want to give up on the tools of probability and statistics but you still need to bound the types of uncertainty that is entertaining. If you assume that there's no balance whatsoever, you get, it's really not a very good guide for decision making. The outcomes in terms of decision making are going to depend on a version. Just like risk aversion is a dislike of like not knowing outcomes. There's more generally uncertainty aversion. It's a dislike uncertainty about probabilities over the future and events. So this gets in this trade-out between kind of worst case versus best guesses. How diverse are we to these forms of uncertainty. Now how the implementation works is the following as you put in these uncertainty components to the model. There's subjective uncertainties which you're not quite sure about. There may be very, very highly dimensional. But then you line the calculations that tell you which parts of those uncertainty components matter and which ones are largely inconsequential. So computationally or what makes for the methods are to figure out the components of the certainty that really matter. They have the most adverse consequences for the uncertainty, a decision maker. And either you look to close the gap on information or else you figure out or you embrace those forms of that or you acknowledge or you confront that adversity. And an outcome of all this is that we might have some baseline probabilities are kind of best guesses at probabilities. But the outcome of this is kind of an uncertainty probability adjustments that are pertinent for valuation along with robust decisions. These uncertainty adjustments depend on the nature of the decision problem and depend on what we're trying to accomplish. But there's kind of a nice set of probability tools that allow us to capture these adjustments. And so these would be adjusted probabilities that are distinct from best guesses. And they're not the probabilities the decision maker believes in. They're the probabilities that help to design smart actions going forward. So let me return to climate science here and climate policy uncertainty. There's many calls for immediate climate policy and implementation, which I'm certainly sympathetic to. We're facing limits or understanding of timing and magnitude of climate change as an impact. And this is led to the apprehension of some. How do you how we're interested how a decision maker confronts us on survey in a setting in which there will be future information about the damage severity. Think about crossing that threshold and it becomes revealed how steep that is. But we suspect the value of further empiricism is really quite limited. So we're really talking about problem where pushing economies into realms that they haven't experienced. And so, so just looking at current evidence can only get us so far. So, you know, the aim is to apply recent developments of dynamic decision theory to kind of guide how we incorporate this uncertainty. So let me go back to that. Maybe the outcome is pulse experiments. Now I'm just going to tabulate the kind of limiting responses. I'm literally what I might do is I might take those those impulse responses and just discount a matter very low discount rate. And then show you what I'm going to call the climate sensitivity. So after 144 different models, this is what those kind of discounted impulse responses look like to changes in emissions. And, you know, this captures that, that in that range I was talking about in that previous diagram. So you have to think about how I form this histogram. I'm basically treating all hundred and forty, forty outcomes equally. So it's like assigning the exact same weight to all hundred and forty four model combinations, which may not be the right thing to be doing here. And you may, well, yeah, there's, there's, there's uncertainty about how you might want to weight these different model combinations. There's also be uncertain damage thresholds. So here what we're going to imagine is we're going to capture these uncertainty thresholds by a jump process. And then we're going to jump to 20 possible different, you know, trajectories for the damage function curvature. So each state in that sense is going to correspond to a value of that curvature. And we'll start off, say, as just a baseline probability that there's a uniform distribution over the 20 different potential curvatures. One could use other, other baselines. Now the decision major does not know ex ante when the jump takes place. Instead, he'll follow what's done and kind of possible modeling. There's there's some type of jump intensity. I just have an increase as I, that's making jumps more and more likely as I range between why, between why lower bar and why upper bar. Now I can write this down all, all probabilistically, but you know, it's my knowledge of how to do this is really pretty sparse. And so it's a case where I wanted to be more robust and not having to rely like precisely on probability calculations also makes considerable sense. So I talked about these ambiguity adjusted or probabilities. So in terms of climate sensitivity with 140 different models, I can imagine taking the original red histogram treating all models alike and say, well, I'm not sure that's the right way to weight things. Perhaps I should tilt the histogram and look what happens. And so here I've tilted it using a blue hit using a blue histogram with the purple been the overlap of the two histograms. And so I move things up because it's, yeah, and this comes out of a formal calculation, but it's intuitively clear why you'd want to go upwards because that's the case which I'm being bigger concern to to the decision here. Suppose there's more climate sensitivity than is captured by these a mean of this of this original red history. And then what are the consequences of making that shift. Similarly, there's that this this there's there are these probabilities, which we've assigned over the different curvatures. So, so think of this gamma three as a measure of that damage function curvature, how much damage I'm going to do once I cross this on this threshold. We're looking with things that are so called exponential quadratic here and that's a kind of quadratic coefficient in the tail. Now I start off in the red histogram and that's a that's that's one in which we are treating all different gamma threes as equally equally likely. And then if I am modest amount of robustness moves me to the blue histogram. I'm saying well I'm not. Now treat them all equally likely to seem like that's a stretch what happens if I move it a little bit. I can push it further. Depending upon how concerned I am about that mis-specification robustness that pushes me to the middle one. And then if I'm extremely concerned I get pushed all the way to the one the right. And so what I'm doing here is kind of this mapping between the type of parameters I have to input into these calculations into into these probability these these are these adjusted probabilities and this idea of looking at the probabilities goes back to robust Bayesian decision making. You know many many decades. And so, and so looking at these and trying to assess which one of these look like crazy we might think the one light is maybe too extreme maybe the one left is too passive that those type of calculations I find to be revealing. So I'm going to apply this now those these to the social cost of carbon. So the social cost of carbon I described it heuristically but it's actual meanings and targets different across two different applications. I'm going to be training what these applications but the insights all had, but, but there's also similar insights that carry over to the other. So what I'm going to be using is the so called one based on the Govian tax policy. So I'm going to invent this fictitious social planner. I'm going to ask that the fictitious social planner to figure out the socially relevant amount of carbon emissions instead of the ones that would occur in a market economy. There's an externality here. And then from that I can look at the shadow price for that planner's problem of carbon carbon emissions and that's not called that the social, the social cost or value of that of carbon. And then from that one can figure out what the corresponding Govian tax policy and carbon emissions that that corrects that externality. So the question is how what does uncertainty do to this so called social cost of carbon. What is other measures of the social cost of carbon that that one that that instead imagine that you you conjecture about a future of the world and then you do small changes in the emissions policy you do a local perturbation and then you are from that you can kind of you know back out again a type of asset pricing type calculation and this kind of social cost and many calculations are based on the latter one. Although it's the ones I'm going to show you are based in the form. So I'm just going to kind of show you the outcome. I'm going to take you to the kind of the logarithm of the social cost of carbon coming on the calculation. So, you know, look at look over a rate of temperature anomalies before I hit 1.5 degrees. Now if I treat all if I treat the baseline probabilities is just the right problem is just the probabilities and solve this problem. I'm left with a run line and so if I go through those different amounts of robustness. So if you look at the green is an intermediate case say, then you then you can see that you've got like, maybe a 30 potentially up to a 30% increase the social cost of carbon by adjusting for the uncertainty. And this is adjusting for uncertainty both in terms of the climate side, as well as the damage side. So the value of this illustration can be very important and and and be non trivial. And there's kind of these quantitative methods for doing it. So now what happens after you jump. So this is a case we're going to act your, your, your, you're going to have to take action. You're going to cut back on emissions. So social emissions right from the outset. Now, now there's this information gets revealed about how severe the damage damage parameters. Well, one possibility is it's not very severe at all. The quote good news and other possibilities are that oh it's more severe than I thought. There's kind of a asymmetric response in the emissions afterwards there is certainly a good news response over a small range of these gamma curvature of this gamma three that lead to larger emissions but then things flatten out and sort of says a pretty strong asymmetry in the nature of this response due to the uncertainty of version faced by the decision maker. And so, just to summarize our decision maker identifies to key solution that identifies to key results, the planner exhibits initial caution about damages are more fully revealed. This information with this information the decision may be more wary or more bullish, but there's a pronounced asymmetry responses with so small fraction of more bullish responses and clustering responses that are more cautious. So these are the type of using these tools of uncertainty. And I also think about these type of dynamic, these dynamic considerations and these tradeoffs between how adverse we are to, to the uncertainties and how that affects our actions. So in my remaining time, let me just, I'm not talking just very briefly about financial stability and, and central bank policy this isn't going to be any attempt it's a broad based critique of central bank policy night. I think that central banks are faced with very interesting and important challenges here. So, if I go back to the construct of so called systemic risks that that was really featured at the original crisis financial crisis that earlier financial crisis which we, which we experienced the global financial crisis. There's been lots of work done for modeling. There's been lots of repairs and existing quantitative models. I think the more kind of fundamental modeling successes, although have remained to be more largely qualitative. We're still sorting through different aspects of that. So called systemic risk. What, what are the things like what are the consequences of these kind of big of it, big perturbations to your world financial sector. And I asked to integrate climate change in that current understanding. And that's, and that's going to be quite a challenge, a modeling challenge I think it's a very important one going forward, one that I certainly embrace, but I don't want to overstate exactly what we know at this juncture. Now, climate change is different than a lot of crises type considerations which we're concerned with and thinking about banking crises or thinking about the financial crisis alike. So the time scale, we seek to quantify the uncertainty. So we go through like, think about changes over decades, multiple decades in the life that's very different than the type of challenges where we think about when we're facing other type of financial crises and I think and that's very important consideration. And there's also a challenge for, for say regulators in terms of whose models we use to assess the exposure of the national institutions. And this distinction is can be very, very important. And this is a point that's been made by this paper forth coming in general finance called the limits to model based regulation since that they say you have to rely on the models of the people being regulated, you're open the door to distortions that they may understate, relative to what an external regulator might might confront just as exposures, which they might have to say, say climate change. And this issue about whose models are we going to use in order to do the regulation also comes in play here thinking. So for me, I think the important challenges for how do we quantify these exposures to a decline run survey. I already talked about the nature of the uncertainties we're facing here all the way from not just pure risk to thinking about model ambiguity model specification their consequences and the like. So what about this climate change. Are we thinking about what there's this fundamentally says systemic aspect to it, or are we thinking alternatively are we thinking about that well maybe everyone in the financial sector quantifies this in a way understates what it is and that spills over. That becomes a source of this systemic concern. The problem here is we can't let kind of expect these financial institutions to turn loose their existing modeling expertise, because we're talking about something that we have very limited historical experience on. And so there's, there's potential a legitimate concern that we have a private sector might collectively underestimate the magnitudes of exposure to climate change. And I think that's something worthy of potential consideration. I mean, what this should do is seems like it ought to open the door to even more discussions hard discussions about how we put regulator and regulated under the same page as what climate exposures are. What nature, what's the precise nature of those exposures and how to, and how we do that in a way that's meaningful for decision making. How do we do that that that would help the financial institutions in their own dynamic decision making as they confront uncertainty. So, so I know the central banks have been good in the past of trying to pull wisdom and the like. I think there's much more that can be done here about kind of really thinking through from the ground zero how we quantify exposures to climate change. I think this is really a very much a little open question. And, and, and itself we can start getting people on the same page on this that they can be very productive. But there's been a lot of focus at the start on so-called scenario based stress test and some of these go out for upwards of 30 years. Some of the motivations for these I think have been not well conceived. But the idea is to confront extreme uncertainties to have to climate change. And at least you'll see some writings that say well we're going to we don't know how to assign probabilities to things we're just going to produce scenarios as well. And decision makers like the financial institutions, they don't have that liberty. They have to think through dynamic decision making in order to do smart. In order to engage in smart courses of action. Now when I explore events through well defined scenarios that extend through three decades and then investigate tail tail events the climate system. Now these scenarios. I talked about before we really have one has to think hard about about how to put them on the table table to begin with. And how far can you go with just thinking about stress scenarios when they play out over three decades without thinking more comprehensively about the full distribution of the possibilities of climate change. And there's limit there's great limits to what you can imagine doing here with just avoiding probabilities all together playing things out over 30 years and not putting some type of dynamic information structure. So here let me take you a figures from the Bank of England report. These are just illustrations that I of course the Bank of England of course has more ambitious ideas on the table I so so I don't mean to be trivializing what they're doing here. But this is a useful illustration here because you'll see these different trajectories as an early and late policy trajectory and no at no additional policy action trajectory. And some of these trajectories follow each other and then eventually break off. Those patterns are very interesting but they suggest that for the scenarios has to be well at some point in time. Now, I don't know what's going on. I don't know which path I'm on until some time in the future that all of a sudden I'm going to branch and then I'm going to adapt to that. And this is your making we already saw this intertemporal trade off here between how you behave when information become available in the future. So these trajectories it seems that it showed probabilities should, I don't think to be avoided completely, but some type of probability bounds have to be at least be entertained. The information structure seems to be has to be put on the table in order to, in order for us to respect the financial sectors to have meaningful responses to to these types of scenarios. So, to me it is limited stress test and it's important not to overstate what the value is their static typically with no one sitting on the path. I mean, potentially miss these two lessons I talked about from decision this trade off between bad outcomes versus performing well over likely outcomes. You could, it's one can perform really well under bad outcomes alone and perform miserably under under under under other ones. And we should expect the decisions to respond recursively to state dynamics and information revolution. So the push beyond these type of stress test to add to add to add in a more dynamic structure to them. There's a, there's a potential here for providing this misguided paths for economic environmental outcomes without explicit dynamic model. I already talked about the danger of these emissions trajectories without picking through the potential consequences that they might have for endogenous policy in the future. And I worry that the stress test answers might implicitly start conditioning on a path. If you tell me what's going to happen over 30 years and of course I can, I can design a policy that I can design a policy that confronts a climate change of that nature. But that's not what we want the answers to be doing. In some sense, a more idealized stress test, which is, of course, infeasible would be to imagine the banks submit to the regulator, a whole range of their, their full menu of policy outcomes and then the banks themselves could run the stress test based on those answers. But that that's more pie in the sky at this juncture. But I think shunting probabilities and pushing dynamic information structure the background is, is kind of productive and perhaps the whole notion about 30 years stress test and this at this juncture is, is, is, is a premature, as opposed to thinking more short term in terms of how these in terms of responses to climate change uncertainty. As you go more short term, one of the interesting forms of uncertainty that these institutions are going to face is policy uncertainty occurring from outside the central banks, which is, which, which puts essential banks in an awkward position and trying to assess the uncertainty is coming from other aspects of government. So I, I don't have a simple solution to have that to say fix the stress test problem, but I just want to. I agree that there's, that we assign too much credence to what can be learned from them. So that let me just kind of close here. I think fiscal policy is the biggest potential the tool for comforting climate change with monetary policy plan a more supportive role. For me the time horizon over which climate change uncertainty plays out is different than other forms of turbulence on the radar screen of central banks. This creates unique challenges for oversight for regulation. I think understanding better the sources of subjective uncertainty in models used by the private sector and by governments in regards to climate change will make oversight all the more effective. Thank you very much.