Welfare and time inconsistency
Posted July 4, 2008on:
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.