Monday, 12 November 2012

Discounting Ethics in Macroeconomics

For macroeconomists (and perhaps philosophers)

In the Ramsey model (aka the representative agent model, the infinite life model, or what Romer calls the Ramsey-Cass-Koopmans model), agents care about their children’s utility as if it was their own. However, because they are impatient, they discount their children’s utility as they do their own. They therefore act as if they live forever. When teaching this [1] we say that the decentralized equilibrium is identical to the allocation that would be chosen by a benevolent social planner, who maximizes the utility of the representative agent.

When we teach the OLG model, we normally describe this model as involving agents who do not care about their children.[2] We note that the decentralized equilibrium would only be equal to the optimal allocation by chance. This is often done by showing that it differs from the golden rule allocation (the allocation that maximises steady state consumption), but some texts (e.g. Blanchard and Fischer) note that it would also differ from an allocation where the social planner showed some impatience over the utility of the unborn. In either case it is assumed that a benevolent social planner would put some value on the utility of the unborn.

It strikes me that the treatment of the two models is inconsistent. The claim about the Ramsey allocation involves an ethical assumption, which is that we allow the current generation to value the utility of the unborn. The benevolent social planner takes that valuation. Putting it another way, the benevolent social planner only maximizes the utility of the current generation, and makes no independent judgment about the utility of the unborn. Textbooks do not usually put it that way, but it seems to me this has to be what is being assumed.[3]

If we applied the same ethical judgment in the OLG model, where agents were entirely selfish, then the benevolent social planner should aim for an allocation which attempted to exploit the unborn as much as possible for the benefit of current generations. They should not be using a social welfare function which gives any weight to the utility of the unborn, and certainly not be thinking about the golden rule allocation. Instead, they should reflect the preferences of the living generations.

No one as far as I know tries to do this, presumably because it appears morally abhorrent. We want to overrule the selfish preferences of OLG agents. However, why is this acceptable in an OLG context, but not acceptable for agents in the Ramsey model?  If Ramsey agents had impatience (a rate of time preference) of 5% pa, then they are giving the utility of their children a weight of between 0.35 and 0.2 compared to their utility today. That is not so different from a weight of zero.

This point is clearer still if we look at the Blanchard/Yaari Model of Perpetual Youth, where agents do not care about their children but face a constant probability of death. A social planner that maximized the utility of the current living generations would discount at the same rate individuals do: impatience plus the probability of death. However I have not seen any papers that do this. Calvo and Obstfeld take a utilitarian perspective, and explicitly note that there is no necessary connection between the rate (if any) that the social planner uses to discount generations and the personal rate of time preference (with or without the probability of death). Once again, why is this distinction made in the context of this particular OLG model, but not when we look at the Ramsey set up where agents do care about their children?

It seems to me that if macroeconomists want to be consistent[4] they need to do one of two things. If they want to continue to insist that a benevolent social planner should use the personal rate of time preference of the current generation to discount future generations, then they should also make the social planner ignore the utility of the unborn in OLG models where agents are assumed not to care about future generations. They should also be transparent about the ethical assumptions they are making in the Ramsey case. (The potential double meaning in my title was deliberate). Alternatively, if they do not want to adopt this ethical position, they need to allow the rate at which the social planner discounts future generations (if any) to differ from individuals impatience in the Ramsey set-up as well as OLG models.[5] I have my own view on which is the better choice, but the point of this post is to suggest that at the moment macroeconomists are collectively just being inconsistent.

[1] This post reflects the masters teaching I have just completed. I used to follow Romer in teaching the Ramsey model first, and then the OLG model. This year I have experimented with the reverse order (in the spirit of Obstfeld and Rogoff), which has helped highlight the issue I discuss here.
[2]This is crucial. If we described OLG as involving agents who would like to give Barro bequests but for some reason could not do, then my inconsistency argument does not apply.
[3] Future generations would only be happy with this if they gave the utility of their parents a much higher weight than their own. Somehow I do not think this is very realistic.
[4] The only grounds to be inconsistent would be that agents who give a weight to their children of zero should be treated differently than those that give it a non-zero weight. I cannot see what philosophical argument could be used to justify this, but I am not a philosopher.
[5] This is what the Stern Review on climate change does. 


  1. Hmmm. Interesting. Not sure what my response would be. But doesn't the exact same problem come up in a model with no time and only one generation? I'm thinking of e.g. the Optimal Tax Literature, where the economist adopts a generalised utilitarian SWF, but models agents as self-seeking.

    Maybe it's the difference between true selfishness and "non-tuuism"? Der AdamSmithProblem and all that. People aren't selfish, but want to go about their daily lives without having to figure out all the many ways their actions might affect others?

  2. Manufacturers of products that result in persistent organic pollutants (POPs)do exploit the unborn. Mothers dump these POPs into their offspring before birth. I would think that mountain top removal mining companies also discount the environmental needs of the unborn.

  3. If you takes care about your child exactly like you takes care of you (same discount rate for you and your child) and if the discount rate (and the utility function) of your child is the same as your's, as far as economic decisions are concern (of course you may different views on ethic), you and your child are the same agent. A redistributive policy implemented by the social planner will not change the Euler Equation on the economy (i.e. the Ricardian equivalence).

    However, if you discounts your child say 1% more than yourself (a very small difference !), there are now two agents in the economy and redistributive policy will have a (small in the 1% case) effect on the aggregate Euler equation.

    This make a big qualitative difference between the two models: redistributive (instead of ethic, sorry, I am continental :) issues are absent in the first but appear in the second.

    Thus, I see no inconsistency; but I usually not refers to the "family story" in the Ramsey-Cass-Koopmans model: useless, and confusing.

    I wonder how relevant is the distinction between redistributive issues “within cohorts” and “between cohorts”. You have heterogeneous agents in both cases. In fact you can conceptually distinguish between unborn from an economic point of view (no access to any market) and unborn form a political point of view (no weight in the social planner objective). If you link the two concepts, the social planner should not weights future generation at all (as you say it appears morally abhorrent; but we do the same for people living in the poorest countries); if you preserve the distinction, you have to choose a weight for future generation, but the weighing problem is the same as for different agents living today. Let say one man, on weight.

    1. As Benjamin says: The real inconsistency is in pretending that we (or the social planer) care about future generation when we clearly do not care that much about people living right now (and a lot of people do not even have kids).

    2. "If you link the two concepts, the social planner should not weights future generation at all (as you say it appears morally abhorrent; but we do the same for people living in the poorest countries); "

      This point has been made before in defense of using the market discount rate, which is basically the same as not giving future generations any weight at all.

      A defense in positive terms might go something like this: people are known to have radically different values for within in-group members and others. We consider poor countries today to be outsiders, but identify with the human race a century from now. This reconciles the contradiction, and in fact is probably how most people who want to take strong action on climate change do think about the issue.

      The moral defensibility of thinking along these lines is an entirely separate question. In philosophy we typically require internal consistency, whereas I suspect that moral intuitions are not internally consistent except on the terms above.

      My own view is that we should take whatever action is needed now to avert global warming, and worry about its implications for current policy toward poor countries later. An excess of consistency...

  4. Didn't Stern and Nordhaus fight this out?

    1. They took different ethical positions, but I'm not sure macroeconomics really took this on board, otherwise we would not have the inconsistency I referred to.

    2. Environmental economists discuss the discount rate(s) all the time – but everyone either use different discount rates or use the same discount rate for different reasons. At least this far, I have never been in a discussion about the discount rate where two people shared a position (and the differences are far from marginal).

      I think very few environmental economist believe that the market interest rate create the socially optimal outcome in dynamic problems such as the extraction rate of non renewable resources or use the market rate to discount future benefits in CBA´s (the market rate is, after all, a point while the range of discount rates with reasonable justifications is very broad).

      It is, however, a hard discussion to have since there certainly isn´t any agreement on what “preferences” are (e.g. “tastes” or “beliefs”) – and thus (or in addition to) not even on what “utility maximization” is (and by then we haven’t even arrived at the social welfare function yet – or on e.g. what “tastes” people have).

      PS: I have never seen anyone explicitly argue that the discount rate of the Ramsey-Cass-Koopmans model would be normatively justified (because of the “impatience” parameter), except by reference to the real return in investments (if another argument exist – I would like to see it) - but why would we choose to stay in some second best equilibrium instead of correcting it?

  5. I simply wanted to take time to make a comment and say I have enjoyed reading this post. Now I have an idea what Ramsey-Cass-Koopmans model is all about.

  6. Surely, a key point here is that “representative agent” is a metaphor. It is not real. It cannot be observed in the real world. The concept exists only in your mind and in the minds of others who share your belief in representative agents. You are free to describe your metaphor in any way you see fit. It is inevitable that different people will describe any unobservable metaphor in inconsistent ways.

    This can be seen by considering descriptive questions about other metaphors. Is the “invisible hand” a right hand or a left hand? Is the “money multiplier” a person or a machine? Does “God” have a beard? Alternatively, consider different questions about the representative agent. If an agent has a view on the well-being of future generations then do they also have a view on other issues which might impact on economic decisions e.g. poverty in Africa, global warming? If so, what are these views? If not, why not?

    Attitudes to each of these questions will vary depending on belief in the specific metaphor. If you believe in the metaphor then you may take the question seriously. If you don’t, you will probably think that the question is silly. Your personal answer to each of these questions will vary depending on an arbitrary picture in your mind’s eye. As a metaphor is unobservable, no-one will ever be able to prove that your picture is wrong.

    More interesting is to ask why people believe in unobservable metaphors; why they convince themselves that they are real, even when they don’t fit the facts; and why they convince themselves that there is no alternative to this belief.