 Good afternoon and welcome to today's energy seminar. We have with us today an old friend of mine, not too old, a good friend of mine, Tom Rutherford from the University of Wisconsin, known Tom since about 1980-ish. No, it's just in years ago we met. Tom was actually a student here and since then has had a very prolific career, which took him first to the University of Toronto then to CU Boulder, then to ETIH in Switzerland and now finally to the University of Wisconsin. Tom is probably the preeminent person who models both trade and energy environment and climate change. It's a very unusual combination. He may even talk a little bit about that today, but it's a pretty big subject because the models are fairly different. Fortunately, Tom is an expert on modeling methodology, so he does both sides of that game using somewhat different techniques. Tom is also a former Peace Corps volunteer and still goes back to see if his bridge is still standing in Kathmandu 25 or 30 years later. He's a very well-rounded guy. I think I remember you're also a musician as well, but wouldn't it be there? So without further ado, Tom is going to talk to us today about capital malleability, which probably seems pretty arcane, but it has to do essentially with turning over and or modifying the energy system infrastructure, which seems to be a very important thing to know about these days. So he's going to talk about that and actually his co-author on this paper is Christoph Orenger who did do a talk just about a year ago in this seminar on a big trade study that they ran for the Energy Modeling Forum, which is one of my projects. So with great thanks to Tom for that as well. So without further ado, Professor Tom Rutherford. Boy, it's really fun to be back to Stanford. So I'll try to keep myself on a short leash because I can sort of go off on tangents about how great it was to be a student here, but all I can say is like really enjoy yourself because it's a great place to be a student. I came here in 1980 thinking I was going to learn how to run development projects on a large scale. I had heard about this thing called the critical path method and I thought oh yeah I'll learn about that and then we'll go off and do stuff. So and it wasn't it was really a matter of meeting Alan Mann who was yeah so basically one thing led to another before I knew it. I was here for the duration and I really liked it and I learned a lot and I still I guess putting the talk together today I have this urge to give a talk where I talk about ideas that have sort of came across in across the transom at different points and how they stay with you for a long time. So you can have little challenges that come across that are interesting and one of them was Putty Clay. So Putty Clay I'll talk a little bit about what that is and how it works and then I'm going to report on this paper and it's a little bit embarrassing to be giving a paper that's really not ready for primetime but it's it's the idea of the paper was motivated by this notion that Putty Clay was something which was fundamental and omitted from North House's dice model and we should show people about how important this is to the social cost of carbon. It turns out after doing all the analysis we can find circumstances where it matters but in most cases I think Bill made the right choices about how he set up the model. So in some ways this is sort of reassuring perhaps to the climate community that the approach has some settings but I'm going to explain what that is and how it works. I I tend to be a little bit just driven by what I find interesting and I end up talking about that so my co-author Kristoff kept saying make sure to bring it back to what the issues are and talk to a broader audience and so I'm but I'm sort of inherently sort of like I'm curious about how things work and I'm trying to try to inspire probably a little bit of inspiration about how you go about looking at stuff and maybe somebody is interested in the modeling end enough to make it worthwhile but anyway so I'll do my best. So the motivation here has to do with emissions of efficiency improvements and how we think about what the consequences are of mitigation measures to reduce carbon emissions. So the basic sort of story has been for me goes back to Ada Macro which again was not that far from this very site was it called the slack the three the IBM 360 where you remember that where that machine was I think that was right it was down the street from Turman not that far from here we had them so when I arrived in 1980 we had a model Ada Macro the model lived in a shoebox in the corner of one of the TAs or the RA's offices it was a stack of cards it was like this long so if you wanted to do a run then you'd go out and type in new cards with new data or what other or you might do something really brave and change an equation or two and would put it in the box and you're bringing the box to the IBM 360 and you run it through and then next morning you get there at eight o'clock and you get a stack of printouts on 11 by 17 paper telling you what had come out back from the thing and sometimes you would say you know formatting error in line three or sometimes sometimes you get interesting results but it was really hard and I perhaps the biggest thing I contributed to Ada Macro was convincing Ellen that we should pay for disk space on the deck 2060 that was over in Margaret Jack's Hall and reported the thing over to Digital Fortran and got the thing to run there and that was a big change because suddenly it became a much more uh engaging way to interact with the model you could make changes and so forth so that was the the Ada Macro model which was mainly looking at energy shocks and that led to Global 2100 which was a uh a model that was the basis for Manon Richel's 1992 book on on integrated assessment looking at issues at the same time Bill Nordhaus was at Yale that's almost exactly the same time was working on the DICE model and DICE as we see it really ended up dominating the dialogue about this and I would say largely the reason is because Bill is such a good writer and he's a very clear thinker and uh he's not a modeler I mean Alan was not a great modeler pretty good at modeling but but basically Nordhaus was not a modeler but he basically knew how to ask the right questions he's very careful and you know would be systematic about how to do things so I'm going to look here at an ongoing dialogue we had about my malleability it goes back to my our initial discussions with Bill in 1985 I remember this conversation about does malleability matter you know and when and when when does it not matter so that's the thing we're ultimately trying to interest that interested in understanding is how do the policy designs that come from a model where you assume that the techniques you use for doing things can be changed overnight to a model where you account for the fact that it takes time to recover how does that you know how does that matter in a putty clay world and how does this affect the cost of abatement so this is this degree of capital mobility is crucial to the ease and thus the structural adjustment that's going to be required for ambitious policies if we think about net zero or other things that are looking for aggressive policies in the short run then that's where that we anticipate that this uh factually matters and this is oftentimes it's sort of a standard sort of um uh reference is to simply say sort of premature retirement of capital is often trotted out as being the main cost of a climate of a overly aggressive policy is like oh we're going to have to walk away from all this capital but in fact in most cases if you think about certainly in the case of carbon that's what has to happen right you have a whole large fleet of coal flying plants you can't if you you know there was some what's the statistic I remember was 2006 China installed a new installation of generating capacity in China was the equivalent of one quarter of the U.S. whole fleet in one year so there's this large sort of group of plants outing there and the question is how do we abate things and that's going to come down to how rapidly does the quasi-rent on that capital fall to zero at what point does the cost of of the the embodied carbon cause this to want to go away so that's the main sort of idea and then the third thing we'll make a point out here is has to do with the fact that putty clay matters the most when you have uncertainty that means so it's not the sort of uncertainty that typically arises in an assessment where you say we're going to we don't know about these parameter values we're going to run the model a zillion times and look at all the results it's instead uncertainty where you don't know the decision makers in the model are uncertain about the future and they have to hedge against possible outcomes so when there's hedging that means that they anticipate the fact that the decisions I make today have consequences for what I'm able to do tomorrow and that's that's where putty clay really plays an important role because you get one choice like how much electricity do I use how much non-electric energy do I use what what type of capital do I install do I buy a do I buy an old gasoline car do I buy a new gasoline car do I buy an electric car I mean these these sorts of decisions are all sort of putty clay the putty clay model captures those things and when there's uncertainty is when this this matters the most because if you're in a putty putty world I buy the electric car today lo and behold it turns out that they come up with direct air capture technology such that the problem goes away I can't simply flick my I can't change over to I can't reverse my decision right so there are two aspects before I go further with putty clay I'll come back to that I just want to emphasize two aspects of the climate problem which are important to bear in mind and I'm sure students are working on this are aware of this but I the two things and I try to give you some examples to argue about why this is these are important issues one thing is that climate change operates on a very different time scale than economic activity so a long a long term investment in economics is like 30 40 years a most of these climate events play out over a period of a century I mean there's things can happen rapidly but we'll see the second thing is there's a high degree of variability so there's lots of uncertainty in the in the short term as well so we have this seasonal variations in temperatures on the order of 25 degrees centigrade whereas over the period of a century you might have the average temperature going up by one or two degrees so there's this both of these things contribute nature of the problem if I think about the time structure this is a comparison between the return to investments in economics an economic investment where we have a sort of middle of the road depreciation rate of say about seven percent you have a interest rate that's three or four percent and here we're looking at two comparable investments the dashed line shows the investment in physical capital economic investment and the black line shows the investment in environmental capital so you can make an investment environmental capital by not emitting carbon today and the idea of the investment is you don't emit carbon you have a marginal impact on temperatures and damage in the future and that this compares the time trend of those things we see that this is the key point is that the time horizon over the environmental investment is much much longer simply has a long tail day it's set up so that the area under the curves is roughly the same but basically you have a very different profile a little bit of math I don't know I wasn't sure how much math to do but so think about understanding this effect you say well we're going to we're going to we're going to bait carbon today and that's going to affect the temperature in the future well how do you do that well you can do that and you could either think about it by just rerunning the model that's the way that most of the integrated assessment models you perturb the emissions and look at what happens or you can also just run a single nonlinear program to retrieve that so here I have a function where I'm looking at maximizing the temperature at a given point in time t hat in the future we have this vector s that's the state of the climate and there's many components of that so we have an n vector characterizing the state of the climate in year t and we're going to temperature is one of those states and we have emissions and the key thing is that if you tell me emissions and you tell me initial state of the climate then that tells me that the temperature is over time but so that means that temperature is not going to change but if we solve this problem we get back a Lagrange multiplier on emissions over time that tells us that Lagrange multiplier tells us the change in temperature at that point in the future with respect to emissions at a given point in time so you can set up the model and retrieve the whole profile of how emissions in one ton of carbon less today how many degrees centigrade does that change the temperature in the future and so when you do that using either the model so here in this analysis we're working with both the Dice climate model and another one that came out recently in nature the I forget anyway so that's a different one but both of them have this property that if you emit carbon that that carbon affects temperature long a long way in the future essentially like as a permanent change in temperature and furthermore that's operating on a timescale such that the timescale that matters to economic decisions say an annual timescale is basically doesn't matter in the climate in other words here I compare and you can't even see the difference because the lines are the same but here I compare a one a five and a ten year timescale on the climate model and it doesn't change the the economics of the thing doesn't change the overall gradient is driven by the climate timescale and other stuff is not doesn't really matter so therefore the number of years per period again for looking down the list of stuff that build it right ten year time intervals if you're thinking about climate that's the main sort of effect of course then we have we interact this gradient that tells us how temperature changes depending on climate emissions with assumptions about what's the discount rate what's the damage function how much does how much does damage go up what happens to GDP so all these factors that describe how much economic activity is at risk and if you bring together those economic variables present value prices GDP damage function those things are all different and then you end up getting a social cost of carbon that brings back all those damages in the future but one of the things when you do this gradient calculation is this gives you a way to understand where exactly does the damage come from right in other words I am in an additional ton of carbon today how much of that is damages that's experienced by my kids how much of it is experienced by my kids kids you know in other words if I were to bribe someone in the future for having the right to admit more carbon if I had a ability to make a transaction say here I'm going to you know pay five dollars and I'm going to amend an additional ton of carbon and that's that's something that'd be willing to accept this profile then from the temperature profile gives you a handle on how that so this is from 2020 that's the damages the damage profile 2020 30 then the profile goes up higher 2040 the profile goes up higher so this is showing what's happening over time with an ongoing against the backdrop and if we normalize that by the emissions over time so if we're in the first best world then the damage function is going to be coming down but if we normalize it by the emissions profile these are fairly stable so basically the overall profile this is just making I'm just making the point that in this in these models we're we're we're bringing when we do an integrated assessment model we're bringing back future damages to the present and that's not only looking at the social cost of carbon as a single number but it actually in addition to that we get a profile over time of where the damages occur the seasonal variation I'll just point out that seasonal variation dominates vanderby's local warming model estimated with Madison data so this this is just to remind ourselves that we have now of course this varies around the world some places have more seasonal variation than others but if you look at for many places in the U.S. this is not that uncommon that the variation the black line is the estimated is the estimated temperature change the blue line shows the actual variations over these years I forget I can't really this is not exactly fitting I guess I should it's so that's over over years and then we have then the the red line shows that the linear trend that's going on that comes from the the climate estimation so that's sort of the background that's what integrated assessment is a framework where you can make a simple assumptions about you you can have a model that characterizes temperature response to climate you can pour in assumptions about damage damages you can pour in assumptions about GDP growth population growth and then that gives you a framework for assessing what the damages are that are induced in the future by activities today for the present and the challenge we're thinking about now is okay so if we're in this sort of world where we're doing thinking about best response what's the best reply that's a world where we have to think about how costly it is to get from here to there and the fact that we have a dynamic model doesn't mean that we know very much about what the adjustment cost is the adjustment cost is sort of separate the fact that we keep track of what happens to client with capital in every period that's sort of that's not enough to tell you what the speed of adjustment so the speed of adjustment really comes back to life you Hansen I I spent a couple years in Bergen sort of between my masters and my PhD working at the Norwegian School of Economics had a really fun time there was with a project run by Victor Norman, Agnar Sanmao, but all the guys at Honoless High School their main sort of competition was at the University of Oslo was life you Hansen now he he passed away shortly after I arrived but his modeling work was really profoundly influential and it's kind of interesting because I in Norway in fact all over Europe I'd say Johansson and Tim Bergen were the two economists that had the biggest influence and yet Johansson was really kind of unknown in America and I didn't until I was putting together slides to talk I looked at Wikipedia I didn't I never knew this before that the reason you don't he's not known in the US is he wasn't allowed to come here because he was in the Communist Party in Norway and therefore he was not granted a visa to visit so it's kind of amazing anyway so he was the guy who had this basic idea about keeping track of of vintageing capital and I'll explain how that works so this this vintage models have this predominant assumption of factor substitution here we're thinking about labor and capital but really labor and capital is not where most of the action is if you think about vintageing it's going to matter a lot in terms of either missions or energy use these things that are that are the crucially important factors that drive economic output so both of the in the the key thing is that we have to keep track of an x anti-production surface and an x post and the key idea here is that you get a choice so here in this huge paper from 72 makes this trade-off when you think about the labor capital the factor intensity labor intensity of output so labor the ratio of labor to capital as we increase labor inputs there's diminishing returns is the key assumption so as you get as you add in more labor you takes more and more capital hold output at the same level and the key point idea here in putty clay is this idea when you pick a labor capital ratio x1 x2 x3 you go up to the x anti-curve and you read off what the output is at that point per unit and that's going to be held the same overall subsequently that's going to be the way you have to operate the technology so the amount the decision is made once at the beginning about where you're going to be in the iso-quant and after that you have to live with that choice so if you think about the trade-off and now I'm getting back to this sort of idea about the trade-off between man's approach to integrated assessment and Nordhaus's approach man had this idea that we have to be concrete about things one of his favorite um some of his favorite interactions were with chance star who was the the the scientist who was basically in charge of epi and they basically had this notion that we want to think about exactly what the solution is to these problems and you think about energy or you think about climate and allen was a big fan I remember having a discussion with him actually in 86 where he was talking about no no it's all about elect you have to decarbonize electricity and electrify everything that was the basic sort of story and this was something so his idea was that the dice model was really not adequate because it didn't capture the essence of what the message is we had to send about how to deal with climate change so allen early on got this idea no we have to find ways to produce electricity which are low carbon and then electricity is a much is is the one technology you have that can replace the existing energy thing so that was the basic notion and merge was this idea that we think about track what's happening with technologies in different places it's multi-regional so it can basically look at at burden sharing issues and it also had this electric generation and non-electric energy now there were certain shortcuts that were made in merge so merge did not keep track of capital stocks of electricity and non-electric energy so a number of things that are that are not perfect about it it's been improved I'd say that the air to merge is probably is Jeff Blanford's model for the US is probably the closest to this has a lot of interesting detail and so the thing is that it lives on in the US dialogue but the basic sort of notion of merge was this idea that we have this trade-off between capital and labor and between electric and non-electric energy and then the key thing is that we have these technologies and fuels they go to energy cost and then on the up so on the on the input side there's putty clay going along between how much electric and non-electric energy you have per unit of output as well as how much labor and capital and that gives you a short run slow response over time then this can drive demands for different fuels and different costs of course then it's integrated assessment model so it captures both emissions and what happens to climate and the key point here is what's how much does technology drive things so this policy versus no policy dimension you also have this technology versus no technology so it gives you a framework think about the value is of a new technology and this is it's a framework that basically drives the basic virtues of these models is you have the explicit representation of a problem you have a framework for for for assessing alternative approaches there's this logical appeal of the of the equilibrium framework you have an explicit climate and technology constraints you can introduce risks of uncertainty and can all all these various factors can be embedded the problems are there's oftentimes a misunderstanding of what the issues are and what the model's capabilities are i'd say that's the main the main message i'd say for modesty is important so the simpler the model the better the framework doesn't you know basically if we move away from optimizing behavior then things get really complicated really fast and you also have to sort of understand all this underlying economic theory and so forth and that's that's a challenge and so this blackbox approach is becomes difficult right so and this is where it goes back to this this great paper from 85 about the the energy modeling model about the role of what the what's the role of model models in the policy process right analysts gain access to policymaking on the base of what they know and models provide a framework for assessing the eyes paper is about the you know how models get evaluated is this just tick boxes of what's in the model and also about the misuse of models as symbols right so there's the variety of different things from this paper i think are relevant my approach to models so is this idea that they provide a framework for second order agreement and the idea of the model we have to be humble about what we can achieve the idea is if you're trying to make a claim about an issue then you should be able to the existence of a model that substantiates a particular point of view should be a sufficient condition but not an necessary condition in other words before i listen to your story i want to see a set of assumptions gives rise to that story part of this goes back and again i threw in these slides the last minute because this is something there's very few things in graduate school you can remember i can remember precisely the day of this lecture this was uh david luenberger luenberger was a electrical engineer who is quite famous there's this thing called the luenberger observer knows all about control theory and somehow and i don't i never knew him that well but he somehow had this idea he's going to learn economics and he decided he's going to join the ees department and teach economics and so at that time there was like three or four different economics classes you could take you know craps taught the course over in the business school there was a class in the econ department but luenberger's class was so great he was so clear and precise he it was the old school so he used variance book but one of the things he he introduced this idea we had to he assigned a problem where we had to do something and he said well let me explain how you use a model and then he proceeded to to bring in this make reference to the 50th anniversary of the golden gate bridge so the golden gate bridge was going to be open to pedestrian traffic for the first time ever it had never been opened pedestrian traffic this was something i'd worked as a bridge engineer in the peace corps so i was kind of aware of this that trucks are about 150 kilograms per square meter human beings particularly if they're having fun together 400 500 kilograms per square meter they can get really heavy so the question was is it safe and so there were several different proposals for how to go forward with that one of them was a reduced form method where you keep track of strain gauges on the bridge keep track of how many trucks are there try to predict what's going to happen from the strain gauges to what whether it's gonna how much it deflects the other post was to say let's uh let's use a finite element model characterize the characteristics of all the pieces of steel on the bridge and then use that to simulate what happens and the key thing is this is this notion of this x post for this x anti assessment and you know that of course the predictions were from the structural model were much closer to what actually the deflections were that were observed and so that i thought that this model sort of captures the idea about why we want to you know have a framework for looking at things so now we go back to dice and so i'm thinking okay well let's look at the dice model let's think about the social cost of carbon and let's assess how robust this is to our assumptions about putty clay that was our original idea the the canadian environment ministry wanted us to assess um so have a perspective on social cost of carbon we said fine we'll we'll use this an extension of this we have a other versions of this model many there are many many versions of dice around but here we're going to basically be thinking about putty clay in the notion about how much abatement we undertake so that means the abatement decision is not made in every period but it gets remade for new vintage capital so when you install a new capital you have to buy additional costs are undertaken and that induces additional costs down the line you have to pay those costs and full and that gives you a framework for understanding how the decisions we make today affect the future okay so our version will be one that works on an annual time step we need that in order to look at sort of aggressive policy in the short run it incorporates sort of putty clay uh capital adjustment and it it also is going to incorporate policy uncertainty under either learn than act or act and learn settings so learn than act is where we basically you can do a lot of bunch of simulations different assumptions and then make a decision at that point the actual learn says we have to make decisions initially and live with the consequences of those outcomes so the research questions we're interested in is how does that influence the cost of intermediate climate policy and such as net zero by 2050 how does the social cost of carbon depend on assumptions regarding capital availability how does the revelation of increased climate damages affect near-term abatement to what extent the model responses depend on putty putty and versus putty clay capital adjustment and then uh how does this affect how are these things affected then by policy uncertainty and that's one of the things I think I find interesting is that there's always this rolling if you've worked on this for a while there's this rolling horizon and this is I think a characteristic of the political processes that there's always aggressive policy claims are made but they always are at some point in the future and then the the affected parties those who have a have a ox to get gored by the policy they're always they're not necessarily engaging the debate about what's the appropriate thing but they're always trying to rule the horizon out further and was it one of the sporting events I forget what it was last year Super Bowl the Exxon ads sort of talking about 2070 objectives just like you know always pushing things forward and so that's the idea is to think about how does uncertainty about when we actually get serious about climate affect things I should say that this week's announcement by EPA sort of changes things there this is this talk was motivated but by relatively modest objectives where there seems like they're actually getting more serious about it which is a good important sort of dimension so here in this analysis we're going to do some sensitivity analysis where we think about in order to identify what matters we're going to think about the climate cycle so we have this other alternative model to dice this fair model we've calibrated and then we have the capital mobility and that affects sort of the abatement policy so this and this is all based on this Ramsey model it's a Ramsey growth model which combined with simple climate model and produce a framework for cost benefit one of the things that's important to bear in mind with the Ramsey model let's see if I got the next I don't where do I put the objective function well there's I'll just do it here so if you think about what we're doing is we have a you have a objective function that says maximize the sum over t of l sub t divided by one plus delta to the t times u of c sub t over l sub t so this is a utility function is diminishing exhibits diminishing marginal utility it goes like this it actually goes down to minus infinity and this is going to be as a function so this is u as a function of c divided by l so c over l is per capita consumption this isn't the population this is a discount factor that puts less weight on on future generations so this is a this is something that's quite controversial what the right level of delta is but the key point here is that this is a modelist looking over time and in the dice framework it's looking at average sort of global consumption divided by so this is per capita global consumption if we if we take this model and put in heterogeneity across across households then the dominant effect is also to do with redistribution within time in other words the differences in income across around the world are huge compared to what we have that's induced by climate so it's important to bear in mind we're working in a very uh it's a very constrained box that we're working in for thinking about this problem okay so so this is then looking at the abatement in the x anti curve on the right hand on the left hand side we show what the GDP costs are per unit of abatement and on the right hand side i'm just emphasizing the fact that this trade-off between capital labor and energy or emissions has to do with the point you're going to be operating on this curve and once you make the decision you're stuck with that so aggregate production then depends on capital labor and that's going to be in the putty putty model it's an aggregate effect in the putty clay model the output in a given period is a combination of output from extant vintages y x sub t is things that existed before the start of the model uh y n sub t is going to be the new vintage production you introduce in that time period and y v sub t is going to be vintage production that's stuff that's been installed since the beginning of the model but it's updated so that's going to be y v sub t is represents all the investments that have occurred beginning at the first part of the model so the key thing is and this is we get back to the the framework thinking about um that again thinking about chinese investment in coal fired plants here you think about the fact that the extant production is a result of the of the characteristics of all the existing fleet and so here in to take the dice the uh dice model and put in vintaging you have to keep track of what the outputs are of all the previous vintages that are operating at that point in time and what their emissions are so part of the model is understanding what is the quasi rent which is lost if you walk away from an old capital stock from previous years and so that's going to be uh represented here and this is this idea that we have to make a decision the endogeneity of the the abatement decision here is not going to just be how how efficient do we make new cars it's also when do we discard the existing cars and so that's the decision here which says that the vintage output in period tau is going to be one is going to be less than or equal to one minus delta times the vintage of output in the previous period and so therefore that if that constraint is slack if it's not in the quality that means that you're making a decision to to walk away from capital so that and that's part of the abatement measures and if we think about policy measures on the table saying we want to go to zero emissions over a relatively short period that's something that has to be operational to the decision and that's something that it's a uh characteristics of the model which is not estimated that's something that has to be parameterized you have to know what is the investment what are the characteristics of the existing i guess mainly it's going to be the automotive fleet and the generating capacity for for uh for electricity new vintage production then is a combination both of new vintage labor as well as investment so i sub t minus one is going to be investment l n is going to be how much new vintage labor comes into the economy so there's a there's going to be an aggregate labor stock part of it gets tied up with the existing capital and then there's new vintages what happens the people that are newly entering into the stock of course you pick up additional labor if you have premature retirement then in the periods after you have premature retirement that's going to be give a boost to what the amount available on new vintage labor is and then there's also an abatement decision that's made for that vintage um and finally this is the thing that again um i found really kind of mysterious when we first what's amazing is that you can capture this whole sort of complexity of of um evolving sort of energy intensity or carbon climate intensity can all be captured by this equation that keeps track of how much new vintage capital you have and how much extant capital you have v or i'm sorry a vintage capital you have and this then determines the whole sort of evolution so basically you make decisions about new vintage and you have to live with that going forward it's a little bit um you get this property that essentially all the decision the decision you make on new vintage characterizes what the cost is over the full life of the capital stock and correspondingly there's also emissions then that emissions in time t then is extant emissions from all like old capital stock the new vintage emissions and the and the uh existing capital you've invested before and there also may be this script e sub t and the dice model is emissions that come from non non energy sources and then so this is keeping track of how this this evolves over time so the putty clay framework these two four sorts of abatement we have to basically make decisions about how much we want to abate emissions in new vintage capital and how much we want to retire extant vintages so uh so and that gives you the then consumption in time t is is and plus investment is output uh diminished by damages diminished by abatement cost and so the abatement cost decision is something the abatement cost is how much you lost of output the decision is if you're going to put on something that captures carbon you're going to have a loss of energy efficiency as this is capturing this idea that investment decisions affect abatement decisions affect the overall cost of the of the of the operation okay so let's look at a few numbers i'm not a lot but just a few things here putty putty versus putty clay i think about a ramsey model which ignores climate entirely a b a u model where we have a pure externality or an optimal policy where you trade off costs and benefits and then we also then think about how is this affected by the depreciation rate so we have a four percent rate it's a relatively low one reference rate is seven percent i think in the original dice model bill used ten but seven is sort of closer to the the averages in the ocd or have a ten percent as another alternative and then finally we have climate climate damages there's this reference case from the dice 2016 which for which north house received a fair amount of flak uh handful at all in nature climate change a couple years ago produced an alternative estimate and then we have a couple alternative uh learn then act versus act then learn so if i look at what's going on along the baseline we have uh the climate damages uh and capital depreciation for different emission levels so here if we look at the on the on the right we have the ramsey model which is sort of that that's the baseline model with no uh no climate damages and the right hand side we see what the effects are of the high damage so and this is just pointing out that the that there's separability that the baseline is is affected but it's relatively modest in this in this run so in the ramsey reference and hs dam coincide the climate damages are ignored in the ba u the higher damages lead to lower output which in turn slightly lower emissions so it's but it's relatively these interactive effects are relatively modest if we think about the optimal model then it matters a lot and so here we have the basic assumption about what the damage rates are and that's the thing in this sort of integrated assessment framework um the the level of of abatement is driven a lot by the damage estimates and the damage estimates are the thing we know the least about as it seems as though with every time we turn around the damage estimates are are perceived to be going higher and so that but and so that means that the model to a certain extent is going to be driven largely by that assumption the other factors whether or not you have reference or how much the the depreciation rate is that stuff is all second order compared to what the damage assumptions are um so we think about that's so that's depreciation and there's the ba u and there's the optimal policy so we can see that there's a little bit the open policy is going to be quite a bit lower and so damages will be quite a bit uh but then emissions or how much the overall emissions then depends a lot and here we're looking at so we saw that putty putty and putty clay not a big difference in uh in many aspects of model but over here if we look at emissions there's a big difference so here if we the key thing is for in the high damage assumption so we have the handsome at all damage function in the putty putty model you have an immediate drop because you can basically reform the entire capital stock whereas over here if it's a putty clay model then you have to live the decision to reduce emissions rapidly is a decision to walk away from existing capital so it's going to be a much lower the response rate is much it's much slower uh the capital uh depreciation rate if the capital depreciation is lower then you basically if it's as low as four percent then in the in the putty putty model you may actually have uh the overall emissions may go up over time whereas in the putty clay model you can see that there's a jump there where the the damage is down rapidly so then again this is just looking at what the emissions are by vintage for the high damage case so here we see uh in the putty putty model it's a relatively smooth um uh reduction over time whereas in the in the putty clay model in the putty clay model there's a big difference the red line shows what happens to new vintage emissions so this demonstrates that uh emissions in the putty clay world where we have to live with the fact that we can't change the entire capital stock we can't afford to be blasé about what the amount of abatement is in the new capital so this basically tells us that policies which mandate substantial changes in the short run for new vintage capital are not that far off given the fact that you don't have access to the entire capital stock so that's that sort of justifies this notion that aggressive policies there's no real big difference in terms of what the overall uh social cost of carbon is but there's a big difference in what the marginal abatement is and that's because the way to think about this is that the new vintage investments made today anticipate the fact it foresees a future where carbon prices will be rising and so therefore the decision to abate is is reflecting the fact that they anticipate the carbon tax rising substantially um so this is just looking at emissions from extant capital new vintage and vintage capital so the new vintage is going to be going down but you can see here that in the abatement in the putty clay model with when you have an aggressive policy that's with a high damage you're basically going to walk away from substantial portion of your of your extant capacity so this is a model where you have to have some shortages in the if you know this is basically something where the the the mechanism you have for abatement is by uh abandoning old capital and uh you want to make new capital as efficient as possible but that by itself is not going to be enough so finally there's this difference between the social cost of carbon and the marginal abatement cost in the in the putty putty model those two are exactly the same but in the putty clay model they're different and for exactly that reason that the the shadow caught the marginal the social cost of carbon reflects what the damages are that are experienced going out in the future brought back to the present that's the damage but that's and that's going to be the the carbon price at that point in time but the decision about the marginal cost of abatement the abatement decision is reflecting the anticipation that those prices are going up so therefore you have much higher levels of abatement in new vintage capital and finally we can look at you know we can look at discounted utility through a given year and look at that in terms of what the tradeoffs are and again with it's going to depend on if you uh want to have prescriptive or descriptive discounting but if you basically calibrate a model to what's existing capital the tradeoff here is basically this is looking at the consumption investment and overall welfare so we're going to have a thing where the the optimum mitigation reduced the return to capital in short runs where you have consumption goes down but then you have a big gain out here in the future and that's basically capturing the fact that your foregoing consumption in the near term to increase consumption long term that's sort of that's the the story that's being told the gray line reflects if we use existing discounting rates the discount rates that are present in the dice model that are calibrated to what's observed about rates of abatement that are rates of consumption growth and interest rates it's it takes a long time for it to break even so it's essentially that in the in this framework even with the high damage case there's a relatively long period over which the net net gains don't add up so the final thing i'll just and this is relatively price if we think about probabilities of going to net zero by 2050 2060 2070 so here we have different levels or we may go back to the optimal policy of the probability five so here i'm posing it as though the abatement measure the net zero targets are on top of existing methods so we write down the deterministic equivalent model again i won't bore you with the details but here we see a much bigger difference between the models so this is this idea that if there's uncertainty then the hedging is much more important here because in the putty putty model the idea that we're going to have a net zero that simply says you say well that's fine net zero is coming we're not sure exactly what's going to happen but when it comes we can drive everything to zero right off the bat because there's lots more melodyability but if we're in a putty clay world basically you want to act right away because you anticipate that you might be in a world where there's much higher reaching that target is going to be much higher if you can't reduce emissions from existing capital because the only way you have to reach some of those targets is by walking away from a large amount of capital stock so that's sort of capturing this idea between looking here at learn then act versus act and learn you can capture you can calculate some decision theoretic metrics like the the expected value of perfect information it's not huge the fundamental problem is that this is essentially you you get big differences in terms of what happens in terms of policy but in terms of overall cost this is not hard and this is just the elephant in the rabbit the overall fraction that's the thing that's fresh around the climate it's a fraction of overall economic activity it's not huge it's not a big factor but it basically it's it's something that matters so here we've just looked at sensitivity so I apologize for being a little bit my again Christof was charting me for not getting more having a very I mean in some sense this is one of the things with modeling is you do sense even analysis to see what matters and you may discover that it's not as big a factor as you you can construct examples where it matters but it's it's basically not something I'd say on the whole I come away from this thinking that Nordhaus made a bunch of good decisions about his design of a small thanks very much time we have time for a few questions in the room now any anybody have any questions they want to ask volunteers no one so you actually talked about the regionality of merge and whatnot yeah have you guys actually thought about doing a regionally disaggregated version of this analysis given the difference in the economies that you already alluded to what's I mean the only thing I just I made a mention there of the heterogeneity if we think about brooms notions of goodness versus justice we have these notions of trading off you know what how much abatement should we undertake we have this idea of trading off the present versus the future but if you bring in enough poor countries then the the wealth differences and the income differences we have across countries dominates what the induced differences are that are induced through climate action so the thing is that's something that I'm not sure exactly how to do that in this model because the model is just going to tell you you tell it okay how much do we attach carbon you're gonna it's going to do something if it gets to give the money away to developing countries it's going to give as much money as it can so that's that's sort of the biggest challenge these trade issues are a big issue like we have a big project we're going on now about the effect of border carbon adjustments on developing countries for the world bank and but that's it's much more that that I don't think you need an integrated assessment model to look at those issues because it's not really about the question is here and now so if you have a 15-year horizon I think you've captured what is primarily in the debate any any questions from the audience so the the other one was going to ask we can pursue this more at dinner is in the trade regime there is this concern now about whether the IRA program here and the carbon border adjustment mechanism in Germany are totally inconsistent with each other and what to do about that have you guys already thought about that no the thing is that's definitely something that we are our work initially I mean Carolyn fit Carolyn is much more aware of what the issues are but clearly that is the challenge like how do you ascribe that's the challenge with climate is you can there are all sorts of different ways to skin the cat and how you give credit from one versus the other it has as big fact it has big it matters a lot for certain industries so the challenge we have in this is that the data is not even that I mean the effect the sectors that are most affected we don't really know very much about the you know it's it's a challenging it proves also just to get a a first-order estimate of the effects is is difficult difficult but you know the I feel like I'm star wars you you guys maybe are only hope and how to figure that out I mean obviously treasury needs to decide who's going to get what credit for which elements in the IRA but at the end of the day there is this big kind of trade overlay yeah which I think we'll continue to dominate in one form or another I mean the thing is that my the talk I give about trade is border carbon adjustments curb your enthusiasm Chris did a little bit of that last year but it sounds like you're a little bit more in that direction I'm yeah anyways I think we're just about out of time so let's thank Tom one last time if any questions he'll be around for a little bit thanks