[MUSIC] We have finally reached recession where we can discuss the results of a DICE Model. And we are going to do this by comparing the results of the DICE model with the results of another very influential and well known report, which is Western Review. Which was carried out quite a few years before the DICE model at the behest of the I believe it was prime minister at the time of the then prime minister Gordon Brown. And we will see that these two approaches share the same conceptual framework, even if the specific assumption here and there are different, but they come up with radically different suggestions and therefore it is imperative. It is essential if we want to use this type of approach is seriously to understand why the answers are so different. And in a way to choose between the two, we can't really sit on the fence and saying only one hand, on the other hand, if we want to use these approaches to inform policy and to tell us something about how the world works and how the world might work. If we take certain courses of action, we have to make sure that we in some way believe the models. Therefore the focus of this short session is to understand not just what the DICE model says, but to compare it and to try to understand why the two approaches, despite the similarity of overarching modeling, give such different results. So remember again, the DICE model optimizes over the investment fraction, so how much I should invest in productive activities and the abatement fraction. So how much I should invest in climate debating strategies at each point in time. So I have a part of money that is variable, it is for me to decide and I have to decide everything I invest I give up consumption today, but I have to make an extra choice with respect to the usual optimization exercises. I don't just have to decide how much I want to invest in a productive initiative also, how much I want to invest in the abatement fraction. From a theoretical point of view, we have seen in previous sessions that the rate of return at the optimum should be identical and there is a no arbitrage argument that underpins this equality, but in reality that needn't be the case when we are away, for instance, from optimal solution. And I change all these quantities here in order to maximize with discounted utility. So once I've obtained the optimal path, I can ask a number of questions. For instance, very important policy questions such as how fast should we ramp up the abatement effort? What will the temperature anomaly look like at the end of the century or at any point in time along the optimal path? What is the social cost of carbon with social cost of carbon is, in plain language the carbon tanks, that in a rational world if we believe in all of this, we should impose on carbon. So you can immediately see what hugely important answers these models are supposed to give and that's why it's so crucial that we understand where these answers come from. So these are the main results from DICE. It says to act optimally we should invest today, we should invest today more than we actually do, but actually we should not invest at a break-neck rate. We should ramp up over time our investment in abatement initiatives from about 20% today going up over time and why waiting? Well, I think, you know the answer by now because to some extent it is embedded in the way the model is constructed. Remember that the model assumes they were going to be richer in the future. So does for the stone review, by the way, since we're going to be richer in the future. It says it makes more sense to make sacrifices when we're richer then today. Also in the DICE model, there is an ever increasing improvement in carbon technology. So carbon intensity is going to go down over time all be to the declining rate. So not only are we going to be richer, but we're also going to be smarter in the future. So if you put these two things together, intuitively, you can understand very well why the diced model says, act more than we are acting now but don't do a front loaded acting. Don't do a front loaded investing because this will be a long way from optimal. It also says along the optimal path, the temperature anomaly by the end of the century will be around three and a half centigrades. We could do better but it says it will not be optimal. And at this point it is crucial to stress that in the DICE model there are no tipping points. In the DICE model, there is a damaged function, it is the damage inflicted on the economy via the temperature anormaly. And this damage function is quadratic. So as I increase the temperature, the damage increases quadratically, if a double the temperature that damages four times as large, there is a long big debate on the correct exponent and I won't go into that. But the key feature is that in for DICE model, there are no tail events. There are no tipping points. There are no abrupt climate changes. If we uncertain that the nature of the answer could change. I mean the nature because it means if I become very, very afraid of a low probability disastrous events that might justify acting earlier because later might be too late. So that is something that is important to keep in mind. And another very important outcome of the DICE model is that the social cost of carbon is approximately $30 per tonne. $30 per tonne translates into 9 cents per gallon on gasoline, which is not a very high tax. And this tax, social cost of carbon obviously equals the carbon tax and in a rational world in which we internalize the externality so we price the externality. There will be the social cost of carbon such that the emitters of carbon are- I wouldn't like to punish because in economic terms is really not correct, but they are made to pay in a way to compensate for the social cost that they inflict. The study of externality is a lot more complex with Bigouvian and Coasian externalities. But let's just keep it simple. So social cost of carbon equal tax, equal 30. Dollars per ton, approximately nine cents per gallon of gasoline. So reasonable results and not alarming results in by any stretch of the imagination. Well, let's look at this stern report, according to Stern to Professor Stern, to act ultimately, we should ramp up the abatement effort very sharply. When an initial abatement fraction of about 50%, much higher than dice and the social cost of carbon is about $300 per ton. To increase to $700 per ton by mid century. This is these are staggering differences, and the conceptual approach followed by the two models is identical. The key difference is the social discount rate, which is 1.5% in dice and 0.01 according to Stern. Let's see what the implications are of these numbers here. By the way, how did 0.01 come about? It is a somewhat strange argument that says, well, there is some probability that humanity might disappear in any case, and I estimate this probability of being 0.01%. So let's put this discount factor here. But the under apart from this little wrinkle, the underlying philosophy in the stern approach is we should treat future generations exactly as it were today's generations. This is there is an enormous amount to be said, pros and cons about this approach, about this is not an approach about this assumption. And we'll discuss some of the consequences of this position and to see whether we feel comfortable with this assumption here. But let's try to analyze a bit more carefully where the differences come about. Remember that in integrated assessment model, the only discount rate that appears is a quantity that measures how much we care about the welfare of future generations relatives to ours. Is the rate at which we discount utility. And we have also seen in the previous lecture that the equilibrium return on capital, which I indicate by r star here is given by the sum of rho plus gamma g. Rho is this discount rate which professor Not House dice, sets at 1.45 and Stern set at 0.01%. g is the rate of consumption growth. And we have seen that in the dice model that rate of consumption growth is closely linked to the ever increasing total factor of production. And gamma is the elasticity of a marginal utility of consumption, roughly how much I'm willing to trade off a loss on income today to avoid a loss of consumption in the future. Now, a key observation is that it really makes no point in looking at rho or gamma or g in isolation. If we did a net present value approach, what really matters is the total discount factor, which is the r star. So despite the fact that we don't explicitly used a social discount factor, r star when we're doing integrated assessment models, all the ingredients are still there. And therefore even if they don't appear explicitly in the discounting when we assume a rate of growth and when we assume a utility function, we specify g and gamma. Therefore all these elements come into play into an integrated assessment model and determine r star. If we have very different r stars explicitly because we put a different role or implicitly because we put a different gamma og, we're going to get very different results. Now in the Stern review, a value of gamma equal to one is chosen. This represents a logarithmic utility function. This is not a conventional choice. This implies an extremely when we look at gamma as risk aversion, which is not what we're doing here, but they would imply an extremely low risk aversion. Economists tend to prefer values of gamma higher than one. Stern in particular uses the value close to 1.5. The growth in the economy is assumed to be 1.3% and this gives, there is a real rate of growth and this gives an equilibrium rate of return on capital of 1.4%. Let's go back to the equation here. I put gamma equal to one, I got g equal one 1.3%. Rho is 0.01%. I put everything together, I get approximately 1.4%. This is an outlier estimate. It is very different from any estimate of at least the current return on capital. It might mean that in the future, return on capital might be much lower, but I don't think it is reasonable to assume that this would be so with certainty. Perhaps we can make a dispersion of rates of returns on capital and introduce uncertainty. But it would seem logical to introduce the uncertainty around a central estimate of the the rate of return on capital, not around an outlier estimates. And what are the implications for Professor Stern's extremely low rate of return on capital? And to explain this I'm going to bring to the fore what is called the wrinkle experiment. Wrinkle experiment is a thought experiment, something that physicists like to do a lot and sometimes also economists like to do because they can't do, we can't do real experiments and therefore we like to do thought experiments. And this is also to probe our responses and see is what I assumed, actually consistent with the way I would respond in this situation. And what is the situation in the wrinkle experiment? Well, the situation is described here. Imagine that we discovered today a strange feature in future climate, in the future climate system and this strange feature I can abate today, I can eliminate today. And the strange little wrinkle in the climate will cause damages equal to 0.1% of net consumption starting in 2200 and continuing at that rate forever after. So it is a damage of a 10th of a percent in 2200. And then it continues at that rate. Another question is, how much would we be prepared to pay today in order to avoid the effect of this raincoat? So pause for a second and think yourself. So how much I'm thinking in 2200. These are not my children. These are not Their children, it is a pretty distant generation. And it's not that something dreadful is going to happen to this distant generation. They're just going to have a loss in consumption of 0.1% and this loss of 0.1% continues at the rate forever thereafter. Well, because of the extremely low discount rates, with the Stern approach this future damage, even if small but integrated over an extremely long period of time implies that we should give up today more than 50% of today's world consumption, in order to divert this future negative outcome. There is another way to look at it. Remember that the Stern approach agrees with DICE that we're going to be richer in the future. Therefore, in 2200 in the world or Professor Stern, the per capita consumption is going to be $87,000 to be compared with consumption today of $6,600. And therefore the conclusions here are that in order to eliminate this wrinkle, if I take the Stern approach, I should be happy to reduce consumption per capita today from $6,600 to $2,900. To avoid a reduction in consumption in 2200 from 87,000 to $86,900. And similar proportional reductions thereafter. Printing this way is not a one off. I have similar proportional reductions thereafter. So this gives food for thought. There is no right and wrong answer. You might say yes, absolutely, I would do it. Or you might say no way. This is absolutely not something that I find consonantal resonant with my way of assessing my own benefit and the benefit of future generations. As I said, there is a huge economics and philosophical debate in this area, but the fact that there is a huge debate doesn't mean that we cannot set out the terms of the debate and make informed choices ourselves. So the Stern policy recommendation in the Wrinkle case stems from the near zero discounting used by Stern. With this discount factor, we would trade off a large fraction of today's income in order to increase income in the distant future by a very small amount. And there is another important feature about having an extremely low discount factor. Decisions become, let's say on a hair trigger. Meaning by that they become extremely sensitive to uncertain events in the distant future that continue for a long period of time. Because we are adding up, we are integrating all these future losses or benefits whatever it might be over virtually infinite point length of time with very little literally discounting. Now moving away from the Wrinkle experiment to be much more relevant and important, climate change decision making. What I've tried to highlight is that the Stern approach and the DICE approach give radically different answers because of a serious of, not a series but one key difference in assumption. What should we use about the discount rate. Now, it's essential to notice that both the Stern review and the DICE approach do not allow for the possibility of tipping points. Do not allow for the possibility of very negative tail events. So that is not what differentiates the two approaches. It might very well be that if we increase the possibility of really negative outcomes, perhaps because of tipping points, perhaps because of abrupt climate changes, then the conclusions of a DICE report might change. However, this is in a way, a different type of question. Why is it different? Because this has to do with describing the world. Describing the world is difficult, but it is not impossible. As we gain knowledge about abrupt climate changes, as we gain knowledge about how the climate works, we can expect to make this distribution of losses more and more precise over time. But when it comes to the social discount factor, when it comes to the discounting that we should use, well, there is no scientific discovery, they will tell us what approach is the right one. And yet we get such different answers. So to me, if I were to say, given what we have discussed, what social discount factor do I find more not right, but more resident resonance with my ethical intuition, I see the point that we should not neglect future generations, but I find the totally and completely generationally altruistic approach by Stern. I find that it does not resonate with the way I feel about present welfare, the welfare of my children, welfare of their children and the welfare of future generations. And the example of the Wrinkle Experiment brings it to the fore I think in a rather clear way. Personally, I would put a discount factor somewhere in between the North House and the Stern, but considerably closer to the North House than to the Stern. However, this is my preference and I am not claiming for a moment that this preference is more valid than any other one. But this is the key point that I want to make. And this is the key point I have trying to make throughout this course, ultimately deciding what course of action we should take about climate change depends on knowing the facts and on understanding what our decisions depend on. And these elements, what discount factor should I use depends very much on how you feel about intergenerational fairness. And therefore understanding these issues puts you in a good position to make an informed judgment as to which policies are more desirable today. Whether we should invest a lot now, wait for later, impose a carbon tax, etc. Thank you very much. [MUSIC]
