Welfare and time inconsistency

Hi all. Good to see people commenting on re-thinking interest rate policy here, I am going to give it another day for people to make comments (as I am waiting for some specific people) and then I’ll start writing things up on the weekend – so if there is anything you want to add, go there are add it!

Today I’m going to ask a couple of questions to Rauparaha (or anyone else that knows some stuff) about time inconsistency (using smoking as an example), an issue that Rauparaha covered here. Now I know close to nothing about this stuff – but hopefully a discussion on it will enlight me, and potential other readers 🙂

Ok, so this is the way I see the issue, tell me where I’m wrong 😉

Effectively the intra-personal smoking externality appears to exist as follows. Before smoking you don’t want to smoke in the smoking period, when smoking you want to smoke, after smoking you wish you hadn’t smoked in the smoking period – this stems from hyperbolic discounting.

Another way to view this is as follows, there are three you’s in different periods of time. The middle you wants to smoke, however the first and third you’s are suffering from this choice (the first you can’t make what he feels is an optimal decision, while the third you has to bear the whole cost). As each “you” values their own state fully, but values the state of other “you’s” less than fully, we have a negative externality that is not internalised.

In this sense we can increase welfare by taxing cigarettes in a way that include this externality costs, and then cutting income taxes. The increase in taxes ensures that if the second you values the smoke at less than the first and third you’s rate of dis-pleasure they will stop. If they value it more, then at least the first and third you’s get lower income taxes 😉

However, now it comes to the question. There is a difference between the purchase and the consumption of a good. If you just don’t buy the cigarretes then you have pre-commitment. If you do buy the cigarretes, you know you will end up in the time inconsistent game. As a result, since you choose whether to buy before consumption, isn’t the individuals choice still optimal – as he is effectively picking between these two games.

Secondly, I have a more general question. The first you makes their optimal choice based on hyperbolic discounting – which means that they heavily discount the value received by the second and third you’s. However, as these are all separate “you’s” the social planner would not want to discount at all. As a result, if we could “pre-commit” by forcing the second you to do something, why does that mean that true underlying welfare is higher (given that society values each “you” equally)?

In the case of smoking it is actually the case that the “third you” must suffer more than the “second you” to have this problem in the first place – but this is because the first you does not make a choice. In cases where the first you makes a choice, why is the time consistent choice going to be the best one, when the first you will heavily weight satisfaction in terms of their own benefit – not the benefit of future selves.

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  • Jon Elster’s book Ulysses Unbound is very good on these kinds of things. Pick it up if you haven’t read it.

    To your questions:

    1. I suppose folks could always argue that the first period self self-deceives about the ability of later-period selves to engage in restraint and only have a couple of smokes. Of course, at any period, the current self can hire in some self-restraint mechanisms. It’s not hard. If I were a smoker and I wanted to quit, I’d give $500 to a colleague down the hall and tell him that if he caught me smoking, he gets to keep the money. Ideally, somebody honest but somebody you don’t like enough to be happy to be giving him money.

    2. I suppose the argument would be that the gains to the smoking you are less than the losses to the “feeling the effects” yous. That’s question-begging though absent some kind of hedonometer. What evidence we have suggests that smokers overestimate the risks of smoking rather than underestimating them, so that ought to knock out stories that smokers are misled. Hyperbolic discounting still could hold, but why would it hold more on smoking than on anything else? Proves too much.

  • Hone

    I agree with the observation about ” separate “you’s”” (I am less convinced by the purchase vs consumption discussion – not sure I get it).

    We may think we observe time inconsistency but usually those observations come on the assumption that preferences remain the same through time. If preferences are fundamentally changing through time decisions may look as though they are time inconsistent but in fact we are dealing with, effectively, two different individuals with entirely different preferences, not time inconsistent preferences per se.
    Oh and we cannot possibly predict how those preferences will change which would make price-setting for an externality tax bluddy difficult.

    Smoking seems to me to be a commitment problem that doesn’t necessarily follow from hyberbolic discounting – although hyberbolic discounting does introduce time inconsistency.

    I heard an interesting pointy of view on a podcast recently (can’t remember who the speaker was). It went something like:
    If Jane starts smoking when she is 15 there must be some benefit to the smoking – maybe people think she is cool and she likes that. If Jane quits smoking in her early 20s, the probability of smoking related illness virtually dissappears. On those lines it is rational for the current Jane to start smoking.

    It turns out it is Jane’s later self that is unwise for not quitting as Jane had previously intended. It is unfortunate that Jane didn’t have a commitment mechanism to ensure that her later self quit or perfect foresight to know that her later self couldn’t quit. But that isn’t necessarily an externality, just an unintended and uncertain consequence of a decision – recognising that while Jane didn’t quit most of her friends did.

    If people’s decisions are time inconsistent (and I believe they are) that doesn’t say anything about a role for Government to intervene and encourage people to take time consistent decisions. If we accepted that there was such a role for Government, where would it end? Forced communal exercise while the Government chiefs checked up on you through a two-way tv?

    Frankly I don’t think my current or future self would be happier with lost freedom but rock hard buns. Maybe that is just me.