Rambling on Philosophy, Economics and Global Warming

Philosophy was once a passion of mine. I viewed it as a field of intellectual problems which required no specific knowledge, the perfect mental exercise. Then I got older. I realized what I viewed as philosophy was an ideal far removed from what philosophers actually do.

I lost interest in the field, but I never lost interest in the idea. I still love to examine philosophical issues, and I like when it involves other topics I’m interested in. Today I’m going to talk a bit about one philosophical issue involving global warming.

This issue came up in a guest post at Anders’s blog, written by a moderator there, Rachel. She discusses cost-benefit analyses done regarding global warming:

One assumption which is often made in these cost-benefit analyses is that future harms and benefits are worth less than harms and benefits which occur today. Philosophers call this discounting the future and they seem to disagree with economists on the merits of discounting in this way. They argue that whether something is good or bad has nothing to do with the time in which it happened. Harms are just as bad regardless of whether we endure them today or the people living 100 years from now endure them.

Unfortunately, Rachel misses a key distinction. Philosophers (may) disagree with the notion she describes because philosophers look at morality, not economics. A murder today is morally repugnant as a murder tomorrow. An economist can believe the same yet observe a murder at a time when a city has only 10 people is more economically damaging than a murder when a city has 10,000 people.

The distinction between economic and moral standards is key when examining the global warming issue. The two standards need not give the same results. A “discount rate” justified by one may not be justified by the other.

Rachel goes on to say she thinks some discounting seems reasonable. One example:

If we want to compare the prices of things at different times then we need to adjust them in ways that make such comparisons accurate as commodities change in price over time. So this seems fair enough to me.

Is basically just her accepting we ought to try to account for things like inflation. A dollar today is not worth the same as it was in 1964, and it won’t be worth the same in 2064. Money is an abstract we use to try to represent the underlying value of things. Of course what should be interested in is that underlying value, not an abstract.

Things get more interesting when Rachel discusses another point:

I’ve heard other people argue something similar: future generations will be wealthier than us and so this is justification for discounting the costs and benefits we leave to them. The philosopher Derek Parfit disagrees with this and says “These two arguments do not justify a social discount rate. The ground for discounting these future benefits is not that they lie further in the future, but that they will go to people who are better off“. ( source: http://faculty.smu.edu/jkazez/parfitsocialdiscountrate.pdf)

Unfortunately, she misrepresents Derek Parfit’s actual view. Parfit does not disagree with the idea she expresses. He doesn’t say it is wrong to think measurements of costs and benefits should depend upon the wealth of the individuals. What Parfit actually says is it is wrong to represent an issue like that with a single “discount value” calculated entirely on time. He’s right. We can’t pick some value, say 2%, and expect it to correspond with people’s wealth indefinitely.

Parfit says “we should say what we mean.” In other words, if we say the economic considerations of wealthy people should be treated differently than those of poor people, we should hold to that standard. We shouldn’t mask it by saying we’re discounting on time; we should say we’re discounting based on wealth.

Rachel seems to get this idea regarding the next point she discusses. She discusses the issue of how uncertainty should affect our decisions then says:

I think what he’s saying is that when we justify an outcome because it is uncertain, our reason is not because it occurs in the future, but because it is uncertain.

This is absolutely correct. When using a single “discount value,” that value is intended to represent many different issues. It is a proxy for things like uncertainty and wealth and disparity. All Parfit says is it’s a bad proxy so we shouldn’t use it. That does little to support Rachel’s conclusion:

I accept that maybe some discounting is useful, discounting commodities for instance, but it seems to me that some of the other things we discount on the basis of time, are unjustifiable and at odds with our reasons for discounting them in the first place which suggests to me that our conclusions are probably wrong.

Parfit calls into question discounting things “on the basis of time” because he thinks time is a bad proxy for them. Even if he’s right, that doesn’t say whether or not we should discount them. He’s not looking at whether or not we should discount those things. He’s only looking at the statistics of how well time can proxy them. To show the difference, let’s consider a mental problem Rachel discusses:

It took me a while to understand this so I’ll elaborate with the example that Parfit gives. Suppose some radiation is going to escape from somewhere and potentially cause a billion deaths in 400 years. If we discount those deaths at 5% per year, then a billion deaths in 400 years is worth less morally than one death next year. This is indefensible.

Rachel goes on to accurately explain uncertainty could justify weighing one life now with a billion lives in 400 years. However, there’s another issue we should consider. Suppose Bob is the guy whose life is on the line today. Suppose he is 30 year old business owner. If he dies today, his business will collapse. If he survives, his business will grow and grow. In 400 years time, it will have become a major company which has had major economic impacts on the world.

Would Bob’s death today be better than his company growing for 400 years at the cost of a billion lives? Morally, I think we’d all say no. I think we’d all say no even if only a thousand, or even a hundred, lives would be lost. But what about economically? From an economic perspective, some lives are worth more than others. The homeless man on the street corner doesn’t contribute as much to the world’s economics as the guy who owns a local grocery store.

If we accept that, it seems inevitable we must accept a life of a person today could be worth more (economically) than the life of a person in the future because of “interest” on their life. We If we accept that, must accept it may be possible doing nothing about global warming will cause the world’s economy to be better overall, even if it comes at the cost of some number of lives.


If a strong economy is all that matters, there is no question we should discount future costs for a variety of factors. It may be, as Parfit argues, those factors can’t be represented by a single proxy (time). If so, we’d need to use more variables in our formulas or find some other approach.

But a strong economy is not all that matters. We don’t take the GDP of each year for a country, sum it up and say that’s the value of the country. There are a lot of other things we care about. What kind of decisions can we make if we ignore them?

Economics is like all forms of statistics. It may give us an answer, but we have to decide what the question is. We have to decide what we value.

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7 comments

  1. The subject of discount rates is usually a foreign concept to most people, and I often hear mangled explanations of what discount rates are, and even worse arguments for why one particular discount rate is more or less appropriate than another. What is common to all of these arguments is that the individual’s desired outcome ALWAYS takes priority over the basic fundamentals of discounting. If someone wants a high present value, they’ll argue for a low discount rate, and vice versa, and they’ll latch on to whatever argument they can find to support their position.

    I deal with discount rates every single day. (I am a CFA Charterholder, and I have an MBA in Finance plus a couple of other finance industry certifications. I work as a professional investment manager, and I’m personally responsible for a few hundred million dollars worth of client assets. For me, getting a discount rate wrong can be very costly.)

    That said, let me share with you some basic fundamentals from the world of financial economics. A discount rate for calculating the present value of a given future value consists of 4 separate components. They are:

    1. Time Preference (aka the “Risk-Free Rate”),
    2. Inflation Expectations,
    3. Expected Loss
    4. Risk Premium

    (N.B. There’s a different framework and formula for stock investments)

    I’ll go through each component in sequence.

    Every living human being has an innate “Time Preference”. Simply put, people prefer a good in the present to an identical good withheld from them until some time in the future. A widget received today is always valued higher than a widget to be received tomorrow. An individual’s rate of time preference can be expressed as ratio of the number of additional future widgets one must receive to be indifferent between that and a given number of present widgets. For example, if an individual is indifferent between x widgets today and x(1 + t%) widgets in one year, his rate of time preference is t% per annum. Individuals’ rates of time preference are subjective and variable. Different individuals will have higher or lower time preferences (and no one answer is “right”). The same individual will likely have different time preferences at different life stages. Furthermore, one individual can simultaneously have different time preferences relating to different time periods. For example, an individual’s rate of time preference between a widget today vs. tomorrow will likely be higher than between a widget 365 days vs. 366 days from now. All we can say for certain is that time preference is always positive for rational human beings (N.B. central bankers are not considered rational beings.)

    When we replace a widget with a unit of money, we have to add the second component, expectations of future purchasing power since the value of money is not a constant. Imagine a guaranteed investment that will pay $x in one year. If the investor has a time preference of t% per annum, and expects prices to be i% higher in a year, the investor should be willing to pay any amount up to $x/[(1 + t%)(1 + i%)] in exchange for the $x in one year. This is the basic math that goes into calculating the discount on a Treasury Bill.

    When we add uncertainty to the equation, we have to include the last two components, but they’re two distinct concepts. Instead of a guaranteed Treasury bill, consider a 1 year corporate bond with a p% probability of defaulting within a year, and an L% loss in the event of default. Instead of getting $x of principal back in 1 year, the investor would expect to receive only $x(1 – p%L%).

    Additionally, because people are generally risk averse (preferring a guaranteed outcome to an uncertain outcome), investors will be willing to pay less for the riskier alternative. An individual’s degree of risk aversion is like time preference in that it is also subjective and variable. (Different investors are more or less risk averse, and an individual might not be consistently averse to similar risks over different time periods). Risk aversion is almost always positive (some research in behavioral economics finds certain conditions where individuals are risk-seeking instead of risk averse). For an investment of a given risk (typically quantified as the standard deviation of the distribution of expected returns) an investor might demand an additional risk premium of r% per annum. In other words x guaranteed, risk-free widgets in 1 year would be worth the same as an expected but uncertain x(1+r%) risky widgets in 1 year.

    Taken all together, find the present value and discount rate of a bond with a face value of x = $1000 and repayment in 1 year given the following assumptions:

    1. Time preference (risk free rate) of t = 1% per annum
    2. Expected inflation of i = 2% per annum
    3 Probability of default of p = 5% per annum and a loss given default of L = 80%
    4. Risk premium of r = 3%

    The bond’s present value would be
    $x (1 – p%L%) / [(1+t%)(1+i%)(1+r%)]
    = $1000 (1 – 5%(80%)) / [(1+1%)(1+2%)(1+3%)]
    = $1000 (0.96) / (1.061106)
    = $904.72

    This is equivalent to a 1 year discount rate of 10.53% (i.e. 1000 / 1.1053) or approximately equal (for small values) to t% + i% + (p%)(L%) + r%. For periods longer than 1 year, each factor is exponentiated by the appropriate number of years.

    If we were to apply the above to the cost-benefit analysis of climate change mitigation, the concepts would remain the same.

    A real-world measure for time preference would be the interest rate on long duration government inflation-protected bonds. The 30-year TIPS security currently yields 1.19%. http://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=realyield
    For publicly funded mitigation projects, this is an excellent non-theoretical measure of time preference because it represents the actual rate at which the government can finance the project.

    The inflation component can be ignored if the calculations are done in constant dollars. Otherwise, the nominal 30 year bond yield (currently 3.46%) can be used to represent both the time preference and the inflation expectation components combined.

    The expected loss component must reflect the possibility that a mitigation action might cost more than anticipated or deliver less than the projected future benefit. Feel free to fill in your own numbers here, but every public project I’ve seen has had a non-negligible probability of cost overruns and of outright failure. (Solyndra being but a single example.)

    Lastly, the risk premium will depend on relative estimates of uncertainty (i.e. which of the following two outcome carries more uncertainty? Taking mitigating actions which have uncertain effectiveness and costs, or not taking action and bearing the uncertain costs of adaptation.) Different individuals can have different views on this, viewing mitigation actions as either insurance, or a significant risk in their own right. In my opinion, there is no single answer. Each particular mitigation policy has unique characteristics and has to be assessed independently.

    Ultimately, if you ask someone to forego $x today in mitigation costs, it is only worthwhile (economically speaking) if they can expect at least $y in benefits in n years where:

    $y = $x (1+t)^n (1+i)^n (1+r)^n / (1-pL)^n

  2. Russ R., thanks for your comment. While I understand all that, I get bored whenever I try to sit down and work it out.

    For those who can’t tell, his “time preference” variable is what this post has been largely about. The other ones are simple statistical issues, and they can be determined with whatever precision our data can justify. The time preference variable is the one we can’t do that for. There’s no objective way to determine how much people prefer things (in general) today over tomorrow. There’s also no objective way to determine how much we should care about future generations. Because of this, there’s a lot of room to argue what that time preference discount rate should be.

    Also, if you agree with Derek Parfit, there shouldn’t be a single time preference variable. Instead, there should be multiple variables addressing the different aspects that variable tries to cover. The formulation Russ R. provided stays the same. We’d just disagree about how many variables to use and what values to assign to them.

  3. I’m not sure we’ve covered it all.

    There is some sort of calculation necessary for the observed historical trend and the expected future tendency toward improved methods. If someone wanted to build a structure the same height and footprint as the Eiffel Tower in 1989, 100 years after the original was erected, he would use much less iron. More steel, likely, (an alloy of carbon and iron) and maybe a lot of aluminum. Similarly if that someone wanted to link phones from New York to California, the 1889 method would use a metric mega buttload lot of copper cable, while the 1989 method would involve (Eiffel Tower-like) Microwave repeaters and fiber optic cables, and a whole lot less copper.

    It seems to me that certeris parabus and under “Business as Usual” the tasks of bringing the undeveloped parts of the world up to modern standards over the next century will NOT require the same degree of investments as it required the past century. Again, cell systems not switchboard networks. LED lights and TV not hot vacuum tubes. Aluminum cars with ceramic engines instead of Detroit Iron. Testing a drop of blood on a chip instead of 10 mL of blood in a tube. Over and over we see that it just takes less resource, in “modern” conditions, to do the chores of the past. How do we measure that sort of improvement, and how do we discount our calculations for what investments will be needed in the future to accomplish the goals of the present?

    Provided, of course, the Government doesn’t require wind-powered generators rather than various flavors of nuclear power…

  4. Pouncer, what you describe is (effectively) a matter of pricing commodities. It’s sort of a counterbalancing to inflation. The value of a dollar may go down, but the value of a lot of commodities goes down as well. A television which costs $500 today may cost $250 in a few years. Even if the value of a dollar dropped 10% in the same period of time, the “purchasing power” of it in regard to that television will have gone up.

    I have no idea how we’d account for an issue like that. Economic indexes usually use things with more stable prices (like basic foodstuffs), but we obviously can’t do that when looking at global warming. And we really can’t hope to predict how many efficiency improvements there will be.

    Or at least, I don’t think we can do any of that. Maybe someone has a way to get an estimate that’s more than a wild guess.

  5. I’m almost tempted to estimate a discount rate for the number of “protons” used to accomplish a function. The lighter stuff, more efficiently made, using fewer intermediaries and wastes…

  6. I took a graduate course in environmental ethics (as a required part of the curricula in the MSc in environmental science). And while all kind of ethical thinking and “standards” can be invoked in applied ethics, and are – when it come to rational decision-making under uncertain constraints (ie, the future), nothing beats benefit-cost estimating (which is also a required course).

    While individuals all have differing schedules of expectations from environmental resources, only BC analysis aggregates the needs and desires of all people involved in the social nexus about our environment.

    How does that apply to global warming? Assuming the most recent published estimates of ECS are valid – ie, about 2C for a doubling of carbon dioxide – I find it difficult to gainsay the benefits of some planetary warming, from hedonic, lowered heating costs, and increased food productivity. The last in particular means more foodstuffs on less land than the alternative.

    Naturally, there will be some losers in the process. Some populous coastlines will suffer, for example, Certain low-lying populations may be jeopardized. But the example of the Dutch who have carved out a third of their nation from the dangerous North Sea show us that this defense of civilization and expanded agricultural productivity from a salty overwhelming sea is possible.

    Improved technology has made this possible at an increasingly less costly rates. Technology transfer to less developed nations, in other words adaptation, becomes the policy solving process that is required.

    Some global warming is more desirable none at all. I know this is heresy to those who sacralize nature. But even if we do, how can we possibly know what nature wants? We cannot. We can only be human about our needs, and accommodate the luxury of preserving as much “nature” along the way. Humanity cannot escape being “mankind the manager of nature,” anymore than the western forests where the buffalo roamed and Indians lit fires to re-grow the forests can be completely restored.

    In other words, I’m arguing that the sorts of precautionary and nature’s rights philosophy of eco-ethics that could have worked in other places and times cannot be applied here and now without the enormous sacrifice of humanity.

    Since this would be immoral in the way of the Holocaust, there is no other way forward than humanistic environmental economics and decision-making.

  7. Orson, thanks for your comment. I’m afraid I’m not convinced though. I’ve never found people’s claims about the effects of global warming convincing, whether those effects were beneficial or harmful. My impression is we don’t have the knowledge to draw any firm conclusions about what those effects will be.

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