Simon Dietz, London School of Economics
Are Economists Getting Climate Dynamics Right and Does It Matter?

Thank you, Simon, for joining us and the virtual floor is yours.

Thank you very much, Glenn. And thank you to Michael, Stephie, Oscar, and Toan as well for having me as part of your seminar series. So this is the joint work with Rick van der Ploeg, Armon Rezai, and Frank Venmans. And I think all of them are here with me today and at least Rick and Armon will be joining me for the Q and A session at the end. The title of our paper and my talk is, “Are Economists Getting Climate Dynamics Right and Does it Matter?” So, hopefully the title of the talk speaks for itself. But before I tuck into the detail of the paper, I’d like to provide some motivational and background material. Because I expect that not all of you will be familiar with economists models of climate change. So, this talk is about the models that economists have built of climate change which are otherwise known as Integrated Assessment Models, or IAMs. And in particular we’re interested in IAMs that have been built for cost-benefit analysis. These fall into two categories. So traditionally IAMs have been purely quantitative and the most famous example of a quantitative IAM is Bill Nordhaus’ DICE model for which he essentially won the Nobel Laureate. But there are other quantitative IAMs. The two other principle examples are the FUND model by David Anthoff and Richard Tol, and the PAGE model by Chris Hope which we used on the Stern Review. Within the last six years or so we’ve also seen the emergence of so-called analytical IAMs. These are slightly simplified models capable of yielding closed form analytical solutions that can be interpreted as policy rules, if you like. I’ve listed here in front of you three of the main examples of these. And I’ve put in bold the paper by Golosov, Hassler, Krusell, and Tsyvinski in Econometrica in 2014 which is by far the most cited one of these. Now the term IAM is subject to different usage by different scholars. So that can create some confusion. So I just want to be clear about what we’re not talking about today. So the term IAM is sometimes also used to describe more detailed models of the energy system that are used in a kind of cost effectiveness analysis. So they’re given an exogenous or predetermined carbon budget and they’re used to figure out what’s the least cost way of staying within that budget. We’re not talking, there are lots of those models and we’re not talking about them today. And the word IAM is sometimes used to describe models in specific sectors, like agriculture and land use. Again, we’re not talking about those today. And so when we stick to talking about cost-benefit IAMs then really one of the key points I want to make to you at the beginning is there are actually not that many of these models. So, the ones we’ve, the list you can see in front of you is not exhaustive. But it captures most of the main ones. And so one of the claims we’re going to make later on is we’re going to take these six models and run them and we’re going to say that this is a representative sample of cost-benefit IAMs. Okay. So what does a cost-benefit IAM look like? Well, here’s a simple flow chart that tries to capture the essence of that. It is basically a model of long term economic growth coupled with a model of the climate. And that was the essential insight which I think won Bill Nordhaus the Nobel Laureate. In his case, taking a Ramsey-Cass-Koopmans model and coupling it with a simple climate model. So you have production, capital, savings, consumption, and welfare. CO2 emissions are a byproduct of production and they go into the climate and cause global warming. And global warming triggers impacts or damages back on production again. And what we’re going to focus on in our talk is the part of an IAM which we can call the climate module. And that basically comprises two things. The first is a carbon cycle model which takes CO2 emissions and maps them into the atmospheric CO2 concentration. And then a warming model which takes the atmospheric CO2 concentration and maps that through radiative forcing, in other words, changes in the earth’s energy balance through to changes in temperature. So we’re going to be interested in the climate module of IAMs. And I’m going to use module and model interchangeably. So I apologize for my flexibility of language. I hope you can get the essence of what I’ll be talking about. Now a key point I want to make at the beginning is that we economists have basically built our own climate modules. So we read the science literature and then we build our own. And up to now there really hasn’t been, for example, a kind of platform where economists would build their economic model and then go couple it with a climate model built by climate scientists. So we’ve developed our own. And economists climate models, or climate modules are very simple in the scheme of things. So what you can see on the left hand of the slide here is the equations of the DICE, Bill Nordhaus’ DICE climate module. Starting from emissions in A12 going down to the second equation of the warming model in A18. So, six or seven equations in total. By contrast, climate scientists build models of different degrees of complexity but the kind of gold standard climate model is extremely complex. It takes the atmosphere and the oceans and breaks them down into lots of little boxes where the laws of physics can start to constrain the relationships being modeled. So there’s a sort of a big difference in the complexity of these models. More over, and this is, I think sort of some of the background for the talk, since we economists have built our own climate models and since we make reference to other economists climate models when building new ones, there is this potential for sort of parallel and divergent development of the models. And that really sets the scene for asking the question in this paper. So given that economists have been developing their own climate models and have been building on each other’s and reading each other’s papers more than interacting with the climate scientists, are we actually getting climate dynamics right, and does it matter? So, that’s the question that we asked in the first part of the paper. Are economists getting climate dynamics right? And we argue the answer is no. So what we’re going to do in the paper is we’re going to take the climate modules of the six IAMs I showed you at the beginning of the slide set and we’re going to run them in two experiments alongside a large sample of climate models from climate science. And we find that firstly, almost all the IAMs, the economic models, respond much too slowly to an impulse of CO2 emissions. With obvious economic implications. In addition, almost all the economic models ignore positive feedbacks in the carbon cycle which result in less CO2 being taken out of the atmosphere the more the concentration of CO2 rises in the atmosphere. Now, naturally the question then is, okay the economists models are not replicating the behavior of the state of the art climate science models. Does that matter? And we argue it does. Firstly, if the economic models have a too slow a temperature response to CO2 emissions then it follows, and we show, that optimal carbon prices, optimal carbon taxes if you like, are too low. And they’re more sensitive to the discount rate than they should be. Secondly, failing to account for positive carbon cycle feedbacks also leads to carbon prices that are too low. Intuitively because with positive feedbacks there’s less capacity of the atmosphere to absorb CO2. And that especially is the case when atmospheric CO2 is high. So for example, in high emissions scenarios. But I want to just be very clear at the beginning. So, are we saying that this is now the most important issue in climate change economics and that everyone should forget about other things. Absolutely not, right. This does not matter more than the issues we’ve been worrying about the last few years like damages and discounting. You can just add it to the list of stuff we worry about. But unlike, perhaps damages and discounting, we can see a way to fix this quite quickly in the sense of at least bringing the economic models into conformity wit
h the climate science models. And we make some suggestions of how to do that. So, that’s an introduction to the paper. Glenn, I don’t know if there are any questions that would be worth fielding at this point. Otherwise I can carry on. You’re on mute at the moment.

I think that was a great start. A great overview to the literature. So no questions yet, thank you.

Okay, thank you. Well, that could mean one of two things but let’s assume it means that. Okay, so let me take you right into the paper and these two experiments that we subject our models to. So the first one is a replication of a well known experiment in climate science. So, we take a large sample of climate models from the climate model inter comparison project, or CMIP. And we subject them to the a test where we put in 100 gigatons of carbon against a background concentration of atmospheric CO2 of 389 parts per million which is the 2010 level. And we track the temperature response to that emissions impulse. So how do we do this? Well, the 256 climate models constitute all combinations of 16 carbon cycle models and 16 warming models from climate science. Atmosphere, ocean, general circulation models. And you might be thinking to yourself, my goodness, how the heck did they manage that? Well, these are reduced form representations of the underlying 16 by 16 models which were produced in the climate science literature a few years ago. So it’s not that we went around the world running the super computers at the different research stations. We were able to rely on reduced form representations which are nonetheless exact for this purpose. So we did this. We put in the 100 gigatons of carbon emissions impulse and we tracked the temperature response. And what you can see here is very characteristic. So the response here looks like a step function. The temperature jumps up very quickly. Within 5 to 10 years of the emissions impulse and reaches, settles down to it’s steady state level, more or less. And then it’s permanently elevated, okay. Now when this experiment was produced a few years ago it caused quite a stir, actually. So it was remarked by the authors who presented it that it is a widely held misconception that the main effects of a CO2 emission will not be felt for several decades. And that’s what the previous chart showed you. And I must admit that circa 2014, 2015 I was very much subject to that misconception. I used to tell my students, there’s a long delay between a CO2 emission and the resulting warming. And that is, you know, central to the economics of climate change. Well, it turns out that it isn’t. So going back to this impulse response by the climate models, what we do now is we take the six IAMs that I set out at the beginning of the talk. DICE, FUND, and PAGE. As well as the three analytical IAMs, and we do exactly the same thing. And what I want you to be thinking about at this point, what I want to sort of argue is we want to see the economists models replicating the CMIP models. So when I superimpose these on this chart we want to see them in the distribution. Close to the best fit. That’s what we want to see. And that’s what we actually see. So that they are, you know, all over the place and generally not close to impulse response of the climate science models. I want to draw your attention to two things in particular. The first one is less relevant for our purposes is that these models produce very different long run temperature responses to the input, the emissions impulse. But more particularly I want to draw your attention to the fact that with one exception, one important exception, the IAMs take a very long time to heat up in response to the emissions impulse. So in the CMIP models, peak temperature after the emissions impulse is attained within 10 years. In the IAMs it ranges from 55 years in the case of the 2013 version of the DICE model, to 180 years in the case of the 2016 version of the DICE model. So this is what we call this too sluggish response of the IAMs. The exception is the paper by Golosov, Hassler, Krusell, and Tsyvinski. Golosov et al 2014 in Econometrica. They actually assumed no delay between emissions, the emissions impulse and warming. And that assumption turns out to be accurate to a first order. The second experiment looks at–

Simon, could I stop you?

Sure.

If you take back to test one, we have had some questions. This is, of course, a fascinating figure. And it’s not what the usual, Richard Tol has asked. This experiment is not usually run in integrated assessment models where the social cost of carbon is estimated from a small increase in emissions relative to an increasing concentration. This is a large increase. Is that going to be important. I mean there are some non linearities in these models. So you’re sort of calibrating against a pretty sizable impulse, carbon impulse here.

Yeah, so this is like 100 gigatons of carbon pulse, which is about 10 years of industrial fossil fuel emissions, which is a large pulse. And we’ve done this because this is the sort of benchmark climate science experiment and climate scientists like to see their models are robust to large pulses in emissions. But it’s a good question. So we don’t currently, in the paper, show, replicate this for different sizes of pulse. But I think it’s clear in the literature that the story I’ve told you would hold for different size pulse. So for example, there have been some previous papers which have submitted the climate science models to very different sizes of pulse ranging from small pulses to enormous pulses. And those show that the step function response is broadly replicated across the scale. And we’ve also seen some of the IAMs in previous papers being tested against a small pulse of one gigaton and they also demonstrate this long delay. So although we haven’t done that yet in this paper I think it’s pretty clear that’s what we would find for different ranges of pulse sizes.

And just, my own question is, there was a recent paper that said, oh nothing we’re going to do in the next 20 years is going to make too much of a difference. But that’s of course because they’re talking about we’re on a different path, a different incremental path over the next 20 years. While this is a very different. Here you get a big bang within a decade, but of course the size is so big.

The corollary of this result is that you would actually get a fairly rapid temperature response to reducing emissions.

Right. Gil Metcalf has asked, are there any combinations of the 16 carbons cycle models and the 16 general circulation models inconsistent in some ways? Are they?

No, to my understanding they can, I would sort of think of it as be treated as orthogonal. So indeed, we’re just replicating an experiment in climate science where they took the 16 times 16. They are modeling entirely separate parts of the climate response to emissions. So, as far as I understand this is legitimate to look at all combinations. And we are, as I said, replicating an experiment originally undertaken by, for example, Kate Ricky and Ken Caldeira.

Great, okay thank you.

Okay, thanks for your questions so far, folks. I want to show you the second experiment that we’ve undertaken. This is focused on the carbon cycle response. So, what we do here is we take the, for simplicity’s sake we just take the best fit model from the previous. The best fit CMIP5 model from the previous experiment, add a calibrated carbon cycle feedback to make a model called FAIR. And this model is designed to incorporate carbon cycle feedbacks and it more or less exactly replicates the temperature response to emissions historically. And what you can see in the chart here is yearly uptake of CO2 by carbon sinks as a function of rising atmospheric CO2. So what I mean by yearly uptake is I mean removal of CO2 from the atmosphere by the oceans and the terrestrial biosphere as the atmospheric CO2 concentration rises. And you can see that what FAIR says is that yearly uptake of CO2 by carbon sinks is actually slightly decreasing as atmospheric CO2 rises. So what’s going on here? Well, in order to explain this first I’m going to show you Henry’s Law. Now, if you’re into diving you’ll probably know about Henry’s Law. I’m not into diving. I swim about as well as a shopping cart. But it’s useful for our paper. So Henry’s Law says that if you increase the pressure of a gas above a liquid then more of it will dissolve into the liquid, okay. And if Henry’s Law applied to the atmosphere what we should see is uptake of CO2 by the oceans should go up as atmospheric CO2 goes up. But that’s not what we see in the climate science models. And the reason for that is carbon sinks become less effective as CO2 increase in the atmosphere. And the reason for that is principally saturation of the ocean carbon sink. Although there are some other factors at play including temperature effects on the effectiveness of the ocean-carbon sink and also the effectiveness of the terrestrial biosphere as a carbon sink. Okay, so this is a representative response of the climate science models in this experiment. And now what we’re going to do is take the six IAMs and do exactly the same thing as we did before, compare them. And again, what we would want to see is the six IAMs sitting very close to the response of the FAIR model. And again, what we see is that their responses don’t look much like the FAIR model. So most of the IAMs actually follow Henry’s Law, essentially. They’re taking more CO2 out of the atmosphere at the margin, or annually, as the atmospheric CO2 concentration rises. With one exception, which is David Anthoff and Richard Tol’s FUND model which has a carbon cycle feedback built into it. And actually does deliver a decreasing relationship between yearly uptake and rising atmospheric CO2. Now, atmospheric CO2 is not the direct driver of these feedback effects. It’s principally temperature and CO2 absorbed cumulatively by the carbon sinks already. But those things are proportional to atmospheric CO2. So that makes it a most convenient plot in this way. So, the results of the second experiment again show that the IAMs are getting climate dynamics wrong with the exception of the FUND model in this case because they are not capturing carbon cycle feedbacks and therefore they are over estimating, in a sense, the capacity of carbon sinks to absorb CO2 and with economic consequences that we will discuss in just a moment. So those are the two experiments that we run. And it’s on that basis that we claim that the answer to our first question, are economists getting climate dynamics right, is no. And I should say that there are obviously other kinds of experiment that you could run with IAMs. But these two are particularly compelling, not least because they were identified by the National Academy of Sciences as being important tests of the validity of climate models.

Simon?

Yes, I’m at the end of that section, so questions.

Okay, so, not surprisingly, there have been some interest in how you might do this with statistics as well. Thinking about econometrics. So, Zach Miller suggests that you could, an easier way might just be to take the general climate models, the general circulation models and just fit statistical models to those data and that would give you a good representation. There’s also, more broadly than that, I think there’s a third way. Rather than fitting to the climate models which are these calibrated, very detailed but calibrated models. One could use econometrics to pull out this impulse response from the data. And Jim Stock has done some work in there. But there’s also, I think a sense that the climate models maybe are missing things that are apparent in the observed data. My own work with sea ice is that, again arctic sea ice, they’re pretty slow in plotting that decline. But here it’s really a comparison with economic models with climate models without sort of the econometrics of data.

Yeah, so very good question. So just to re-emphasize one thing which is that we, the climate models we run are reduced form representations. So in a sense we’re already taking a simple climate model and doing a fit of the underlying climate models. But it is true that, to my knowledge, none of the climate models that we use are econometric in the sense of using econometric techniques to fit observations. And that is an interesting approach. And sort of a big debate, I think. Which is probably not helpful for me to get into or even a bit above my pay grade about the benefits and dis-benefits of these kinds of approach. I think the climate scientists put a great emphasis on the physical constraints of their models. The laws of physics and how they constrain them. The one point I do want to make though, which I think is really quite germane. Even though the climate science models don’t do a perfect job of replicating historical data for some climate variables, what I really want to emphasize is the FAIR model more or less perfectly replicates the historical emissions to temperature relationships. So it is really carefully calibrated to do that. Now, that doesn’t necessarily mean it’s going to project the future properly but just so everybody is clear that this model does do, essentially an exact job of replicating the past record.

Okay, I’ve got one question I’m going to allow, Brigitte Rath Tran to ask her question.

Hi, thanks. Really interesting and I remember learning that aerosols and small particulate matter can partially mask warming and I’m wondering if that could be part of the explanation for the discrepancy if the economic models are based on data and to the extent the aerosols do tend to increase with emissions which may not be affixed to relationship. Should we be accounting for that versus sticking to the climate models?

So I think that firstly, that the climate science models take aerosols into account. And also the IAMs typically can too because they deal with other greenhouse gases and other forcing agents, like aerosols which is like a negative forcing agent. They typically deal with, there are different ways we can deal with that. One of which is to just have like an exogenous vector of forcing from other gases and aerosols and so on. So, I don’t think that aerosols are playing a material role in the discrepancy between the IAMs and the climate science models here. And they’re not being ignored by either category of model.

Thank you.

Great Simon, why don’t you go on?

I will, now I had this, the third part of the paper was kind of taking the first experiment and digging more deeply into what’s going on. But I can see that if I go through that section I’m going to run out of time to do the bit that the audience is going to be most interested in, which is the, does this matter? So what I’m going to do is I’m actually just going to jump through this section, which contains some spectral decomposition and some things like eigenvalues. So you might be relieved. So, I’m going to jump straight to the part of the paper where we try to figure out whether this matters or not. And our strategy for this is the following. So, we want to control. You know, the IAMs are different in roughly two respects. They have different climate modules but they also have different economic modules. And we want to control for the differences in the economic modules. So we’re just looking at what difference the climate module makes. So what we do is we take the DICE 2016 economic module, so the production function, the welfare function, and so on and so forth. And we are going to couple it with different climate modules. We’re going to couple it with climate modules from four different IAMs and we’re also going to couple it with the best fit climate science model. And that’s what you can see in the table here. So we run standard DICE 2016. That’s like the DICE economic module and the DICE climate module. We couple DICE to the Golosov et al 2014 paper. That’s GHKT14. We couple it to the Gerlagh and Liski paper, GL18. And we couple it to the Lemoine and Rudik climate module, LR17 in the AER. And then we couple it with a model we call FAIR-Geoffroy. Geoffroy, the lead author of the paper with the warming model. And that’s the best fit climate science model, okay. And now we’re going to run our IAM in two different ways. We’re going to run it in a welfare maximizing setup. So maximizing discounted utility. And we’re going to run it in a cost effectiveness setup to study the least cost way to stay within a two degrees limit. Which is a policy relevant use of IAMs. So here are, this is the welfare maximizing part. And here is the optimal carbon tax trajectory in the five different combinations. And you can see that carbon taxes, optimal carbon taxes or carbon prices, vary by a large amount. Just because of differences in the climate module. So initial carbon prices are between 11 and 57 dollars a ton in 2020. Increasing to between 77 and 358 dollars a ton in 2100. These differences in optimal carbon taxes result in corresponding differences in optimal annual CO2 emissions. Ranging from 33 to 40 gigatons in 2020 and from zero to 50 gigatons in 2100. Optimal warming varies by a large amount as well. So in 2100 the range is between two and four degrees above the preindustrial level. So, this is the, you know, this is part of the evidence that I’m showing you to make the claim that this matters, economically. I want to just draw your attention to the kind of wacky looking temperature response of the Golosov et al model in this experiment. So it has to be said that temperature is only implicit in the Golosov et al climate module. But you can back it out using their assumed relationships. The problem is they calibrated their model without taking into account non CO2 greenhouse gases. So when you add those back in, which you have to do, because they’re not trivial here. You actually get their model starting at a temperature which is too high, right? So that’s what’s going on in that particular model. I’m now going to show you the same sequence of charts for the case of staying below two degrees. So here are the carbon prices that would be required to do that. You can se again they exhibit a wide range from 13 to 143 dollars a ton in 2020. With the difference peaking about 406 dollars a ton in 2050 before the backstop price in the DICE economic module kicks in and we start to see prices decreasing. Naturally that leads to very different emissions trajectories and a policy goal that we talk about a lot in climate change is net zero. So in these models, the time at which net zero is achieved ranges from just before 2050 to beyond 2100. And even though temperature is constrained to two degrees in this run of the models the trajectory of temperature is still substantially different between the different models. So that, to this point, I’ve basically tried to show you that differences in climate module lead to large differences in economic policies as represented by optimal carbon prices, optimal emissions, and optimal temperatures. But within the climate modules there are a lot of differences from one module to another. From say, the DICE climate module to the Golosov et al climate module. So in order to link this part of the talk back to the beginning, we would like to dig a little bit more into what effect this long delay between emissions and warming has and what effect the positive carbon cycle feedbacks have. So, I’m going to show you some further results now where we tried to look at that in a controlled fashion. Glenn, are there any questions that would be good for me to take at this point?

Yeah, there was a question from Richard Tol about the, you know, did you try to recalibrate the temperature graph so that, let’s say everyone started from the present, you know, the 1.1 degree warming. And if you re-calibrated to reproduce the present would that be important?

So, I think that we didn’t, no. We made sure they all have the same climate sensitivity. So they all have the same long run response. But I don’t think we constrained them to start off at the same point at the present. I think that our primary objective was to reproduce as closely as possible the runs of these IAMs as they were designed, as they were originally set out.

Great and in the standard DICE model it’s argued that it has one of the highest carbon price series. How does that align with the more rapid warming of the alternative climate models?

So the DICE 2016 has at the same time a very slow temperature response to an emissions pulse but it gets very hot in the long run. If I were to jump back to experiment number one you would see that it has the most sensitive reaction to emissions in the long run. And that’s really what’s going on there.

Great.

Okay, thanks. So, now I’m going to show. To isolate the effects of delay we need to construct additional models. Because although the different climate modules I’ve showed you so far have different delays between an emissions impulse and temperature, there’s also a lot of other things that are different from one model to the other. So we’re going to construct two artifact models which have the same long run temperature response to an emissions impulse but they just reach it at different speeds. In particular, the two artifacts that we look at reach the peak temperature response to the emissions impulse five times and 10 times more slowly than the best fit climate science model, okay. So they, that time, that delay in the benchmark climate science model, the best fit model, is 11.2 years. So that’s why our two artifacts are called Delay 56 and Delay 112. And 56 years is about the time from the emissions impulse to the peak temperature response in the fastest IAM, which is DICE 2013. And Delay 112 is kinda in the middle of the distribution. We could have taken this further. We could have looked at a 15 times delay or a 20 times delay, but this is enough to make the point. So what you can see here, in the table, is that all else being equal the longer is the delay, the lower is the optimal carbon tax, the welfare maximizing carbon price, the higher our emissions but the lower is the warming response. Because of course, with a long delay even though emissions are higher, the temperature response is more sluggish, okay. So this is the basis of our specific claim that a too sluggish temperature response to a CO2 emissions impulse leads to carbon prices that are too low. Now another implication of having a too sluggish temperature response to an emissions impulse is that perhaps these IAMs optimal trajectories are more sensitive to the discount rate than the best fit climate science model. So that’s a kind of a, something we explore at this point. So we take these three models. The best fit CMIP5 model, the five and 10 times delay artifact models, and we calculate optimal carbon prices under the standard DICE discount rate which is a pure rate of time preference of 1.5% and elasticity of marginal utility of just a little bit under 1.5. And we compare that with a case that we call public discounting where the social planner, not the households in the model but the social planner has a pure rate of time preference of 0.1%, so that’s the same as the Stern Review, and an elasticity of marginal utility of one. And what you can see in the table is, as you would expect, with a lower discount rate optimal carbon prices are always higher. But what’s highlighted in bold is that they, the difference between optimal carbon prices in the public discounting case and the standard discounting case, the difference gets bigger the longer is the delay, okay. So if we’re in the Delay 112 model changing the discount rate assumption pair increases the optimal carbon tax by about 70%. In the best fit CMIP5 model, only by 50%. Okay, so that specifically substantiates our claim that not only does a long delay lead to carbon prices that are too low, but it also makes them slightly more sensitive to the discount rate then they actually should be. I’m going to move on. This is my penultimate result. This is trying to specifically isolate the consequence of ignoring positive feedbacks in the carbon cycle and what effect that has on economic policies. So we do that by comparing a pair of models here. DICE-FAIR-Geoffroy has the feedbacks. DICE-Joos-Geoffroy doesn’t have the feedbacks. And you can see that when you include the feedbacks carbon prices are higher, welfare maximizing emissions are lower, and warming is lower, okay. And this is intuitive. So if you ignore the feedbacks you over estimate the capacity of the carbon cycle to basically suck up the, sequester the CO2 that we put up into the atmosphere. If you include the feedbacks the carbon cycle is less capable of doing that and that is going to drive up carbon prices and drive down optimal emissions. And although we don’t show it here, this will matter more in the future and on higher emissions trajectories. Because that’s where the weakening of the carbon sinks really kicks in. It’s not such a massive issue in the short run. Okay, so and that substantiates our result that ignore carbon cycle feedbacks leads to carbon prices that are too low. Now before I wrap up, I just want to make a comment about staying below two degrees. Because this comes out kind of directly from our analysis. So, as some of you might know, since DICE 2016 Bill Nordhaus has been arguing that limiting warming to two degrees is infeasible in his model, it can’t be done. Therefore we shouldn’t, it’s not worth talking about, okay. Well, our analysis suggests this isn’t case if the DICE climate module is taken out and replaced with the best fit CMIP5 model. In our analysis DICE 2016, it is actually feasible to stay below two degrees, but it is prohibitively expensive as you can see. The reason that our model can actually do it is we use a more appropriate scenario for emissions of other greenhouse gases. Which is lower than the one that Bill uses when he runs his experiment. I’m happy to talk about that more in the Q and A if you want. If we take the DICE 2016 climate module out and put the best fit CMIP5 model in, you can see that the carbon prices required to stay below two degrees, okay, so this is not changing any of the economic assumptions about abatement costs and so on. They’re much lower, much lower, okay. So our analysis suggests that because DICE 2016 gets very hot in the long run, if you would switch to the best fit CMIP model you would find two degrees is not only feasible but it’s actually, it doesn’t appear to be prohibitively expensive. And this is not a claim about optimality. Really just a claim about relative costs. So those are my results. I’m happy now to spend five minutes wrapping up. I don’t know, Glenn, whether it would be worth fielding any questions at this stage or whether we should, I should do the discussion.

Why don’t you push on and finish and then we’ll have a general question and answer.

Okay, thank you very much. I will do that. So, just to summarize what we’ve shown in this paper. So, we’ve shown that economic models respond too slowly to a CO2 emissions impulse. Except the Golosov model, by assumption. What I didn’t show you, the section I skipped was kind of breaking that down. Most of the economic models actually remove CO2 from the atmosphere too slowly. So that can’t be the reason why the temperature impulse response is too slow. If anything that would make it too fast. No the reason, fundamental underlying reason, is that the economic models have much too much, in the sense, temperature inertia. So if you increase the forcing, the models take too long for the temperature to go up. We’ve also showed that the economic models mostly imply that marginal or yearly removal of CO2 by carbon sinks rises with atmospheric CO2 but actually the fundamental climate science suggests that it falls. And the FUND model is a notable exception in reproducing that qualitative relationship. We then moved onto say, does this matter and we found that yest it does. So a sluggish temperature response leads to carbon prices that are too low and excessively sensitive to the discount rate. And failing to account for carbon cycle feedbacks and this weakening of the carbon sinks also results in carbon prices that are too low. Which leads me on to what to do now. And this is where we, I argued earlier in the talk, this problem is, in principle, fairly easy to fix. Because we can, to fix it, if we’re running a quantitative IAM where computational and complexity can be handled, then we can put in the reduced form representation of the representative climate science models into our IAMs and run them with those instead. That’s obviously actually what we’ve done in this paper, so we provide the MATLAB code for that to be replicated. Now for analytical models where we would like to derive reduced form, or closed form, I’m sorry. Closed form analytical solutions. Kind of policy rules, sort of the climate equivalent of something like the Taylor Rule. Then we argue that actually a very simple relationship which will capture all of the stuff going on in the climate science models that I showed you, just draws warming as a linear function of cumulative CO2 emissions. And that’s what we show in the final slide. So this is a chart from the IPCC fifth assessment report. It shows that if you plot warming as a function of cumulative CO2 emissions you get a quasi-linear relationship. So for analytical warming it may, it would be faithful to the physics. Capturing the feedbacks and the fast response to actually write down this simple linear relationship. So those are some recommendations on how to go forward from here. Can I just say at this point that, thank you very much for listening and I’m very pleased to take questions now, thank you.