In this part of the course, we're going to look at several important interrelated things. We're going to revisit the net present value approach that we've already used when we introduced the concept of a levelized cost of energy, we are going to establish the optimal level of investment in a project given preferences and a fixed endowment; fixed endowment means how rich we are at the moment. We're going to find the relationship between the interest rates, the return on capital, and the return on a welfare preserving investment invoking no arbitrage arguments, and this will lead us to the simplest version of the Ramsey equation and the Social Discount Factor. This is a big plan for this part, and we'll go in chunks and little bits at a time. Starting from the beginning, let's revisit the ideas behind the net present value approach, which, as I said, we've already employed when we looked at the levelized cost of energy. The net present value approach simply says, look at the future benefits or costs that you're going to incur, discount them with an appropriate discount factor, get the total sum, and decide what to do based on the cost of entering this initiative. If the difference between the cost present and the future discounted benefits is greater than zero, if I have more benefits, do the initiatives; if it is negative, if I have less benefits than discounted costs, don't do the initiative. Well, this is a very general strategy that applies in particular to the projects relating to climate change. For instance, should I spend money today to invest in a solar panel? We shall see that a really important quantity in all of this is the discount factor. This is always true, but normally when I look at these net present value approach in the context of I don't know, and industrial decision, I'm discounting cash flows over a few years. If I'm looking at a solar panel in isolation, I should also discount the cost today and the benefit it provides over 10, 20 years, the lifespan of a solar panel, perhaps they're slightly longer today, I don't know, but over a reasonable number of years. Therefore, the discount factor makes a difference, but it's not a huge difference. However, when I'm using the net present value approach in order to look at the climate change problem in its entirety, the vast majority of the damages occurs a long way in the future, and therefore, the choice of a discount factor becomes all important. Now, if we assume that future costs are known and how much the investment will yield with certainty, then the only thing that we don't know is this discount factor. Obviously, there are very strong assumptions when we say, "I know the future costs and I know how much the investment would yield when it comes to climate change." We'll revisit this point, but I am focusing here on the importance of a discount factor. Before delving into details, let's try to make sure that we understand why it makes such a big difference. Well, because the choice of a social discount factor will determine such all important features as deciding when to act, should I give up a lot of consumption today in order to abate climate damage in the future? Should I wait? Also helps me in deciding which abatement strategy I should undertake where I get the biggest bang for the buck. The net present value logic offers one answer to both of these questions. You might say, does it really make such a big difference? As we shall see in future sessions, two very well-known economists, Nobel Prize winner Professor Nordhaus, Yale University, and Lord Stern who was commissioned in 2005 to produce the Stern Review, came up with different discount factors; five percent according to Professor Nordhaus, 1.4 percent according to Professor Stern. You might say, well it is three and a half percent difference between the two. Does it really make such a big difference? Yes, it does. If Nordhaus is correct and the correct social discount factor is five percent, the net present value of future damages from climate is eight dollars per ton of CO_2 emission. If this number were correct, given these low cost, very few or possibly none of the current large scale projects to curb emission makes economic sense. Wind turbines, carbon sequestration, solar panels, biofuels, you name it, currently, all have a higher cost than the PV of the damages they will abate. Nordhaus' conclusion is that today we should mainly invest in climate research, become more efficient and we should have a slow ramp up in our curbing of carbon emissions. As we shall see, I'm exaggerating his position a bit here, his position is more nuance, but I'm trying to set out two polar positions here. Why should we wait according to Professor Nordhaus? What is the intuition? One is, because future abatement costs will decay because of technological progress. Second, because future damages will become what I call more salient. Since I am closer to the damage, I will discount less and they will therefore, have a bigger importance that perhaps is not such a great argument. But the most important bit is that in the future we will be richer, and why does that matter? Intuitively, because if we think of making a sacrifice today, it makes more sense to make the sacrifice when we are richer, the same sacrifice when we are richer than today when we are poorer. To the extent that economic growth will be forthcoming for a foreseeable future, it makes sense to postpone the investment. Well, these are very important prescriptions. Does Professor Stern agree? Well, Professor Stern, whose the only difference is the use of discount factor, he says, no. The net present value of future damages from climate change is $85 per ton of CO_2 emitted. Given this cost, well, we are seeing that most abatement and even negative emission technologies today cost less at $85 per ton. Therefore, we should invest today in wind turbines, in carbon sequestration, solar panel, biofuels, you name it, because currently all of them have a cost lower than the PV of the damages they will abate. Lord Stern's conclusion is that we should act decisively today and implies a massive reallocation, immediate reallocation of capital in the economy. Citizens immediately should change their car models, insulate their homes, pay taxes to build wind turbines, etc, rather than, say, going on holiday. Things get more interesting. In 2004, a Danish statistician, Bjorn Lomborg asked a number of prestigious economists the following questions. Question; would humanity be better off if we invested in controlling climate change or if we devoted the same resources to curbing AIDS or malaria, getting clean water supply, etc? The so-called Copenhagen Consensus concluded that climate mitigation should only be undertaken only after the top priority problems such as curbing malaria are fully funded. Key to their conclusion was the high discount rate that they use in present-valuing the damages of climate change. If I use a high discount factor, those damages are less important than getting clean water supply or curbing malaria. Let me put a parentheses here, or rather two parenthesis, one possibly nested within the other. Danish statistician Bjorn Lomborg is a serious statistician. He has been on a, I call it a climate critical crusade, and what I would say about his work is that his work is statistically impeccable. However, in my analysis of his work, I would say that he has always produced very good analysis of aspects of climate change that tend to diminish its importance or tend to diminish the relevance and the urgency with which we should tackle climate change. I'm using the words carefully here, but I'm not saying for a second that the statistical analysis brought by Bjorn Lomborg is faulty, but if you try to correct a noisy estimator by only taking away one type of errors, you turn a noisy estimator into a biased estimator. That is my observation number 1. Observation number 2 is that we should be extremely careful with these type of questions. Instead of doing climate change, should we put resources in curing malaria, AIDS etc. Because in reality we have AIDS and malaria and lack of clean water supply today and we are not doing anything about it. It is not really that we have a pot of money and we have decided, "Okay, I have this huge investment I want to make, shall I make it into efforts to curb malaria or curb climate change?" An approach of this type is, yes, it would be more rational perhaps to curbing malaria, but in reality, we're doing nothing. We're neither curbing malaria nor trying to abate climate change. Second parentheses closed. These are just my comments and let's continue. Well, you might think that Professor Nordhaus and Professor Stern have two exceptionally polarized views above the correct social discount factor. Well, if that is the case, think again. Professor Weitzman, and we'll have a lot to say about Professor Weitzman from Harvard. Well, what he did, he asked a large number, 2,160, sounds like a date, no, it is the number of PhD-level economists, the following question: Taking all the relevant considerations into account, I'm sure you're proficient at reading, so I don't have to read the full question, but the question is, what is, according to you, the correct social discount rate? This is the answer he got. He got a variety of answers stretching from zero percent to around two percent, four percent stretching all the way to 16 percent, I really do not know how you can arrive at 16 percent, but these were PhD-level economists, they came up with these answers. There seems to be a huge range of uncertainty here which creates a tiny bit of cynicism because it says, "Well, you can get any answer you want depending on the social discount factor that you put in." The messages they would like to convey to you that actually, when we break down the problem in its component, I don't think that there is such a wide range of reasonable social discount factors and what is more important, I'd like to split the determination of social discount factor into two components. One which has to do about how the world works, and in particular, what we can expect about future growth, and the second one is how we feel about future generations and what duty of care we believe we have, or we should have about future generations. We conceptualize the problem in these two distinct ways, we shall see that perhaps it is not impossible to narrow this huge range of possible values for the social discount factor. But the important thing is, I want you to gain the intellectual tools to make a reasoned stand on the matter. Again, the reason why it matters so much is because the damages we are looking at are so far into the future, and when I have a very small discount factor, future damages matter a lot and therefore small differences in discount factor make huge differences in the present value of future benefits or damages. I have a figure to show this. A dollar paid or received in 50 years time is worth $0.60 today if discounted at 1 percent and $0.03 If discounted at 7 percent. In this picture here if you think that 1 percent and 3 percent are too far away, I have similar curves for 1, 3, 5, and 7 percent going out only 100 years. In integrated assessment models that we shall encounter in future sessions, we go out far more than 100 years and therefore this effect is magnified. The last few things before we get started with the derivation. The net present value approach is common but is not universally accepted. There are strands of criticisms from within and from without. Let me explain what I mean. One is the source of criticism from within. With the net present value approach, we assign a money value to future outcomes and we discount. One source of criticism is this is a good idea. Doing so is a good idea however, it is extremely difficult, it's so difficult that it's almost unworkable because we really have too much uncertainty about what the climate damage will be, whether we're going to have tipping points, whether there is going to be abrupt climate change. What the technological solutions would be, what the growth of the economy will be. Who knows what the growth of the economy would be over 100 years? We can barely predict it over six months. We can say something about these separately, I dabbed this Viessmann critique. It doesn't question the validity of the approach but it says, given the nature of a distribution of outcomes, it is unworkable. There are other critics that say doing a cost benefit analysis, one has to quantify and translate into dollar such thing as loss of greater biodiversity, the life year saved or sacrificed by policy, the cost of mass migration. This is too difficult in practice to do, so these critics don't say, well, if we could put a price to the cost of a human migration, it would be fine but in practice it is too difficult to do. Then there is another strand of criticism that says, this doesn't make any sense whatsoever. When I am looking at things like mass migration of refugees from flooded areas and the like, making a net present value cost-benefit analysis doesn't make any sense. That is, it is not the right way of approaching the question. Well, after looking at the NPV approach in a dispassionate way, as usual, you'll be able to draw your own conclusion. I share some of the perplexity of those critics who say these things don't make any sense when we look at things like mass migrations or loss of life due to spread of diseases, etc. I have a lot of sympathy with this. But I always ask myself, what else can we do better? Because if we have preconceived ideas and we simply use the statement, we shouldn't be dealing with this type of method with the net present value approach in order to arrive at the conclusions we have already reached for whatever reason. Well, that is not a very intellectually honest way to go about it. As a bottom line, I always say is good to criticize every approach but always ask yourself, what else can we do better?
