Decision making under uncertainty – maximize expected social welfare

by  -1=e^i pi

Expected social welfare maximization is where you try to obtain the set of parameters (such as climate change policies) that will maximize the expected value of a social welfare function.

A) Introduction to Social Welfare

There is a lot of uncertainty with respect to the issue of climate change. For example, the current (5th assessment report) subjective 95% confidence interval of Equilibrium Climate Sensitivity (ECS) according to the International Panel on Climate Change (IPCC) is 1.5 C to 4.5 C. Progress has been made recently in terms of constraining ECS, with the most recently empirical estimates suggesting that ECS is in the lower half of the IPCC’s confidence interval (Michaels and Knappenberger 2014). However, even with better estimates it seems that the uncertainty associated with ECS will remain relatively large. In addition, there are many other sources of uncertainty that are relevant to the issue of climate change such as uncertainty about the rate at which the climate reaches a new equilibrium, uncertainty about the rate of ocean uptake of CO2, uncertainty about the costs of mitigation policy, uncertainty about the cost-effectiveness of geoengineering and uncertainty about the economic impacts of climate change.

Despite all of this uncertainty, decisions about what to do about the issue of climate change are going to be made. As a result, it is desirable to have a method that can obtain a unique optimal policy response to climate change given all this uncertainty. Thus it is desirable to have a method that can rank policy responses in order to determine the best policy response given all the uncertainty. However, the scientific method alone does not rank policy responses since the scientific method doesn’t tell people what to do. In order to obtain a ranking of policy responses, at some point moral judgements need to be made. But in order to obtain agreement with others about the decision rule, one needs to limit moral judgements to well accepted moral principles in society. This post suggests that maximization of expected social welfare may be a reasonable method to rank policy options even if there is uncertainty. By appealing to egalitarianism, individualism, preference for model simplicity and empirical evidence, this post tries to justify reasonable social welfare functions for the basis of ranking policy responses.

So what is expected social welfare maximization? Expected social welfare maximization is where you try to obtain the set of parameters (such as climate change policies) that will maximize the expected value of a social welfare function. What is a social welfare function? A social welfare function (SWF) is a function that takes the utility of every individual in a society and outputs a real number, which represents the social welfare or wellbeing of society. What is the utility of an individual? The utility of an individual is a real number that represents the wellbeing of that individual. An individual’s utility may be thought of as a function of various things that influence the individual’s wellbeing in society, such as consumption, level of physical health, level of mental health, amount of leisure time, how much freedom they have, type of climate they live in, how many chocolate bars they eat on Wednesdays, etc. Such a function is often called the individual’s utility function and individuals in society tend to try to maximize their utility functions.

B) Additive Separability and Anonymity

Ultimately, it is desirable to obtain a unique SWF to be used for expected social welfare maximization. In order to do this, a reasonable first step may be to constrain the set of acceptable social welfare functions by applying some basic moral principles. Additive separability, in the context of SWFs, means that the social welfare of society is equal to the sum of the utilities of the individuals within a society. For example, if there are n individuals within society then society’s additively separable SWF is W = U1 + U2 + … + Un, where Ui is the utility of individual i. Additive separability may be justified on the basis of individualism and simplicity; a separable SWF treats people as individuals and additive separability is the simplest kind of separability.

The anonymity principle states that all individuals in society have the identical utility functions. Thus if the utility of individual i in society is a function of k parameters X1i, X2i, …, Xki then the additively separable SWF becomes W = Σi=1nU(X1i, …, Xki), where U is a utility function. The anonymity principle can be justified in two different ways. The first is that as information is limited, we cannot know the utility function of every single individual within society, thus the anonymity is a necessary simplifying assumption needed to be able to define a reasonable SWF. A second way to justify the anonymity principle is on the grounds of egalitarianism; under the anonymity principle, everyone is treated equally by the SWF.

C) Utility as a Function of What?

The wellbeing of an individual can depend on many things: from the number of grains of rice they eat per year to the number of freckles on their forehead. However, trying to make utility be a function of pretty much everything isn’t feasible, nor practical. It makes sense to restrict the utility function to be a function of only a few relevant parameters. Economic consumption is arguably the most relevant factor for individual utility in the context of climate change; mitigation policy, changes in average temperature, changes in precipitation patterns, the CO2 fertilization effect, sea level rise, and ocean acidification will all likely have an effect on economic output and thus consumption. Therefore, it makes sense to have consumption as one of the parameters in the utility function.

Other parameters may also be relevant. For example, the happiness of individuals in society may be directly affected by the climate; Tsutsui (2013) found that a temperature of 13.9 C maximizes happiness. In addition, how much individuals value the environment or how much individuals value their health may be relevant. While there are likely many relevant parameters, for simplicity, the rest of this post will treat utility as a function of only consumption. Thus, the SWF becomes W = Σi=1nU(Ci), where Ci is the consumption of individual i.

D) Simplicity and Empirical Evidence

What functional forms of U(C) may be reasonable? One individual may argue for a square root function while a second individual may argue for a logarithmic function. Who is correct? From here, you can take one of two positions. Either you know a priori everyone else’s preferences better than they do, or you don’t. If you don’t then perhaps your best option is to try to infer the average utility function of individuals in society by looking at empirical evidence. This reduces the problem of finding U(C) to a question of empiricism and is arguably a more democratic approach since you are looking at the average preferences of society. This post will assume that one does not know a priori everyone else’s preferences better than they do so will take the latter approach.

When trying to choose a model of U(C), it is important to try to balance model simplicity with the ability of the model to explain observations. A model that does not agree well with observations is arguably an unfit model of human preferences. On the other hand, simpler models often have more explanatory power; simpler models may make more falsifiable predictions or be easier to work with. Therefore, one should have preference for model simplicity. Trying to balance model simplicity with fit to observations may allow one to determine a unique best model of U(C) given the available empirical evidence.

E) Expected Utility Theory

One common and well known model of human behaviour is known as expected utility theory (EUT). Under EUT, an individual tries to maximize their utility, where the utility of an individual over a probability distribution of outcomes is equal to the expected value of the individual’s utility. The utility function that corresponds to EUT is a special type of utility function known as a von Neumann-Morgenstern (vNM) utility function. A vNM utility function is a utility function where U([pa;(1-p)b]) = pU(a) + (1-p)U(b), where a is one possible outcome, b is another possible outcome and [pa;(1-p)b] corresponds to a p probability of outcome a and a (1-p) probability of outcome b. A vNM utility function is unique up to positive affine transformation (i.e. multiplying a vNM utility function by a positive number or adding a constant will not change human behaviour). This means that a SWF that satisfies additive separability and anonymity, and uses a vNM utility function will be unique up to positive affine transformations. Positive affine transformations of the SWF do not change what maximizes the SWF, so using EUT to find a vNM utility function is sufficient for the purpose of social welfare maximization. Furthermore, nVM utility functions can be estimated empirically by looking at human behaviour under uncertainty. The rest of this post assumes that U(C) is a vNM utility function.

F) CRRA Utility Functions

The average utility function of individuals in society can be empirically estimated by looking at the decisions people make under uncertainty. Arguably, the two most common measures of risk aversion are the coefficient of absolute risk aversion and the coefficient of relative risk aversion (RRA). The coefficient of absolute risk aversion is defined as -(d2U/dC2)/(dU/dC) and the coefficient of RRA is defined as -(d2U/dC2)C/(dU/dC). A quick review of the literature suggests that the coefficient of absolute risk aversion is a decreasing function of consumption (Friend and Blume 1975). On the other hand, whether the coefficient of RRA increases, decreases or remains constant as a function of consumption is disputed and there is a fair amount of uncertainty about its magnitude (Outreville 2014). Given all the uncertainty and the desire to balance model simplicity with fit to empirical observations, it may be reasonable to assume that the coefficient of RRA is constant.

CRRA utility functions are defined, up to positive affine transformations, as U(C) = C1-η/(1- η) when η ≠ 1 and as U(C) = ln(C) when η = 1, where η is the coefficient of RRA. If η > 0 then the utility function is risk averse. Using a CRRA utility function in the SWF means that the SWF satisfies the Pareto principle (the property where if a policy can make 1 individual better off, without making any individuals worse off, then society is better off with that policy) and, if η > 0, satisfies the Pigou-Dalton principle (the property where if a policy can make a poor person richer by a small amount and a rich person poorer by an equally small amount then society is better off with that policy). η affects how the SWF deals with risk, intragenerational inequality and intergenerational inequality. η = 0 causes the SWF to be risk neutral and to not care about consumption inequality in society; this corresponds to the decision making under traditional cost-benefit analysis. η = ∞ causes the SWF to avoid all risk and avoid all inequality; this corresponds to the decision making under the strong precautionary principle. η between 0 and ∞ results in a SWF that has a moderate level of risk aversion and values both total consumption in society as well as consumption inequality. The value of η is a prior indeterminate. However, it can be estimated from empirical data. Below is a plot that shows CRRA utility functions for η = 0, 0.5, 1 and 2.

Slide1

 G) Time Separability

An individual may care about more than just their total consumption over their lifetime; they may care about the timing of that consumption. Humans tend to have a preference for present consumption over future consumption and tend to want to smooth consumption over time. The most common way to treat this timing issue is to treat the utility function as additively separable with respect to time. In this case, for an individual that lives for T periods, the individual’s lifetime utility function is Σt=1TwtU(Ct), where Ct is the individual’s consumption for period t and wt is the weight of period t. Often, the weights are represented by an exponentially decreasing function of time, which means that the individual’s lifetime utility function is Σt=1TeρtU(Ct), where ρ is a discount rate.

If one puts this into a SWF with constant RRA and assumes that the utility of a dead individual is zero then the SWF becomes W = Σt=1eρtΣi=1N(t)Cit1-η/(1- η) when η ≠ 1 and W = Σt=1eρtΣi=1N(t)ln(Cit) when η = 1, where η is coefficient of RRA, N(t) corresponds to the number of people alive in period t and Cit corresponds to the consumption of the ith individual alive in time period t. This specification reduces the problem of finding a SWF to the problem of finding 2 parameters, η and ρ, both of which may be estimated empirically.

H) Expected Social Welfare

Since maximizing expected utility is how individuals in society make decisions under uncertainty, it may make sense that maximizing the expected value of the SWF is how society should make decisions under uncertainty, as this is the natural extension of expected utility maximization to the SWF. However, before accepting expected social welfare maximization, it may make sense to look at some other common decision rules.

One common decision rule is traditional cost-benefit analysis. Under traditional cost-benefit analysis, one tries to choose the policy option that maximizes the net present value of benefits minus the net present value of costs. The theoretical justification for cost-benefit analysis is that if there is little uncertainty about the future and any policy under consideration will have relatively small impacts on the consumption of individuals in society then traditional cost-benefit analysis is approximately the same thing as expected social welfare maximization. However, in the case of climate change, the uncertainty is large and the impact of policies on consumption may be large, so traditional cost-benefit analysis is inadequate.

The strong precautionary principle is a decision rule that is frequently used in the context of climate change. Under the strong precautionary principle, if there is any risk that a policy may have a negative impact on society then that policy should not be taken. There are numerous problems with the strong precautionary principle. For one, the strong precautionary principle contradicts itself. For example, if one uses the strong precautionary principle to decide whether or not a new drug should be allowed on the market, one runs the risk of disallowing many perfectly good drugs, causing harm to society. Thus the strong precautionary principle has a risk of causing harm to society so should not be allowed under the strong precautionary principle. Secondly, the strong precautionary principle has many bizarre policy implications. For example, one cannot exclude the possibility that a giant flying spaghetti monster may appear and try to destroy New York; therefore, the US government should spend economic resources to ensure that it can fend off any attack by a giant flying spaghetti monster. Given these issues, the strong precautionary principle does not seem like a reasonable method to make decisions.

I) Empirical Estimates of η

It may be helpful to look at empirical evidence, to see what values of η may be reasonable. The literature on empirical estimates of η is vast and there are many different methods by which one can estimate it. If you wish to read a more extensive review of the literature of measures of η then I suggest Outreville (2014). However, this post will cover 4 different estimates, in order to keep things short.

J) Labour Market Behaviour

One way to estimate η is to look at labour market behaviour. One of the best studies that takes this approach is Chetty (2006), where Chetty invents a method to estimate η from uncertainty in labour market conditions and obtains a best estimate of 0.97. However, Chetty may be misestimating how willing people are to exchange consumption for leisure, so this estimate may be an underestimate. Even after taking this possibility into account, Chetty finds that a value of η greater than 2 is inconsistent with labour market behaviour.

K) Happiness Surveys

Arguably, one of the best estimates for η has been performed by Layard et al. (2008). Layard et al. take advantage of the fact that happiness is correlated with utility and use data on self reported happiness from over 200,000 individuals to estimate η. Initially, Layard et al. assume that happiness is a linear function of utility and estimate η as 1.26 (with 95% confidence interval of [1.15,1.37]). However, happiness is not necessarily a linear function of utility; more generally, it can be any positive monotonic transformation of utility. To check for this possibility, Layard et al. relax their linearity assumption slightly and find a better estimate of 1.24 (with 95% confidence interval of [1.14,1.35]). In both cases, Layard et al. control for various other explanatory factors such as leisure time. Overall, the Layard et al. result gives a surprisingly robust and well constrained estimate of η.

L) Ramsey Equation

If individuals in society have a lifetime utility function of Σt=1Teρt Cit1-η/(1- η) when η ≠ 1 and Σt=1Teρtln(Ct) when η = 1 then this has predictions about the interest rate of society. In such a society, r = ρ + ηg, where r is the real riskless after-tax interest rate, ρ is the discount rate, η is the coefficient of RRA, and g is the growth rate of real GDP per capita (see Creedy and Guest 2008 for a derivation). This equation is known as the Ramsey equation.

Using the Ramsey equation, it is possible to estimate both ρ and η by using data on r and g. However, in the short run, it is possible for a country’s interest rates to diverge from what is expected by the Ramsey equation, especially due to the policies of central banks (which tend to roughly follow a rule known as the Taylor rule). In the long run, the Ramsey equation should be roughly satisfied, so one may be able to estimate η by comparing r and g between countries. Anthoff et al. (2009) use data from 27 OECD countries over a 36 year period and obtain a best estimate of η of 1.18. This is similar to the estimate of Layard et al., although the uncertainty of the Anthoff et al. estimate is much higher.

If people do not value the future more than the present, then ρ cannot be less than zero. As a result, r/g provides an upper bound on the value of η. According to the World Bank, the average real riskless interest rate of the USA from 1995-2014 was 3.88%. In addition, the tax on capital gains in the USA is approximately 19.1% (http://taxfoundation.org/article/capital-gains-rate-country-2011-oecd). This suggests that the after-tax average real riskless interest rate for this period was 3.14%. By comparison, the average g for the USA over this period was 1.475%. This suggests that η greater than 2.14 is inconsistent with empirical evidence.

M) Statistical Value of Life

How people make decisions when it comes to the probability of death can also be used to estimate η. If the average individual in society is indifferent about taking a risk that has a (1 – α) chance of increasing their consumption by ΔC and an α chance of killing them, where α and ΔC/C are both very small, then ΔC/α is known as the statistical value of life (SVL). If the utility of death corresponds to a consumption level of zero then this suggests that U(C) = (1 – α)U(C + ΔC)

How people make decisions when it comes to the probability of death can also be used to estimate η. If the average individual in society is indifferent about taking a risk that has a (1 – α) chance of increasing their consumption by ΔC and an α chance of killing them, where α and ΔC/C are both very small, then ΔC/α is known as the statistical value of life (SVL). If the utility of death corresponds to a consumption level of zero then this suggests that U(C) = (1 – α)U(C + ΔC)
=> C1-η/(1 – η) = (1 – α)(C + ΔC)1-η/(1 – η) => C1-η = (1 – α)C1-η(1 + ΔC/C)1-η ≈ (1 – α)C1-η(1 + (1 – η)ΔC/C)
=> 1 ≈ 1 – α + (1 – η)ΔC/C => η = 1 – αC/ΔC = 1 – C/SVL

For the USA, the SVL is approximately 200 times annual per capita income (Cline 1992) and the life expectancy for the USA in 1992 was 72 years. If the average person is middle aged, then this suggests that they would have on average 36 years of remaining life. This means that total remaining consumption for the individual would be roughly 36 times annual per capita income. Putting this information into the above equation gives η = 0.82. Of course this is a very rough estimate with numerous problems, but it does illustrate how statistical value of life estimates can be used to estimate η. Overall, given the range of estimates given in this post and in the empirical literature, a value of η outside of the range [0.5,2.0] seems inconsistent with empirical observations (upper bound is from Chetty, lower bound is subjective).

N) Finite Statistical Value of Life?

The equation derived in M suggests that if η ≥ 1 then the SVL for a CRRA utility function cannot be finite. Yet in everyday society it is observed that people frequently do risky activities that put their lives at risk, from smoking to sky diving. To show the absurdity of an infinite SVL, take the simple activity of eating a potato chip. Potato chips are unhealthy and can increase your chance of dying. Even if the increase in the probability of dying from eating a potato chip is very small (say one in one sextillion), it is still finite, and the pleasure gained from eating a potato chip is finite. Thus an expected utility maximizing individual would never eat that potato chip if they assigned an infinite value to their own life. Given that people eat potato chips in society, the SVL is likely finite.

Is it possible to have η ≥ 1 and a finite SVL? It is possible provided that the constantness of η breaks down at low levels of consumption and the limit of η as consumption approaches zero is less than 1. One reason why this may occur is that people become increasingly desperate in extreme poverty and, in extreme poverty, the individual’s remaining life expectancy is strongly dependant on consumption. A person that is starving to death may only have a month or two of remaining life. However, if they take a risk then they may be able to afford enough food, which may give them many years of additional life. In such a scenario, individuals may even become risk loving (η < 0).

One may be able to observe a constant η ≥ 1 for most consumption levels and a finite SVL provided that the constantness of η breaks down in cases of extreme poverty. In particular, if the reason for this break down is due to starvation then there should be a discontinuity in human behaviour around the subsistence level of real GDP per capita. Caballero (2010) has found empirical evidence consistent with this. Caballero performs experiments with impoverished Colombians to try to determine their behaviour under risk. Caballero uses a subsistence level of real GDP per capita of 148,000 Colombian Pesos per month to try to see if there is a discontinuity in risk aversion around the subsistence level. Caballero finds that individuals just above the subsistence level are far more risk averse than people just below the subsistence level.

Given that the vast majority of the world has a level of income above the subsistence level, the usage of a SWF with constant η may be reasonable even if η ≥ 1. However, such a CRRA utility function would break down for dead people and for people in extreme poverty. A better utility function to be used for expected social welfare maximization might be a piecewise continuous function that is a CRRA utility function above the subsistence level of consumption and something else (such as a polynomial) below the subsistence level.

O) Discount Rate:

In addition to a reasonable value of η, a reasonable value of ρ is needed. As explained in section L, utility maximizing behaviour suggests that r = ρ + ηg. As a quick example, if one uses r = 3.14% and g = 1.475% (values from section L) and η = 1 then this suggests that one should use ρ = 1.665%. More generally, if η is in the interval [0.5,2.0] then the Ramsey equation suggests that ρ is in the interval [0.2%,2.4%]. By comparison, Nordhaus and Sztorc (2013) use η = 1.45 and ρ = 1.5% for DICE and Anthoff et al. (2009) use η = 1.47 and ρ = 1.07% for FUND. One possible explanation ρ is that ρ is due to the probability of a consumer dying in a given year. As a comparison, the average global life expectancy is 71 years for 2013; the inverse of this is 1.41% per year.

P) Which Moral Judgements Should be Made?

Ultimately, determining the SWF depends on moral judgements. In particular, one likely needs to choose η and ρ. I leave it to the reader to decide, based upon the information in this post, what η and ρ should be, although I would advise against being risk averse about the values of η and ρ as human risk aversion itself depends on η. However, η outside of [0.5,2.0] is inconsistent with empirical observations and the Ramsey equation suggests that ρ lies in the interval [0.2%,2.4%]. Given the uncertainty of these two moral parameters, what researchers could do is perform expected social welfare maximization for different values of η and ρ and leave it up to policy makers to choose the appropriate moral judgements.

References [link]

This essay is from a longer essay on this topic [Expected Social Welfare Maximization-2]

JC note:  As with all guest posts, please keep your comments relevant and civil.

 

207 responses to “Decision making under uncertainty – maximize expected social welfare

  1. Pingback: Decision making under uncertainty – maximize expected social welfare | Enjeux énergies et environnement

  2. Bergkamp, Lucas

    Thanks, the author’s name is somewhat mysterious.

  3. https://en.wikipedia.org/wiki/Euler%27s_identity
    That’s if your question is, what is -1=e^i&#960. If you really mean, who, dunno.

  4. Good background post. As applied to climate science, I’d guess that there is so much uncertainty that it’s probably impossible to get an answer to a straight go/no go question. That is my impression of the disagreement between Nordhaus et al and others like Lomborg and Dyson.

  5. the rest of this post will treat utility as a function of only consumption. Thus, the SWF becomes W = Σi=1nU(Ci), where Ci is the consumption of individual i.

    And it fails right there.

    • You can treat utility function as a function of more than just consumption. It was just treated as a function of only consumption to keep things relatively simple and short. Expected social welfare maximization can be used with more complicated utility functions.

      • Dear Euler’s Equation:

        Are you aware of any attempts to incorporate the concept of “satiable” human needs and universal welfare rights into an appropriate consumption function (or SWF)? Something similar to Alan Gewirth’s concepts is my starting point for this question.

      • Hi opluso,
        I have seen some attempts to treat utility as a function of both consumption and freedom. One way you could do this in practice is to try to look at self-reported happiness indices and look at how consumption increases happiness relative to a freedom index (The World Happiness Report 2013 table 2.1 does this).
        As for human needs being satiable or not, I have a section on the St. Petersburg paradox in the longer version, which suggests that the utility of infinite consumption is finite.

  6. [… T]he Pigou-Dalton principle (the property where if a policy can make a poor person richer by a small amount and a rich person poorer by an equally small amount then society is better off with that policy)

    Doesn’t this ignore the difference between expenditure on consumption, and investment? Taking a bunch of money from a rich person, which they would (likely) invest at a profit to everybody, and giving it to a bunch of poor people, who would likely spend it on consumption, would reduce capitalist investment.

    AFAIK this issue is inherent in just about every system to prioritize “redistribution”. In fact, it would appear to render the whole idea of “redistribution” fallacious.

    • AK:

      Taking a bunch of money from a rich person, which they would (likely) invest at a profit to everybody, and giving it to a bunch of poor people, who would likely spend it on consumption, would reduce capitalist investment.

      Several assumptions are implied by your formulation and make your critique of “redistribution” seem incomplete.

      For example, taking money from a rich person may result in infrastructure development, universal education or national defense. Furthermore, consumption spending essentially IS the US economy, so god bless the profligate.

      Some might even argue that current capitalist investment is overly focused on short-term returns (and favors the already wealthy) to the detriment of longer term growth (which could produce more uniform benefits across society).

      • For example, taking money from a rich person may result in infrastructure development, universal education or national defense.

        Perhaps, but that doesn’t fall under the “Pigou-Dalton principle” I was critiquing.

        Furthermore, consumption spending essentially IS the US economy, so god bless the profligate.

        Nope. Just about everything any consumer buys was created/processed using some sort of “plant” that required capital investment.

        Some might even argue that current capitalist investment is overly focused on short-term returns (and favors the already wealthy) to the detriment of longer term growth (which could produce more uniform benefits across society).

        I would agree with your main premise, and in fact would argue so myself.

        But I disagree with both your parenthetical assumptions: the focus on short-term returns is as much a function of fund managers who are judged that way as anything else. And many of those funds support middle-class retirement. Calling the middle-class “already wealthy” in the current US is tantamount to socialist propaganda.

        As for more uniform benefits, IMO the benefits of a longer-term focus would be just as non-uniform, there’d just be a lot more net growth, so there’d be more to go around. Again, you have to measure “benefits” according to two different standards: whether the profits are re-invested or spent on consumption.

      • AK:

        Just about everything any consumer buys was created/processed using some sort of “plant” that required capital investment.

        Demand determines investment. In other words, without consumption, there is no demand and there is no investment. That’s one reason the rest of the world likes to invest in the US. At least they did until recently, when Chinese consumer demand finally took off.

        Calling the middle-class “already wealthy” in the current US is tantamount to socialist propaganda.

        My reference to the “already wealthy” excludes most of the middle class. The general rule that “the rich get richer” applies in both the US and globally, although the US became more egalitarian due to the socialist mechanisms imposed post-WWII.

      • “Furthermore, consumption spending essentially IS the US economy, so god bless the profligate.”
        Which may be the problem. Stimulus spending to help the economy is usually financed by debt. When the party is over, the debt is still there. And what would be consumption is now interest payments. Spending our way to prosperity. Stimulus spending may be as such: Borrow some money and spend it now. Pay it back later and spend less. A time shift. A credit card. Not recommended for individuals or countries.
        “The most commonly used definition of economic growth is simply producing more.”
        http://www.harpercollege.edu/mhealy/eco212i/lectures/asad/asad.htm
        One can argue that demand drives production. When that production is in China the U.S. is missing out a bit. There are few workers to tax, few corporations to tax. When we grow corn, the most important thing is not how many boxes of corn flakes we buy. It’s the production of corn. I think the idea that demand drives production is watering down our sensibilities. The production value drives consumption. It’s some of both, but we should not diminish value produced by people in our neck of the woods. Take Silicon Valley in the past. Hardly anyone knew or really wanted what they produced. Carbon paper was fine. Xerox machines rule. They produced value.

    • @ AK – Yes, more redistributive economic policies tend to reduce the savings rate, which decreases long run economic output. You can try to take this account into affect by having physical capital in the production function for whatever economic model you use.

      • You can try to take this account into affect by having physical capital in the production function for whatever economic model you use.

        Perhaps, but the problem is that you simply can’t predict the outcome of capital investment. At least, under circumstances of technological growth/improvement.

        I doubt you could even do so in aggregate, much less WRT any specific technology.

        IMO this type of calculation, as with any based on Ricardan principles, ends up getting lost in unknowns (both known and unknown).

        Better, IMO, to assume that humans will adapt to any gradual change in ways that maximize their immediate utility functions, including perceived future utility. Humans are not frogs.

        AFAIK, this will, in effect, invalidate any effort to reach closure calculating a “damage function”. Especially since greater incentive will probably result in greater investment in technological development relative to plant based on current technology.

        This is why I prefer an approach based on properly framing the solution then looking for the cheapest way to accomplish it.

      • “Perhaps, but the problem is that you simply can’t predict the outcome of capital investment.”
        This is debatable. But even if you can’t predict it, as long as you can obtain a probability distribution of different outcomes, you can just plug that into the social welfare function and use expected social welfare maximization to make decisions under uncertainty.

    • Thanks AK for a provocative question that got me thinking. The wealth of a whole nation needs to grow in order to provide better outcomes for all. Consumption is merely a metric of that wealth. In fact I don’t know why our guest blogger decided to discard the macroeconomic approach in favor of microeconomic.

  7. Caballero uses a subsistence level of real GDP per capita of 148,000 Colombian Pesos per month to try to see if there is a discontinuity in risk aversion around the subsistence level. Caballero finds that individuals just above the subsistence level are far more risk averse than people just below the subsistence level.

    Thus explaining why (pre-industrial) marginal agricultural societies have tended to be so strongly conservative, especially towards significant (as opposed to very gradual) changes.

  8. Under its hard-edged modernism, this is another Paris Symphony, with the usual violins.

  9. Frankly I am not sure where the post is going or trying to go. It seems to abstract the problem elsewhere and start at that point. Search for ‘carbon’. Search for ‘energy’. ‘CO2’ appears a couple of times in passing. Clearly not enough of the science that plays into the policy is present in this formulation. There need to be more discussion (at least IMO) of how the author got to his/her starting point. But it always takes me time to figure things out.

    • Hi mwgrant,
      I agree that there is more to discuss. Also, go see the longer version, as it does go into more elaboration. https://curryja.files.wordpress.com/2015/11/expected-social-welfare-maximization-2.pdf

      With respect to how it relates to climate science, you would want to use climate science to justify probability distributions of outcomes for a given change to inputs that affect climate (such as greenhouse gas radiative force). You would then input those probability distributions into the social welfare function (as well as probability distributions of economic models) in order to obtain the best policy for a set of policies under consideration.

      • You cannot factor in Climate Science because there are no Models of Climate that work.

        You must figure out Climate Natural Variability first or you cannot consider Climate.

      • Figure out what caused the Roman warm period, what changed that warm period into the Little Ice Age, what changed that cold period into this Modern warm period. then figure how to factor that into the utility model.

        In the end, a correct utility model will show that more people are best off by using all the fossil fuel that can be made available.

        Bring Nuclear in as needed. Use coal to help our gas and oil last longer, we use that stuff for more than just energy.

        You must Maximize the abundance of low cost energy to maximize the utility of people. People, this is very clear!

      • popesclimatetheory

        You do not necessarily need models, but if you do, you exercise care and document so inherent limitations are clear. Also the statement “there are no Models of Climate that work” doesn’t work. :O)

      • correct place now…bold fixed…

        Thanks for the replies -1=e^iπ and Judith

        My own bias is that structuring the decision is the most difficult and hazardous step—so that I hope explains my comment. Structuring includes determining the decision criterion/criteria. You start with social welfare as the given criterion—but the criterion/criteria actually depends on what is being decided in the climate policy decision. I appreciate that here you providing background on the nature and formulation of such functions. There is more to the story.

        As for

        With respect to how it relates to climate science, you would want to use climate science to justify probability distributions of outcomes for a given change to inputs that affect climate (such as greenhouse gas radiative force).

        I view that as more complicated. For example, conditioning of variables would seem inevitable in, e.g., choice of policy conditions some climate science variables. Again we come back to the structure of the decision, say as might be expressed as a relevance diagram.

        Also structuring time-orders outcomes and decisions. I suspect time ing plays a big role in social welfare.

        Regards,
        mw

      • Inputs into the social welfare function can be tuned in just the same way as the parameters of climate (or any other) models and are even more likely to reflect the modeler’s ideology. For example I being a libertarian socialist would be quite happy to see everyone driving a Versa (officially the cheapest new car on sale in the USA) or even that glorified golf cart called a Google car. My social model would punish bling as well as scroungers. Not just a select few people might regard my social model as a menace.

      • old fossil

        Inputs into the social welfare function can be tuned in just the same way as the parameters of climate (or any other) models and are even more likely to reflect the modeler’s ideology.

        It is good at this time to point out the question of the ‘modeler’. The decision model ideally would be that of the decision-maker or makers. The team* supporting the decision-maker(s) would include decision analyst(s) coaching and keeping the decision characterization and delineation on track. Clearly some sort of buy-in to the decision model(s) by the team members eventually is required.
        ————
        * Note also that the decision-maker(s) have to be an active part of that team.

        Of course just what constitutes a team is quite contentious at multiple levels. Ancillary decisions regarding team membership would be part of the greater decision process, and with similar implementation issues. [Big fleas have little fleas, etc.] IMO it is important to remember that the decision-makers ultimately determine the policies implemented. Decision models are just that—models. Their role is to inform the decision and not to make it.

        mw

    • Well part of this is my fault, since I didn’t want to post a 13,000 word essay. My own mind pretty quickly made the leaps to climate policy

      • There is no good reason to repeat 13000 words that are available in another link. That is not your fault, that is to your credit.

        It takes a long time to scroll down 13000 words on the browsers in some our mobile apps.

        It is much better when you already picked out the related stuff.

        Thanks!

      • As a matter of fact I had quickly looked at the bigger document before commenting and felt that the same observations apply.

    • Thanks for the replies -1=e^iπ and Judith

      My own bias is that structuring the decision is the most difficult and hazardous step—so that I hope explains my comment. Structuring includes determining the decision criterion/criteria. Here you start with social welfare as the given criterion—but the criterion/criteria actually depends on what is being decided in the climate policy decision. I appreciate that you are providing background on the nature and formulation of such functions. Just to me there is more to the story.

      As for

      With respect to how it relates to climate science, you would want to use climate science to justify probability distributions of outcomes for a given change to inputs that affect climate (such as greenhouse gas radiative force).

      I view that as more complicated. For example, conditioning of variables would seem inevitable in, e.g., choice of policy conditions some climate science variables. [We would hope!] Again we come back to the structure of the decision, say as might be expressed as a relevance diagram.

      Also structuring time-orders outcomes and decisions. I suspect time ing plays a big role in social welfare.

      Regards,
      mw

      • Sorry about the bold—an accident

      • MW show me a model of Climate that does work right and can reproduce the climate of the past ten thousand years. Short term correlation does not prove that anything works.

      • popesclimatetheory wrote:

        MW show me a model of Climate that does work right and can reproduce the climate of the past ten thousand years. Short term correlation does not prove that anything works.

        I did not say that there are climate models that work or that there are models that don’t work. I said:

        Also the statement “there are no Models of Climate that work” doesn’t work.

        What do I mean by that. We all know that models have limitations and that those limitations depend on context. IMO then a statement that “there are no Models of Climate that work” not very informative or useful. That is why such statements do not work.

        Even dismissing a model requires sufficient context and explanation. All this broad brush whining about models in blogs has worn thin and even frankly appears somewhat specious.

      • MW Model output that has been presented has not matched real data for decades. That can easily be covered by a broad brush. When model output does not match real data it is wrong. There should be no debate about this. If there are any models that do work, they do not present the model output for those. There are no models that do work for me until I see output from one that does work with proper verification. I mean a model that reproduces the past ten thousand years. It does not need to match all the timing, but it must reproduce the cold and warm cycles with the correct upper and lower bounds.

      • Consensus Climate Models only produce hockey stick output.

      • popesclimatetheory

        There are no models that do work for me until I see output from one that does work with proper verification. I mean a model that reproduces the past ten thousand years. It does not need to match all the timing, but it must reproduce the cold and warm cycles with the correct upper and lower bounds.

        Good :o) Now you are beginning to sketch a context and criteria for your acceptance of a climate model. Now about others criteria and context…? Pushing that further one can raise in particular the question of the timing of a modeler’s own acceptance criteria. There is not much that a modeler can do about others’ after the fact criteria, but from a QA perspective it is reasonable for third parties to expect the modeler to develop and document his/her goals, objectives and criteria before the model is implemented. After all what does verification and validation mean without that?

        Now in the context of decisions about policy where time is a potential critical uncertainty a decision-maker has to go with the information at hand–from all sources including but by no means not limited to model results. In the case of imperfect knowledge such inputs have to be weighed by the decision-maker and the decision(s) made.

        [One option is delaying the decision but it should be considered as automatic in the face of uncertainty just as evoking the precautionary principle in the face of great perceived risk(s) should not be automatic. There are no shortcuts.

        HTH helps explain my view of the importance of context of model acceptance, i.e., my biases.

        Regards,
        mw

  10. The basis of law is that changes leave nobody worse off, called Pareto optimum. You doh’t get to improve the average lot by hitting somebody over the head and taking his stuff, even though others value it at more than he does.

    Richard Epstein is good at showing how the requirement works in real life, or ought to work where it’s ignored by the lawmakers.

    • If Richard Epstein’s mental capacity could be converted directly into electricity I suspect most of our carbon emissions could be offset. Truly impressive intellect.

    • rhhardin,

      “The basis of law is that changes leave nobody worse off,”

      Law goes back thousands of years. Neither in the past nor today is it usually possible to make laws according to your principle. Even obviously socially useful laws, such as pollution controls preserving common resources (e.g., air, water) make polluters worse off (i.e., reduce their profits, which they could enjoy from unaffected areas).

      As for the Pareto optimum…

      “Pareto efficiency is a minimal notion of efficiency and does not necessarily result in a socially desirable distribution of resources: it makes no statement about equality, or the overall well-being of a society.”

      https://en.wikipedia.org/wiki/Pareto_efficiency

      • Polluters do not capture the benefits of polluting. The consumer does. They only profit if they’re the only ones doing it; otherwise competition drives the price down to accommodate it.

        The leaving nobody worse off, aside from that, has to include the benefit that you get from taking stuff from you, which resolves a lot of objections that seem to be common sense against Pareto. See Epstein for how this works.

      • Richard Epstein must come from another planet. We don’t do Pareto optimum on this one, in real life.

      • Actually, we do use it. Epstein can trace it out for you, as well as show which court decisions are wrong on that criterion and how those decisions have screwed the laws up, much as a bad software design decision screws up the future of the project.

        If you get the principle right, by contrast, things fit together in the future pretty easily.

        I have several hundred Epstein podcasts, not indexed for finding Pareto, so it may take a while to come up with a good one to listen to for you.

      • Here’s an Epstein .mp3 (17 minutes) that exemplifies Pareto hidden from sight but at work, in an environmental case.

        From Feb 13, 2013 at the Libertarian, “Property Rights and the Environment.”

      • rhhardin | November 29, 2015 at 10:28 am |
        Polluters do not capture the benefits of polluting. The consumer does.

        And CO2 emitters don’t benefit from more CO2 emissions – the planet and everyone else does.

        But we can close the loop by subsidizing fossil fuel burners to the level of the benefit they are providing. The fact that fossil fuel producers are undersubsidized, robbed of any compensation for the plant growth benefit they are providing, and renewables are oversubsidized by over 50x (5000%) for no particular reason is distorting the energy marketplace.

        The level of subsidy per KW-H should be equal across the board. In truth renewables should be penalized with a surtax for failing to provide a plant growth benefit. Using renewables leaves everyone worse off.

      • recently made up theory:

        The basis of law is that changes leave nobody worse off.

        reality:

        Back in the day, cavemen lived in small mostly familial groups in a basically communal society. They wandered in an out of the caves of fellow group members and took food and other stuff they needed. No problem.

        But as the groups grew larger and less homogeneous the more productive of the members accumulated more stuff than the slackers, who sat around smoking weed. Sharing went out of style, but the wandering in and out and the taking of what one needed continued.

        We come to the making of the first law. The more productive happened to also be smarter, were better at making effective weapons and organizing. They formed a power group and passed the burglary statute. Burglars got their heads bashed in, when they were caught “stealing” stuff.

        Laws are made by the people with the power and somebody is always worse off for it.

      • Joseph

        There will always be a bottom 10% of income earners. The bottom 10% may have more than they did in the past but that last decile will always be with us.
        But I have another point to make. Many suggest a way to reduce income inequality is to raise income taxes on the wealthy, even up to the top marginal rates of the 1950s and 1960s, which was 91%. So lets see what that can do. US Personal Income is $13.4 Trillion. The Federal annual deficit may go back up a little by FY2017 and be around $500 Billion.

        So with that as a backdrop lets see what happens with a return to top marginal rates of the good ol days of more income equality. The effective rate (taxes paid of total income, not top marginal rate) was about 45% for those with the highest marginal rate. If we return to the same effective rate for, say those making over $1 million, then that should increase taxes paid by about $140 Billion. if we have the top 1% pay an effective rate of 45% then that could increase taxes by about $200 Billion. Note that the deficit is going to be $500 Billion and so having the top 1% going back to the effective rate of the 1950s, will only reduce the deficit by 40%, leaving no additional revenue to place in the budget for income redistribution.

        I have no problem with raising taxes on the wealthy. But this has been seen by the left as a way to solve the income inequality dilemma. The amount available to create greater income equality is peanuts compared to what is needed. Despite what Sanders says, high taxes on the wealthy did not create greater income equality 60 years ago. It is a much more complex and nuanced answer than that one factor. Fiscal policy, and more specifically tax policy, is not going to be the solution. I don’t have the answers. But I know where to look and where not to look.

        This discussion mirrors the one on global warming. Some want to go after the simple solution even if it is not causing the problem.

    • But as the groups grew larger and less homogeneous the more productive of the members accumulated more stuff than the slackers, who sat around smoking weed. Sharing went out of style, but the wandering in and out and the taking of what one needed continued.

      We come to the making of the first law. The more productive happened to also be smarter, were better at making effective weapons and organizing.

      You can work as hard as a billionaire and still have no hope of being a billionaire. Society is a rigged system in the sense that those with certain talents and abilities are favored over others. I think wealth accumulation has more to do with genetics and circumstances rather than because you are a hard worker or you knowingly make bad decisions. Although some people are lazy and do make bad decisions..

      • Wealth is seed corn. The rich have more than they consume. So there’s corn planted next year.

        If you redistribute the seed corn, everybody feasts and then starves next year.

        Concretely, a ditch digger with heavy equipment earns a lot more than a ditch digger with a shovel.

        Some rich guy bought the heavy equipment to make himself richer by making the ditch digger more productive.

        Now both of them are richer.

      • Growing inequality is more of problem than wealth creation per se. I am not arguing that we should change the rules, but acknowledge that inequity is built into the system.

      • We have to find a way to hold back those with certain talents and abilities, so the others can catch up. They have been making a noble attempt to accomplish this in our public school systems for decades, but it doesn’t seem to be having a beneficial effect. The permanent underclass continues to grow.

      • If we just gave more money to the rich we would more rich people or something like that, right?

      • inequity is built into the system

        aka

        life isn’t fair

      • I know so you can’t make the moral case that the poor don’t need help.

      • I wouldn’t attempt to make the moral case that the poor don’t need help, yoey. I needed help when I was a poor fatherless kid. We got our welfare checks, our government cheese and powdered milk, our basic dwelling in the project, medical care at General Hospital, etc. We didn’t have to do anything to get this free stuff, except remain poor and fatherless. Do you see where this is going, yoey?

      • I think the problem with the so-called war on poverty was that it was assumed poverty could be eliminated in the foreseeable future (if at all) and that welfare programs alone could end poverty.

        I think welfare programs should be considered more of safety net and that they are necessary because poverty exists and these people need help. But if you have some magical plan that will end poverty so we don’t need welfare programs then I am all ears.

      • That’s a snide comment that just shows your lack of seriousness on the issue, yoey. I didn’t say or imply that there are magical plans. No use in discussing policy with you. I could tell you what you could do personally to actually make a difference in some poor folk’s lives, but I don’t see any indication that you have the inclination or the guts to go for it.

      • All I am saying Don is that “ending poverty” is not the primary purpose of welfare programs.

        I understand that unfortunate circumstances (by birth or environment) can lead one into poverty or near poverty. And no provider of welfare services can really distinguish who “deserves” it or not.

  11. I guess this would turn out to policy makers making the judgment that maximizes their “career utility” and hiring an economist to make the required welfare projections.

  12. -1=e^i pi

    Class this with the Drake Equation, theoretically interesting but operationally useless quantitative exercises where the equation might be correct — but we cannot do more than make wild guesses as to the values.

    “decisions about what to do about the issue of climate change are going to be made.”

    Again, true in a useless kind of way. It’s certainly true if “no binding decisions” are counted as “decisions.” And whatever the decisions, the kind of number-play discussed here will play no substantial role. Rightly so.

    • @ Fabius Maximus – I wouldn’t say it is operationally useless. Evaluating expected social welfare has been done in practice (see longer version of post for some examples as well as how one can use Monte Carlo simulations plus the Newton method to use it in practice). As for wild guesses about the moral parameters for the social welfare function, there is a very rich literature on trying to determine the values; the result by Layard et al. alone is fairly well constrained.

      • Moral parameters: morality is an artifact of a society. It differs widely between societies and varies substantially over time. The generally accepted morality you presupposed does not exist. Name ten precepts of your personal morality (call them ten commandments if you like) and test them for acceptance world wide.

      • Compare and contrast moral values between Muslims and Westerners. Come back and let me know what to do.

      • Believers and the Unbelievers. Do you deny it? It’s happening right in front of you.

      • jim2 compare and contrast moral values between Buddhists and Westerners. Come back and let me know what to do.

      • One hand clapping, shows we all stink.

      • @oldfossil – That is true. Even for things like: more consumption is good, killing is wrong, one should not commit suicide, you can find a person that disagrees. However, you can look at the average preferences for humans and you might be able to come up with some moral principles that most people agree with. Most people agree that everyone should be equal under the law, for example.

      • -1=e^iπ,

        “Evaluating expected social welfare has been done in practice ”

        You’re missing the point. People have calculated the results from the Drake equation as well. But since the results are subject to wild guesses about the inputs, neither policy-makers nor the public relies on them.

        Like lots of confident guesses, these results are deployed by people to support their per-determined views. Perhaps in the future they’ll have operational utility, but that’s a long time off.

      • “But since the results are subject to wild guesses about the inputs, neither policy-makers nor the public relies on them.”

        You say wild guesses but the best data on estimates of the coefficient of relative risk aversion are fairly well constrained. Estimates using tax structures such as Evans (2005) suggests the coefficient of RRA is 1.3-1.6; however this is an overestimate for reasons I give in the extended version of the post. Then you have Chetty’s estimate of 0.97, which is likely an underestimate due to how he treats the complimentariness of consumption and leisure. Then in the middle of those two you have Layard et al.’s result of 1.24 with a 95% CI of [1.14,1.35] and Anthoff et al.’s result of 1.18. There is a very diverse literature on this topic, and I could have mentioned many other results (I recall there was a result that found that insurance market behaviour was inconsistent with estimates below 1). Also, evolutionary theory, finite discount rates and the St. Petersburg paradox all suggest that the coefficient of RRA can’t be too far from 1. And of course once you obtain the coefficient of RRA, you can get the rate of social time preference from Ramsey’s equation and market interest rates. The confidence intervals I gave in the first post of what are reasonable values of the moral parameters based on empirical evidence are fairly generous.

        Yes, a policy maker could choose moral parameters to try to dogmatically get a certain conclusion. But if the choice of moral parameters is transparent then that makes it far easier for people to question the conclusions of such a policy maker. If a policy maker is basing results using a coefficient of RRA of 2 and a discount rate of 0.2% (or alternatively 0.5 and 2.4%) then I think there is a good reason to suspect confirmation bias with such a choice.

  13. This looks like another model… dependent upon factors which are presently unknown, such as climate sensitivity and the holistic effectiveness of the prescribed technological “fixes” for example. So yes, it could be the beginning of a beginning to quantify welfare sensitivity based upon projected consequences of societal trajectories, assuming we can better determine those trajectories and consequences.

    But be careful how sharply focused the crystal ball becomes, because a clear and accurate picture will reveal that many regions will be asked to forgo climatic improvement in order to provide relief for other regions. Hand-waving generalizations in use today will give way to the reality that some will lose in order that some others may win, and all will incur costs along the way. This function will also favor a tiny region presently crammed with people when a huge region with few current residents could become hospitable to many more humans with a bit of warming (climate change).

    But in the end I see the largest failing for this model to be obvious and insurmountable when it comes to striking a course of action: after all of its sound and fury, it will “leave it up to policy makers to choose the appropriate moral judgements.”

    • “This function will also favor a tiny region presently crammed with people when a huge region with few current residents could become hospitable to many more humans with a bit of warming (climate change).”

      I don’t see how that necessarily follows. It depends what kind of economic model you use. If you want to use a model that accounts for the fact that people may migrate to regions that become more hospitable then you can do so.

      • Most models favor static assumptions over the dynamic, and we regularly see policy makers assume that populations should remain in place. For instance, I had no problem moving 4 degrees north to follow an employment opportunity but to the IPCC a person who moves nearly 500 km northward to enjoy a more hospitable climate would join the list of climate refugees.

        More to the point, while I enjoyed your post and thought there are several interesting ideas presented, it appears that your first assumption was to consider the population distribution as is is today, not as it could be in the future. I think this is a trap into which all such models will tend to fall.

  14. There are rankings of social welfare out there that put some very poor and even despotic countries ahead of the US because they use less energy per capita and for other reasons. It is easy to game the system with strange metrics.

  15. Utility as a Function of What?

    In the history of mankind, the one thing that improved the Utility of People more than anything else is the low cost abundant energy that comes from fossil fuel.

  16. if you are interested in Utility Theory you may be interested in Robert Shuler’s Crash Theory. http://www.heliyon.com/article/e00041/

    go to website and scroll down to:
    Wealth inhomogeneity applied to crash rate theory
    http://blog.heliyon.com/post/133786522956/what-economic-crash-theory-says-about-car

  17. -1=e^iπ –

    You say the following:
    ==> “Ultimately, determining which policy options maximizes expected social welfare depends on moral judgements.”

    I won’t pretend to be able to understand your post in great detail, but I have to wonder about such a conclusion. I think I observe that in the real world, people reach varying conclusions about how to maximize expected social welfare not so much because of morally differentiated views but on ideologically differentiated views. In other words, I think that people with basically similar moral outlooks reach very different conclusions about which policies are likely to result in the greatest social welfare. As much as people attempt to ground their policy orientation in complex rationales, I think that there needs to be an accounting for the simple, and strong, influence of identity-orientation, as manifest in “cultural cognition,” “motivated reasoning,” “confirmation bias,” etc. IMO, identity-orientation (translated in to policy perspective) is at least to a large degree, the driver in the association between reasoning and ideological outlook. Although we like to assume (at least for ourselves) that ideological identity is the product of clear-eyed and unbiased analysis, there’s a ton o’ evidence that suggests otherwise.

    But either way, in the end, I think that describing views on policies as being based on differing moral outlooks runs the risk of contributing to the polarization rather than helping to “build bridges.”

  18. I think there is a disconnect here. If the Global Warming Hypothesis is correct the only way to fix it is to stop using greenhouse gases. Any amount of incrementalism risks an incompletion of the necessary solution to solve the problem and some say it’s already too late. You can’t solve this problem with an economic social solution it’s apples and oranges. It is not a human problem, humans ARE the problem. The only solution now is too ramp up nuclear as quickly as possible — Hansen is right! For the people that don’t believe AGW is a problem then it’s damn the torpedoes full speed ahead. Why do you think this is so contentious? As yet there is no authority to say who’s right, that is why the 97% is so important to the AGW folks because that’s the only authority short of the hypothesis becoming theory or law.

    • @ ordvic – But you have to demonstrate that ‘fixing it’ is desirable. What is your moral basis for ‘fixing it’ being desirable for society?

    • No, sorry, I really meant it. Disarms my whole argument just about. Desirability of the planet close to this goldilocks climate, I would think, was self evident as far as human welfare but the AGW thing is still arguable and perhaps, as they always point out (on both sides), having a little extra CO2 may help with the next Milankovitch ice period. So you’re calculations that include the various perspectives may be the only solution here. However as I said I don’t think you can namby pamby about if CO2 really is a present threat so stopping emissions would take drastic measures.

      • OTOH, If a solution included, as I suggest’ a big dose of nuclear the greens would say ‘no it doesn’t’ renewables are the key.

      • The impossible task of trying to ameliorate, as Joshua suggests above, seems to have come to fruition:

        Why the Paris climate deal is meaningless

        http://www.politico.eu/article/paris-climate-deal-is-meaningless-cop21-emissions-china-obama/

        “This year, in Paris, has to be the year that the world finally reaches an agreement to protect the one planet that we’ve got while we still can,” said U.S. President Barack Obama on his recent trip to Alaska. Miguel Cañete, the EU’s chief negotiator, has warned there is “no Plan B — nothing to follow. This is not just ongoing UN discussions. Paris is final.”

        But the more seriously you take the need to reduce greenhouse-gas emissions, the angrier you should be about the plan for Paris. With so much political capital and so many legacies staked to achieving an “agreement” — any agreement — negotiators have opted to pursue one worth less than…well, certainly less than the cost of a two-week summit in a glamorous European capital.

        Climate talks are complex and opaque, operating with their own language and process, so it’s important to cut through the terminology and look at what is actually under discussion. Conventional wisdom holds that negotiators are hashing out a fair allocation of the deep emissions cuts all countries would need to make to limit warming. That image bears little resemblance to reality.

        In fact, emissions reductions are barely on the table at all. Instead, the talks are rigged to ensure an agreement is reached regardless of how little action countries plan to take. The developing world, projected to account for four-fifths of all carbon-dioxide emissions this century, will earn applause for what amounts to a promise to stay on their pre-existing trajectory of emissions-intensive growth.

  19. This sort of analysis is only applicable if one desires more government programs. The government does not have a good track record managing the programs it already has. In the US, the future of social security is uncertain. Obamacare is already in the dumper and was a massively stoopid idea to begin with. And after going into 4 trillion in debt for quantitative easing, and that doesn’t count other government spending, the economy is just so-so. I think the solution to “climate change” is to stop giving money to the UN and do nothing further that would hamstring our economy and future as a strong nation.

    From the articles:

    Because future taxes are projected to fall short of benefit payments, Goss and his actuarial team project that the combined Social Security Trust fund will run dry in 2033. At that time, benefits to retirees and other beneficiaries in that year would need to be reduced by about 23 percent in aggregate. While that certainly isn’t good news, it doesn’t mean that Social Security will totally run out of money and won’t be able to pay any benefits.

    http://www.cbsnews.com/news/will-social-security-run-out-of-money/

    The biggest U.S. health insurer is considering pulling out of Obamacare as it loses hundreds of millions of dollars on the program, casting a pall over President Barack Obama’s signature domestic policy achievement.

    UnitedHealth Group Inc. has scaled back marketing efforts for plans sold to individuals this year and may quit the business entirely in 2017. It’s an abrupt shift from October, when the health insurer said it was planning to sell coverage through the Affordable Care Act in 11 more states next year, bringing its total to 34. The company also cut its 2015 earnings forecast.

    http://www.bloomberg.com/news/articles/2015-11-19/unitedhealth-may-pull-out-of-obamacare-marketplace-stock-slides

    The scale of the interventions has been eye-popping: The balance sheet of the US Federal Reserve Bank has ballooned from around $700 billion at the outset of the financial crisis to peak at more than $4 trillion. So far, this massive “money printing” has not led to inflation because bank lending has not grown proportionately.

    https://www.bostonglobe.com/business/2015/03/01/was-best-way-boost-economy/2A3u8T6lWLzPpPRmssRd4K/story.html

    • This sort of analysis is only applicable if one desires more government programs.

      Presumptive bunk used to complain about the government. Why not just complain about the government without the first sentence, or better yet develop the argument for the first sentence. In any case the tie between the first sentence and that which follows is not immediately obvious.

  20. Formally, trying to maximize or minimize more than one thing at a time is called goal programming. There is a long literature on this. It has become clear that there is no unique solution because it all comes down to the weights of the different goals.

  21. This is ominous. They are indoctrinating kids in climate alarmism creating little militant fanatics. They call them the Hansenjugend:

    http://www.newsobserver.com/news/politics-government/state-politics/article46795925.html

    They tell them their little heads will explode if they don’t join up. They show them a video.

  22. Government funded indoctrination is having an effect. From the article:

    RALEIGH
    Hallie Turner, the 13-year-old girl who took North Carolina to court over climate change, received disappointing news the day before Thanksgiving.

    A Wake County Superior Court judge ruled against her effort to overturn a December 2014 decision by the N.C. Environmental Management Commission.

    Hallie, an eighth-grader at Ligon Middle School who has been marching and rallying against global warming since the 4th grade, is one of a number of teens taking their states and politicians to court over climate change.

    With the help of lawyers from Our Children’s Trust, an Oregon-based climate change non-profit, attorneys from Duke University’s Environmental Law and Policy Clinic, and Gayle Goldsmith Tuch, a Forsyth County lawyer, Hallie petitioned the state Environmental Management Commission to adopt rules that would reduce greenhouse gases. Commission members are appointed by the governor and leaders of the N.C. Senate and House of Representatives.

    http://www.newsobserver.com/news/politics-government/state-politics/article46795925.html

    • Anyone who believes that litigation is really driven by a 14 year old, send me your email address. I have some Enron stock I want to sell you.

    • There is not actual data that supports the flawed alarmist CO2 causing dangerous warming or sea level rise.

      North Carolina has about the best laws to fight the junk science of any state.

      YES, NORTH CAROLINA, YOU GO!

      I have attended a lecture by a person who fought to get that law passed.

    • “Hallie, an eighth-grader at Ligon Middle School… has been marching and rallying against global warming since the 4th grade.”

      There is a term for this kind of environmental activism: child abuse.

  23. Uncertainty – from the article:

    A team of European researchers have unveiled a scientific model showing that the Earth is likely to experience a “mini ice age” from 2030 to 2040 as a result of decreased solar activity.

    Their findings will infuriate environmental campaigners who argue by 2030 we could be facing increased sea levels and flooding due to glacial melt at the poles.

    http://www.express.co.uk/news/science/616937/GLOBAL-COOLING-Decade-long-ice-age-predicted-as-sun-hibernates

    • Well, global warmer climate scientists (as opposed to real scientists) claim that CO2 is the dominant influence on climate.

      If global warmer climate scientists are correct we should be able to avoid solar driven cooling with more CO2. We have enough fossil fuel to test this theory.

      It would be useful to get an estimate of the rate of cooling. It is implied that the cooling would be like the 90s in reverse.

      Since cooling is bad and would be catastrophic, we should start funding the extra coal fired plants that are needed to produce the CO2 that would stave off the harmful and dangerous cold.

      Given that the 90s were “110%” driven by CO2 we should have net warming if the rate of increase is over 2 PPM/Y. Given that the amount of emissions that remain in the atmosphere is declining we would need new coal fired plants to maintain the current level of CO2 increase or, better yet, even more coal fired plants to increase it. Since coal fired generation cost is mostly fuel related, building the coal fired “stave off the cold” plants and keeping them in reserve would not be an undue hardship.

      If increasing the CO2 does not stave off the temperature decline we can take cold comfort in knowing the global warmer climate scientists were wrong. About the only benefit we would get if the global warmer climate scientists are wrong, is cheap coal fired electricity rather than expensive renewable electricity. Hmm, the new coal plants look like a win-win situation.

    • A team of European researchers have unveiled a NOT scientific COMPUTER model showing that the computer output will experience a “mini ice age” from 2030 to 2040 as a result of decreased solar activity.

      The oceans are too warm and the ice volume and extent on earth is too small to support a “mini ice age” in the 2030 to 2040 time period.

      They use CO2 and solar cycles and ignore the ice cycles. They will most likely never be right. They may luck into some short term correlations on rare, small, time periods.

      • Well, i hope you are right. We are at or below the insolation level needed to drop back into the ice age. The planet has been cooling for 9000 years. Historically at current insolation level it has been colder… much colder.

        A little more ice on both ends of the planet and we could be off to the races.

        This concern with global warming does not seem to be reality-based. Cooling is a more pressing and potentially harmful concern. We would be well advised to up the CO2 level to 600 or 700 PPM.

        Unfortunately the ecology minded folks have so mucked things up that reasonable levels of CO2 (600-700 PPM) might not be possible and 500 PPM is about the best we can hope for.

      • PA you write that earth has been cooling for 9000 years while you post a chart that shows the same temperatures for those same 9000 years has gone up and down in the same bounds.
        .
        Your words do not match the data you presented. You qualify, you might be a climate scientist.

      • I believe this is the historical relationship that PA is trying to present.

    • Earth running out of warm period in the 120,000 year cycle

  24. Maybe I missed it, but there’s a critical flaw with what I take to be your function-to-optimize, Jeremy Bentham’s “the greatest happiness of the greatest number is the foundation of morals and legislation”: It doesn’t differentiate between Individual Rights and its absence: The sum is unchanged by taking happiness (concrete: property (wealth)) from some, and giving it to others.

    • I for instance, do not like being stolen from, either by individuals or by groups of people, as is the case of government theft. However, one could argue that government theft makes only a few people unhappy but makes a lot of people happy, and while it may be damaging in the long wrong, borrowing for the unborn to make the party go on maximizes social welfare.

      I read, maybe 40 years ago that philosophers had proven, through the use of predicate calculus, that a society that redistributed its wealth would be a better one than one that does not. Of course, history has proven that’s crud. I think they missed a few parts of human nature, such as people are by nature competitive, and if you remove the competitive element, people stagnate. It reminds me of this post. Or large economic predictions.

      And meanwhile, I posit that in 100 years from now orange gummy aliens will descend upon earth. These gummy aliens will have no interest in our planet if only we reach the 2 degree “C” threshold. Ridiculous you say? I say only it is deep uncertainty. We have no idea how many aliens there are approaching earth right now, how many of those are gummy aliens, how many are orange, and how many can’t tolerate the 2 degree “C” threshold. Let us say it is a problem of “deep uncertainty.” How should we react to it?

      Or if that’s a little too silly, what about meteors? Perhaps we ought to be building a system to alter the course of meteors that might crash into earth and wipe us all out. Never mind that as technology progresses, it (ought to be) far easier to deal with the problem.

      • Predicate calculus provides no such proof, because it is merely a way to represent well defined arguments. It draws no conclusions, any more that the English language draws conclusions regarding what is said in it.

      • “PHIL 200 INTRODUCTION TO LOGIC (3)
        Minimum of 48 lecture hours plus 16 lab hours by arrangement/semester. Recommended: Eligibility for ENGL 100 or equivalent; and eligibility for MATH 120 or equivalent.
        An introduction to symbolic logic with an emphasis on proof systems for propositional and predicate logic

        Those guys thought they had proved it. Unfortunately, that was pre-internet, and its so obviously wrong today I can’t find it. In any event, yes, nothing can be “proven.” Even in mathematics, it is not known whether number theory is consistent or not. Just so far no two contradictory theorems have developed, so it looks good.

    • @ Hutchins – If you want to argue that the utility function should take into account more factors than just consumption, such as freedom, then that is fine. With respect to Bentham defining utility as happiness, it has issues and there are other forms of utilitarianism. Preference utilitarianism is arguably a better way to approach determining the utility function than classical utilitarianism. https://en.wikipedia.org/wiki/Preference_utilitarianism

  25. Here is a simple and elegant Existence proof that there is a solution to the global warming/climate change problem:
    (a + b^n)/n = x

  26. Does anyone actually believe that this is how public policy decisions are made? Maximizing expected social welfare is a mathematical metaphor at best. It is not an accurate model of how decisions are actually made, nor could it be.

    • I agree with David’s observation … however this is a reasonable construct to guide decisions and expose politicians corrupt view of payouts by including their own personal gain from taking positions to satisfy their constituents rather than their informed beliefs after deep and thorough study and understanding of issues. it should be demanded that politicians explain and even be questioned in public) to explain the basis of their understanding of real science as compared to beliefs and feelings and polling of hands. The noise would dim significantly.

      • Danley, I fail to see how this mathematical metaphor does any of what you suggest. I also do not care for your apparent view of political process, which is the actual decision making apparatus of democracy.

    • Is it good to have goals?

      • It is better to have directions.

      • Only the “right” goals – your mileage may vary.

      • The easiest way to travel is always be the one giving the directions. As any pharaoh would tell you.

      • Directions without goals defined?

      • Having a direction and giving directions are two very different things, Arch. I assume you are merely trying to be witty. But the difference between having a goal and having direction can be significant.

      • Agreed. They should not be confused

      • Space Race, War on Drugs, War on Terror…

        https://en.wikipedia.org/wiki/Juggernaut

        Mankind has a love affair with the ‘press’.

      • Grant: Normally a goal is a specific end state while a direction is not. Making more money is a direction while making X more dollars is a goal. World peace is a goal while reducing conflicts a direction. Either that or there is no difference and we do not disagree. Your initial comment was cryptic in this regard.

      • Making more money is a direction while making X more dollars is a goal

        “Making more money” is not a “direction”. It is, at best, a criterion by which to judge the value of “direction”.

      • There will be no peace until the Age of Grace, has come to a conclusion. At least that is what I have read. So I am always a firm believer in sustainability first and foremost.

      • My original comment was a question.

        To me a goal is needed to set a direction and is more abstract. Making more money is a goal and implementing a specific business plan is setting a direction and includes specifying a target value [your ‘goal’]. To me a direction is a response effecting movement toward a goal. For me goals can be set higher than expectations. Also in my frame of reference setting a direction without a goal can be a risky short-cut.

        In particular my original reference the term ‘goals’ then refers to striving to reaching a goal even though in reality expectations may be low. In plain English I decline to automatically defer to pessimism. The latter in the context of decision-making is a prescription for an irrational ‘lack of action’. [However, rational lack of action is not precluded.]

        Still there no need to parse labels to death here, David.

    • @ David Wojick – I doubt most policy decisions are made based on some social welfare function. More likely, politicians are making decisions based on subjective feelings.

      • I would hope that not decision-maker defers to a [decision] model. As noted elsewhere and in previous posts the purpose of models–and yes even decision models–is to inform the decision. For example, one way such a tool might inform a decision-maker/decision-makers is that it might temper the effects of over optimistic and under optimistic perspectives advanced on particular policy alternatives. :O)

      • Elected representatives have staff that does research for them and also, they were elected to represent the interests of their constituency. One can argue to what degree the constituency is represented, but on most matters, they probably utilize a good deal of objectivity. It just might not appear that way to some.

      • When it comes to environmental policy, Congress has typically established broad goals (“restore fishable, swimmable rivers” or “prevent extinctions”) and federal agencies write the specific regulations that execute the laws.

        Because Congress demands benefit-cost justification for major regulations many environmental regulations are explicitly based on social welfare calculations, including estimates of the value per cancer avoided or death postponed.

  27. A decision to maximize expected social welfare, must begin with the maximization of net present wealth –i.e., the finance function. Given uncertainty, the most efficient allocation of scarce resources to maximize the finance function is a free people, voluntarily sharing information in a free enterprise capitalistic economy for their individual interest and mutual benefit.

  28. For me, Climate Etc., is a window into an intellectual and academic world that would otherwise elude me.
    The Paris conference illuminates how the climate issue has become the proxy for a grand political debate about the essence of my very existence as a citizen.
    I see that academics and intellectuals are quite busy inventing maths to quantify happiness and social welfare benefit.
    I hope to be allowed just enough SWF for a happiness ratio of say, umm …
    75%.
    My existence well modeled.
    I tremble.

  29. How about not trying to plan several decades in the future-pointless.

    Society can mobilize quickly just fine without putting guesswork inside complex equations.

  30. “An individual may care about more than just their total consumption over their lifetime; they may care about the timing of that consumption. Humans tend to have a preference for present consumption over future consumption and tend to want to smooth consumption over time. [..] the utility of a dead individual is zero”.

    So the best policy is to aim for economic growth and improved life expectancy. Access to cheap plentiful energy is crucial for both. Most western governments are aiming for the exact opposite, by attacking the cheapest sources of energy and encouraging expensive and inefficient sources.

  31. Individual human reasoning is very complex. The multi-group reasoning that creates public policy is orders of magnitude more so. The idea that this reasoning can be reduced to a simple maximization algorithm is metaphorical best, more likely misleading. It hinders understanding.

  32. Before the white man landed on this continent, there were the Plains Indians, horseless, nomadic and sequestered in small bands. Bands as a group were tribes who communicating with one another. Yet the survival of the band was entirely dependent upon: providers. If father & son and uncle went hunting and didn’t return due to a calamity of weather, wild beast or hostile encounter, those left behind, the band literally disappeared. The loss of providers, small in number with respect to the number in the band, were essential to the band’s survival.

    “While there are likely many relevant parameters, for simplicity, the rest of this post will treat utility as a function of only consumption.”

    The essay’s a priori assumption that consumption is the major focus at issue, I believe is false. We are still dependent upon, albeit in more complex ways, providers. I acknowledge that providers are much harder to assess as to their impact, yet society does place value upon providers over consumers. Further, society recognizes that certain providers are more valuable than others such as the old saw: 80% of the work is done by 20% of the workers.” Certainly not a union friendly statement, nevertheless, egalitarianism is frowned upon by many in society if it is perceived that some one or some group is not “pulling their own weight”. Another reference to an Agrarian culture thinking that still echo in our times. A football team may exemplify such perceptions. Indeed, too much leisure is still viewed as “slough”.

    I would argue that the metric of producers and productivity by individuals and societal groups is a better way to asses Social Welfare Function.

  33. @Eulers eqn. Typo?

    A vNM utility function is a utility function where U([pa;(1-p)b]) = pU(a) + pU(b) …

    Did you mean: U([pa;(1-p)b]) = pU(a) + (1-p)U(b) ?

    • Yes, that is a typo. Thank you for pointing it out.

    • A very interesting post. Are you suggesting it would be practical to use a model of this kind for real decision making in climate policy, or is it more in the nature of an illustrative model?

      It has always seemed to me that the expected utility of providing clean water, electric lighting and education (etc) to those who do not currently have them is very high, and therefore the negative utility of taking away, or even slowing the expansion of, the cheap fossil fuel based energy that is (currently) needed to provide those things is substantial.

      Whereas the expected utility of reducing the temperature by 0.2C in 2100 when almost everyone will be very much richer (if we have not wrecked the world economy in the mean time) is small, and may indeed be negative.

      But Lomborg and others have been making a point along these lines for years. Can utility theory practically support or refute such an argument?
      Isn’t the problem that people don’t agree on either the PMF for climate sensitivity, or the impact of different amounts of warming, never mind the parameters of the utility function?

      • Hi Gareth,
        Yes, I think that expected social welfare maximization can be used in practice. In the longer version of the post (see the link to the longer version at the end of the first post) I mention some cases where expected social welfare has been used and how one can use it in practice (using Monte-Carlo simulations and Newton’s method).

      • -1 = e^i.pi

        OK I have read that now. I think my worry is that if you can’t constrain the inputs well, you can get almost answer you want. The model (all models) just reflect your assumptions back at you, but make them look more ‘scientific’. Eg carbon impacts under uncertainty are 3x carbon impacts under certainty. Surely that is just a result of the ‘fat tail’ on ECS combined with high estimates of the negative impact of 3C or 4C temperature rises? Chop off the fat tail, or adopt more balanced models that realistically include benefits as well as cost of higher temperature, and adaption, and you would get a different result.

        I agree this could have value, but you would need to run the numbers for a whole range of different assumptions, on both the climate science and the economics.

      • Fair enough. Nonsense in gives nonsense out. You would want to use the best estimates available for everything and try to justify your choice of probability distributions very strongly.

  34. Bhutan’s King introduced Gross National Happines some years ago.

    “The 2015 GNH Index At-A-Glance

    91.2% of Bhutanese are narrowly, extensively, or deeply happy.
    43.4% of Bhutanese are extensively or deeply happy, up from 40.9% in 2010.
    Across groups:
    – Men are happier than women
    – People living in urban areas are happier than rural residents
    – Single and married people are happier than widowed divorced, or separated o More educated people are happier
    – Farmers are less happy than other occupational groups.

    Across districts, GNH was highest in Gasa, Bumthang, Thimphu, and Paro, and lowest in Dagana, Mongar, Tashi Yangtse, and Trongsa.”

    I find it interesting that farmers are less happy than other occupational groups. Could this be because they are directly and deeply affected by the vagaries of the weather? Who better understands the realities of uncertainty, and has to bear the very real effects when assumptions about the future turn out to be wrong?

    Calculations about SWF are all well and good, but become rather unimportant in the face of careless Nature, war, civil insurrection, or like matters.

    I have no answers, but remain quite content with my lot in life. Odd, that.

    Cheers.

    • It is interesting that men have higher self-reported happiness in Bhutan. In Canada, women have significantly higher self-reported happiness.

    • -1=e^iπ,

      And now for a different perspective (from Canadian National Post) –

      “Bennett is co-author, along with his comedy writer daughter Sarah Bennett, of F*ck Feelings: One Shrink’s Practical Advice for Managing All Life’s Impossible Problems, a profanity-laced takedown of the happiness-oriented self-help movement, its moralizing “one-name healers” (Oprah, Phil and Laura) and books that promise to make us brighter, shinier and happier.”

      Vive la différence!

      Is welfare what makes you happy or makes you “better”? Do you give a man a fish, or teach him to fish, even though the latter may induce feelings of unhappiness, (possibly in both of you), for a time?

      I don’t know, and I “feel” that I’m in good company.

      All very tricky.

      Cheers.

  35. Lots of mathiness. Little value.

  36. The article give a veneer of logic to social decisions that are actually political. I can’t imagine a politician trying to persuade voters to elect him because he will maximize social utility with his climate policy, so, I conclude this outlines an effort to bedazzle us common folk with so much BS that we won’t simple say, “DO NOTHING UNTIL YOU ARE CERTAIN.”

    Dr. Curry, I’m disappointed.

  37. Curious George

    The formula for “social welfare”is deeply flawed. We should first ask a question: What is a desirable number of people on the Earth? No politician dares to suggest that the population might be too high already (which should render the value of life at present a negative number.) Without a good answer to this question, this article with all its learned formulas is a pure speculation.

  38. -1=e^i pi,

    Thank you for your post on this method of estimating future discount rates for the distant future. It’s well written and I expect it is clearly explained for other economists.

    I’ll try to summarise the concerns I was stating when you were trying to explain the Ramsay equation derivation of discount rates in many long comments on a previous thread.

    I am seeking a reality check on the global average discount rates used in DICE-2013R – i.e., 5.2% in 2010 declining to 3.5% in 2100 to 2.2% in 2300. Engineers do reality checks on estimates. I’d like to see reality checks of the discount rates used by climate economists for projecting climate damages and abatement costs over the next 100 and 300 years. I’d like to know what discount rates have been demonstrated by actual investment decisions over the past century and longer. I would like to see a chart of what discount rates are implied by past societies’ investment decision in large infrastructure projects – perhaps even including as far back as the pyramids, irrigation systems, aqueducts, roads, railways and large public buildings. I am want to know the global average discount rates not just the developed countries’ average discount rate

    Discount rates used for policy options analysis of alternatives for investment are the Weighted Average Cost of Capital (WACC). WACC is higher than interest rates. Sections 2.2.2 and 2.4.2 here explains commonly used ways to derive the WACC http://www.aemo.com.au/planning/419-0035.pdf

    This chart A History of Interest Rates shows interest rates are the lowest in 5000 years in the developed countries: http://static.businessinsider.com/image/5595597fdd08959c4d8b459d/image.jpg
    Source: http://www.businessinsider.com.au/chart-5000-years-of-interest-rates-2015-9

    However, I understand discount rates are much higher in developing countries than in developed countries.

    The discount rates used by climate economists for estimating costs and benefits of CO2 abatement policies seem to me to be much lower (e.g. about half) the discount rates used by governments for making investment and regulatory decisions between competing public use investments such as, between hospitals, education, research, railways, roads, airports, electricity system, etc. For example, Australia’s and New Zealand’s governments use a default discount rate of 10% for comparing options for electricity system investments – i.e., for comparing options between technologies such as coal, gas, nuclear, hydro, wind, solar, geothermal and energy storage. This is the discount rate used for making the actual policy decisions by governments. It seems to me that rates used by the climate economists are not aligned with the rates used in the real world for making public funding decisions and for justifying regulations to influence/distort private sector investments in public-use infrastructure. Therefore, how can the low discount rates used by the climate economists for projecting costs and benefits for up to 300 years be justified?

    OECD has been using 5% and 10% discount rates for comparing electricity generation technologies for over 30 years. The recent report by J.P. Morgan used 10% discount rate for comparing deep de-carbonisation electricity system costs.

    • The original Stern Report (which also relied upon the Ramsey equation) applied absurdly low discount rates combined with economic projection centuries into the future. This was actually taken seriously by CAGWers. Still is, I suppose.

      • -1=e^iπ,

        I accept you can’t answer my question. It’s not for the reason you state, it’s because you are stuck in loop, i.e. stuck thinking only inside the box. You continually misrepresent what I’ve said, it appears to me as an excuse to avoid answering. I clearly stated that the chart was to show an example of the sort of chart I am seeking nut for implied discount rates historically, not interest rates.

        Clearly we have no confidence in each other any more so I recognise you will not answer the question I’ve asked and will continue to ramble on with your economic mumbo-jumbo.

    • @ Peter Lang –

      “I am seeking a reality check on the global average discount rates used in DICE-2013R – i.e., 5.2% in 2010”

      If I use the best estimate of Layard et al. for the coefficient of relative risk aversion (1.24) and I use the inverse of global life expectancy for the social rate of time preference (1.41%), then this is roughly in agreement with the observed after-tax real riskless interest rates for the US. As the world’s real GDP per capita is growing at a rate of about 3% per year, this suggests that world real riskless after-tax interest rates should be around 5.13%, which isn’t too far off what Nordhaus uses.

      “This chart A History of Interest Rates shows interest rates are the lowest in 5000 years in the developed countries:”

      From what I can tell, those are nominal pre-tax interest rates with a risk premium, not real after-tax riskless interest rates.

      “However, I understand discount rates are much higher in developing countries than in developed countries.”

      Yes, there is a higher risk premium, and arguably a higher social rate of time preference due to lower life expectancy.

      “The discount rates used by climate economists for estimating costs and benefits of CO2 abatement policies seem to me to be much lower (e.g. about half) the discount rates used by governments for making investment and regulatory decisions”

      There are two main ways you can deal with uncertainty.
      1. Fiddle with the discount rate.
      2. Leave the discount rate alone and instead take into account the entire probability distribution of outcomes.

      Expected social welfare maximization does the latter approach, thus you want to use riskless interest rates and ignore risk premiums.

      Maybe I’ll give you an example of how the more traditional cost benefit analyses are merely approximations to expected social welfare maximization.

      Suppose that I am a government and I want to decide whether or not to build a hospital. In this case the government wants to maximize:
      Expected(Sum(t = 1 to infinity; exp(-rho*t)*Sum(i = 1 to N(t); U(C(i,t)))))

      However, if the effect of the project on overall consumption is relatively small, then the above becomes:
      Expected(Sum(t = 1 to infinity; exp(-(rho + eta*g)*t)*NB(t)))
      where NB(t) is the net benefit for period t, rho is the social rate of time preference and eta is the coefficient of relative risk aversion. And by Ramsey’s equation, r = rho + eta*g, so one gets:
      Expected(Sum(t = 1 to infinity; exp(-rt)*NB(t)))

      Which is essentially expected cost-benefit analysis using a discount rate equal to the real riskless after-tax interest rate (assuming the net benefits are given in real terms, not nominal).

      Now let’s say that the only uncertainty is the fact that this hospital has an x% per year chance of being destroyed (due to a natural disaster, war, being expropriated, etc.) then the above becomes:
      Sum(t = 1 to infinity; exp(-xt)exp(-rt)*NB(t))
      Sum(t = 1 to infinity; exp(-(r+x)t)*NB(t))

      which is essentially traditional cost-benefit analysis where r + x is the real interest rate with a risk premium. And of course, if you are using nominal values rather than real values, then you would want to add inflation to this discount rate, so you would want to use a discount rate of r + x + i, where i is the inflation rate.

      So overall, expected social welfare maximization using a discount rate of rho can be equivalent to performing traditional cost-benefit analysis using a discount rate of rho + eta*g + x + i.

      • -1=e^iπ,

        Sorry, I should have made my question clearer. I am seeking an independent, check on the actual discount rates that are implied by investments in long life infrastructure projects over the past century, and multiple centuries. That is a chart like the one I showed of interest rates from the Bank of England. By independent I mean without resorting to the mumbo-jumbo economists jargon like the Ramsay equation. Refering to more of the Ramsay and other economic mumbo jumbo is not answering my question. I am asking you for a reality check – i.e. “sneak up on it from another direction”.

        You are correct that the chart is of nominal interest rates. Bu I am seeking a chart of the implied discount rates used in the decisions to build the large, long life infrastructure projects.

      • @ Peter Lang,

        Based on our previous conversations I know this isn’t going to go anywhere. You are being unreasonable and are a lost cause.

        You keep asking me to come up with data on interest rates from centuries ago even though no such data exists and despite the fact that it isn’t very relevant. Then you confuse interest rates with discounts rate and dismiss all economic theory that explains observations about interest rates, including the economic theory that forms the foundation of cost-benefit analysis.

      • [Repost in correct place]

        -1=e^iπ,

        I accept you can’t answer my question. It’s not for the reason you state, it’s because you are stuck in loop, i.e. stuck thinking only inside the box. You continually misrepresent what I’ve said, it appears to me as an excuse to avoid answering. I clearly stated that the chart was to show an example of the sort of chart I am seeking nut for implied discount rates historically, not interest rates.

        Clearly we have no confidence in each other any more so I recognise you will not answer the question I’ve asked and will continue to ramble on with your economic mumbo-jumbo.

      • Good data on real interest rates only exists in developed countries for the past 150 years and for developing countries since WW2. As for ‘historical discount rates’, discount rates are a moral judgement, you cannot empirically observe them.

      • As for ‘historical discount rates’, discount rates are a moral judgement, you cannot empirically observe them.

        If that is correct, then they cannot be applied to policy options analyses and it means the whole concept of low and declining discount rates for carbon pricing analyses is invalid. It would mean that the IAMs are purely a tool of moralists

        Clearly your statement is nonsense.

        Engineers have been using discount rates (WACC) since forever. Mining companies have been using discount rates to decide which of several different opportunities they should invest in. They are not using moral judgments. You seem to be stuck in you little economist’s thought bubble and apparently unaware of the real world operates.

      • “If that is correct, then they cannot be applied to policy options analyses”

        By that logic, murder shouldn’t be banned as ‘murder is bad’ is a moral judgement that cannot be observed empirically.

        “Mining companies have been using discount rates to decide which of several different opportunities they should invest in.”

        Yes, because a mining company wants to maximize profit. ‘Profit is good’ is a moral judgement.

        “They are not using moral judgments.”

        Yes they are. All decisions require moral judgements.

  39. “However, the scientific method alone does not rank policy responses since the scientific method doesn’t tell people what to do.”

    The scientific method hasn’t been applied, if the water vapour feedback is negative then CO2 increases cannot be the major cause of recent warming, and any future warming may beneficial.

    “For example, the happiness of individuals in society may be directly affected by the climate; Tsutsui (2013) found that a temperature of 13.9 C maximizes happiness.”

    The World Health Organization’s standard for warmth says 18C (64F) is suitable for healthy people who are appropriately dressed. For those with respiratory problems or allergies, they recommend a minimum of 16C (60.8C); and for the sick, disabled, very old or very young, a minimum of 20C (68F).

    • Maybe 13.9 C is an underestimate. Tsutsui only did a parabolic model of happiness as a function of temperature; perhaps a cubic model would have been better.

      • Does it matter whether CO2, or any human activity, is causing climate change?

        Suppose you model human activity this way… (1) does the activity cause harm? (2) if yes, reduce activity, (3) if no, and activity is beneficial, increase activity.

        First, this is not an obvious equation. Specifically there is not a “do nothing” option. So the equation is diabolical. It is, in fact, just a subtle reformulation of a Malthusian catastrophe. Under it, all behaviors increase until there is harm. Since activity reduction is never permanent, but only until the answer is again “no harm,” and since with time that definition may change, it is an equation for perpetual increase.

        I am not advocating any action based on this. In fact, you will see that I claim the problem is the lack of a “do nothing” action. However, until population growth and standard of living growth are both zero, there is no do nothing option, and I do not see any significant fraction of humanity going for this approach. While I myself have only one child, that is hopefully temporary. There is a compelling motive under a democratic government in a welfare state to have more children in order to increase one’s future share of human wealth.

        Since human nature in this regard is well known and well studied (economic utility maximization, under uncertainty or otherwise), then the policies that create these behaviors are wrong. It is a simple deduction.

        The policy alternatives are unpleasant. China has given up their one child policy because it does not economically support an aging population, and even the Chinese decline to practice systematic geriatricide. Population in Europe declined under Feudalism, but who would go back to that?

    • Give the poor people affordable abundant electric energy from fossil fuel and then they can become more productive and afford to have AC so they can be comfortable like us. Then they can set their own thermostats. The alarmists want poor people to continue to live without or cease to live and they want us to change to live without. Many of the alarmists think that we should reduce the population of the world to below one billion. They do want genocide. Removing CO2 from the atmosphere can do that.

      Those thoughts come from where the sun does not shine.

    • The Vikings moved to Greenland when the temperature there was to their liking. They moved out when the temperature there became like it was in the previous, natural, cold period.

      I think people have moved to Greenland again. Maybe more than during Viking time. After a few hundred years, it will get colder again. Now those people have fossil fuel and they will not need to move.

      Oops, the alarmists are going to take away their fossil fuel, they may have to move.

    • ulriclyons,

      I think Tsutsui used a few hundred Osaka university students for his study. Maybe the length of the school year, the vagaries of the local climate etc., had an impact.

      I’ve noticed that quite a few people living in places which are a bit chilly in the winter, prefer to take their holidays in warmer climes, and I’ve always assumed they do this because they feel happy about it.

      I’m happy living in the tropics. I find air conditioning at around 24-26 C comfortable, when the humidity gets a bit too oppressive. Each to his own.

      Cheers.

  40. -1=e^i pi, you might find this paper interesting… It spells out an interesting maximization-based reason why a decision maker would be risk-averse above some critical level of current resources but risk-seeking below it. I am told that this bit of theory is very similar to “energy budget models” of risk-taking that come out of biology’s optimal foraging literature.

    http://pages.stern.nyu.edu/~rradner/publishedpapers/72LinearModels.pdf

  41. Sounds like it helps to explain the results by Caballero. Thanks for the link. I’ll take a look. :)

  42. Von Mises would point out that the only utility function that makes any sense is that of price within a free market.

    • “Let us now consider exchanges on the free market. Such an exchange is voluntarily undertaken by both parties. Therefore, the very fact that an exchange takes place demonstrates that both parties benefit (or more strictly, expect to benefit) from the exchange. The fact that both parties chose the exchange demonstrates that they both benefit. The free market is the name for the array of all the voluntary exchanges that take place in the world. Since every exchange demonstrates a unanimity of benefit for both parties concerned, we must conclude that the free market benefits all its participants. In other words, welfare economics can make the statement that the free market increases social utility, while still keeping to the framework of the Unanimity Rule.57”

      Various other destructions of the notion of a welfare utility as presented by the Austrian school:

      https://mises.org/library/toward-reconstruction-utility-and-welfare-economics-0

    • “The problem of “welfare economics” has always been to find some way to circumvent this restriction on economics [that economics cannot make ethical conclusions], and to make ethical, and particularly political, statements directly. Since economics discusses individuals’ aiming to maximize their utility or happiness or welfare, the problem may be translated into the following terms: When can economics say that “society is better off” as a result of a certain change? Or alternatively, when can we say that “social utility” has been increased or “maximized”?

      Neoclassical economists, led by Professor Pigou, found a simple answer. Economics can establish that a man’s marginal utility of money diminishes as his money-income increases. Therefore, they concluded, the marginal utility of a dollar is less to a rich man than to a poor man. Other things being equal, social utility is maximized by a progressive income tax which takes from the rich and gives to the poor. This was the favorite demonstration of the “old welfare economics,” grounded on Benthamite utilitarian ethics, and brought to fruition by Edgeworth and Pigou. Economists continued blithely along this path until they were brought up short by Professor Robbins. Robbins showed that this demonstration rested on interpersonal comparisons of utility, and since utility is not a cardinal magnitude, such comparisons involve ethical judgments.”

      “What Robbins actually accomplished was to reintroduce Pareto’s Unanimity Rule into economics and establish it as the iron gate where welfare economics must test its credentials.47 This Rule runs as follows: We can only say that “social welfare” (or better, “social utility”) has increased due to a change, if no individual is worse off because of the change (and at least one is better off). If one individual is worse off, the fact that interpersonal utilities cannot be added or subtracted prevents economics from saying anything about social utility. Any statement about social utility would, in the absence of unanimity, imply an ethical interpersonal comparison between the gainers and the losers from a change. If X number of individuals gain, and Y number lose, from a change, any weighing to sum up in a “social” conclusion would necessarily imply an ethical judgment on the relative importance of the two groups.48″

      • Is that math book for young Einstein less necessary than that crust of bread for nobody? What utility function can see into the human soul or determine the future determined by any given transaction?
        Ultimately utility is Marxist as one can see immediately by U = U(C).

  43. I would think this piece about expected social welfare maximization could very easily be confused with someone attempting to make a parody of the socialist calculation pipe dream with references to all these individual preferences being too many and too complex to model and therefore we will simplify. The best temperature for all at 13.9 degrees C must have been thrown in for added comic relief. A free market integrates all these individual decisions without needing a simplified algorithm with many assumptions and does it without the coercion required for government enforced policies.

    I can see the final version of this model in the hands of the politicians whereby the politicians have added a weighted part that calculates the ruling parties expected chances for re-election given the acceptance or rejection of the model results. The weight is proportionately 51%.

  44. -1=e^i pi

    1. Do you believe this somewhat defined procedure can actually inform policy makers in a manner that is relevant to reality?
    2. I really don’t see how anyone could use morals, especially on a world wide basis to make any sort of intelligent policy.

    WRT #2, we live in a world where it is considered moral to bury a woman up to her neck and throw rocks at her head until she is dead. To me, this is barbaric, repulsive, disgusting, and very immoral. How would you ever reconcile disparate morals such as this.

    And to me, they entire approach does not seem to be grounded in any sort or reality. I’m sure it’s because I don’t have a grounding in economics, but I can’t see how this would do anything except confuse policy makers.

    • “1. Do you believe this somewhat defined procedure can actually inform policy makers in a manner that is relevant to reality?”

      Yes. You can find the optimal policy option given a set of moral parameters.

      “2. I really don’t see how anyone could use morals, especially on a world wide basis to make any sort of intelligent policy.”

      I don’t see how it’s possible to make decisions without morals (unless you have a narrow definition of morals). Even decisions like ‘I should eat lunch because I am hungry’ couldn’t be done without the moral position that hunger is bad.

      • You can’t prove this is the optimal way to make decisions – in fact, I’m pretty sure there are better ways. It’s just not provable.

        I don’t believe hunger involve morals since even an amoeba will eat to survive. Morality requires a highly developed brain – and all animals get hungry and eat.

      • “I don’t believe hunger involve morals since even an amoeba will eat to survive.”

        Humans have certain morals because evolution favoured humans with those morals, be it killing is bad or hunger is bad. Some moral positions are just so common that they aren’t really controversial.

        “You can’t prove this is the optimal way to make decisions”

        Because that ultimately depends on how you define optimal in that context. What one can do is that given the underlying assumptions of expected social welfare maximization + some moral parameters, policy A is better than all other policies considered.

      • Trying to argue that discount rate is a moral decision is silly and just plain wrong. It might be your opinion and the opinion of social scientists, which includes economists, but this displays ignorance of the real world use of discount rates and how analysts and investors decide what discount rates to use in their analyses. The more you repeat this nonsense the more you damage your credibility. The fact you always dodged answering my perfectly clear questions, and reverting to arguing that discount rates are based on moral values, shows how out of touch with reality you are.

        If discount rates were based on morals, what would they be under ISIS or North Korean regime? What were they during regimes with totally different moral values in the past? If you can demonstrate that real world discount rates are significantly different under regimes with different moral values, you should withdraw this assertions and give an appropriate apology for misleading people (and for your dismissive comments). I’d like to see a chart plotting discount rate versus regimes with different moral values.

      • “Trying to argue that discount rate is a moral decision is silly and just plain wrong.”

        How valuable the future is relative to the present is a moral decision. Discount rates determine how valuable the future is relative to the present and are therefore a moral decision.

        “but this displays ignorance of the real world use of discount rates and how analysts and investors decide what discount rates to use in their analyses.”

        In the real world, most people share some common moral principles such as ‘having more stuff is good’. As a result, investors will try to choose discount rates that maximize profits.

        “If discount rates were based on morals, what would they be under ISIS or North Korean regime?”

        No idea. And people within these groups may have different opinions on what the discount rate should be.

        “I’d like to see a chart plotting discount rate versus regimes with different moral values.”

        How about a plot of social rates of time preference inferred from real interest rates and real GDP per capita growth vs life expectancy? I can do that.

      • -1=e^iπ – killing isn’t always considered to be a bad thing. Killing in self defense is considered OK. Killing Germans and Japanese in WWII was considered the best moral choice by many. Morals just won’t help you determine an optimal policy. The optimal policy depends on the tribe you are in. You can see this at COP21, where the Indians are going to burn as much coal as they want to further themselves. But – what of the environment? Screw the environment, they say, and give us a bunch of Western money to boot. Noble country, India.

      • “Killing in self defense is considered OK.”

        Well that’s killing to prevent killing. So doing a bad action to prevent another bad action can be a net good.

  45. Tsutsui (2013) found that a temperature of 13.9 C maximizes happiness.
    =======
    I call BS on that result. Why do we maintain our houses at 20C?

    • Perhaps we prefer an indoor temperature of 20 C and an outdoor temperature of 13.9 C.
      Perhaps Tsutsui should have used a cubic model instead of a quadratic model, and the 13.9 C result is specification error.
      Perhaps the sample was too small and not representative.

      Tsutsui’s paper was the only one that I found that tried to look at the impact of climate on happiness, so I posted a quick reference. Don’t place too much weight on the result.

      Although, slightly related, the results of Burke et al. (2015) and Nordhaus et al. (2006) found that human productivity is maximized for climates with temperatures of 13-12 C.

      • Thanks for the two new references. However, Burke is not coming up, possibly obscured by a large number of different Burkes who published something in 2015. Can you provide a link?

        Nordhaus is freely available at http://www.pnas.org/content/103/10/3510.full . Though he talks about Africa, most of the data is European. And the conclusion depends on whether one means productivity of individuals or per area of land. For individuals, the coldest (subzero) temps are up to 12 times more productive (perhaps people stay busy to stay warm?). The statistic you referred to is productivity of the land area.

        Obviously productivity is correlated to some degree with happiness, but up to a point and then diminishing returns, one can infer by combining the papers (or by just thinking about it for that matter). Thanks again for thought provoking data.

      • @ Robert –
        Here is a link: http://www.nature.com/nature/journal/v527/n7577/full/nature15725.html
        Burke et al. was also one of the references given in the longer version of the post.

        Yes, it is quite interesting that Burke et al., Tsutsui and Nordhaus et al. all get similar results about optimal local temperature being about 13 C. Note though that as global temperatures increase, the temperature gradient between the poles and the equator decreases, which means that the optimal global temperature should be above 13 C (in terms of productivity or happiness). I believe that Richard Tol got a result of ~16 C global temperature being optimal in a 2009 metastudy, although as I understand it, those results have since been modified to suggest optimal global temperature might be closer to 15 C.

      • What other factors than human productivity and happiness should be considered? None? Many? Some ideas: Biodiversity, preservation of natural beauty, long term planetary stability (e.g. a high productivity civilization might also have a high catastrophic failure rate).

  46. Tsutsui (2013) found that a temperature of 13.9 C maximizes happiness.
    ========
    Academic nonsense. Try living in a place that cold without fire and you will be miserable. Death from exposure will be your constant companion.

  47. Re: Tsutsui 2013 comments: It appears no one actually read the paper. I will obtain a copy and report back on the assumptions. It appears from the abstract it is about weather, not about indoor temperature or survival without housing. 13.9 C is 57 F, which is very good for outdoor physical activity, in fact encourages it, and physical activity produces endorphins. But now I’m also speculating, so we await the arrival of the paper.

    Re: Nickels : “The problem of welfare economics [is] … Any statement about social utility would, in the absence of unanimity, imply an ethical interpersonal comparison between the gainers and the losers from a change.”

    An interesting line of thought, but it is important to also understand that the individual choices are not independent, and therefore it may not be a matter of economics but of adverse consequence (i.e. governance). Consider the problem of water rights. If there is a spring on my land, do I own all the water? If I simply live up-river, am I entitled to all the water? In fact the U.S. does take all the water from the Colorado and several other rivers. Water is topographical, so you can apply the law of conquest to it giving possession to the superior force (there was no economic transaction with native Americans in the western U.S., nor did those natives take resources by economic consent from earlier migration waves).

    But apply this to air. If I breathe all the air and you don’t get any, just because I breathe faster than you, this is not an economic transaction. It is a seizure by conquest transaction. Similarly, if one group of countries elects to pollute all the air and another group of countries finds their air polluted, it is seizure, not economics. No one purchased the air. No one has the right to sell air which would otherwise have been used by unborn generations. Animals have the right to air also, but are not granted status in economic transactions nor compensated for their services (horses, dogs, etc.).

    In other words, first you have issues of governance, of preventing arbitrary seizure by force which is the natural order of things. Only then do you have the luxury of an economy and the ability to discuss things like “ethics,” but the discussion is entirely artificial, an artifact of the unnatural governance.

    So while the narrow argument may be made that comparative utility decisions are not the purview of economics, it is only because they have already been made by governance. I therefore argue that the term “social welfare” is not an economic term or policy but one of governance. I’m generally not in favor of welfare. I just felt the argument about ethics was clever … but spurious.

    • Humans can only survive at 13.9c by producing large amount ts of CO2. That puts cow on both sides of the utility function. In effect happiness becomes a function of temperature an co2 production. 13.9c without co2 yields death given our current technology.

      • 13.9 C is 57 F, at which temperature insignificant energy is used for heating and none for cooling. Computers, appliances and body heat will warm a normal home or office building. I know this because I monitor the utility bills at several residences I’m responsible for, in different climates. It is probably the optimum temperature for apartment dwellings with few outside walls.

  48. Although I disagreed on a particular, the comment by ferdberple enters a fascinating, and I believe inevitable, area. Not whether there is climate change, or whether humans are causing it, but a tacit admission that we will at some point cause it for simple economic utility maximization (call it happiness, whatever you will).

    The energy for star travel – and humans seem to have a deep compulsion in this regard, possibly explained by the unimaginably enormous “utility” of it – requires that our per-capita energy use grow at 20th century rates for more than 2000 years. At this level, mere chemistry like CO2 becomes insignificant compared to the raw entropy that must be carefully managed. With so much energy, the climate will be de facto selected by human choice.

  49. Even now, a committee is meeting to decide your future. You are not invited.