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.
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