Helping me to help me
Matt and I recently discussed whether we thought the government should intervene to correct intra-personal externalities that arise from time inconsistency in peoples’ behaviour. We particularly talked about smoking: models of smoking which incorporate hyperbolic discounting predict that people will want to quit in the future but will never be able to quit when the time comes (and here I’ve horribly conflated two different causes of dynamic inconsistency in the interests of simplicity). I wasn’t able to persuade him that it is in the public interest to correct such externalities, but perhaps this paper(NBER) cited on MR provides a harsher example of the consequences of time inconsistency (and, yes, I know I’m horribly mangling together two different causes of dynamic inconsistency).
The authors find that
…women who are the victims of domestic violence often leave and return multiple times. … We present supporting evidence that women in violent relationships display time inconsistent preferences… We find that “no-drop” policies — which compel the prosecutor to continue with prosecution even if the victim expresses a desire to drop the charges — result in an increase in reporting. No-drop policies also result in a decrease in the number of men murdered by intimates suggesting that some women in violent relationships move away from an extreme type of commitment device when a less costly one is offered.
The problem here is that there is no device available to the women that allows them to commit to leaving the relationship and force their ‘future self’ not to return. A no-drop policy on the part of prosecutors gives them that precommitment power and prevents them from reneging on their desire to leave the abusive relationship. By restricting the womens’ future choice set the state can make them better off. I feel bad talking about domestic violence in such dry terminology, but I think this is a really good example of how economic theory can help understand important ‘real world’ problems. Policies such as taxation of smoking and no-drop prosecution of domestic violence are not examples of government interference in peoples’ lives: they are examples of the government helping people to help themselves.
With the cigarette thing (I’ll talk about the actual issue another time 🙂 ) there are still a couple of issues for me about the trade-off between the current and future selves
1) How are we measuring total welfare here. If a person uses hyperbolic discounting, and their total welfare is also worked out using the same discount method, then shouldn’t their own choice be equivalent to the welfare maximising choice. Ultimately, if we viewed someones future-self as equivalent to their current-self (in welfare ranking) then any choice that involved a trade-off between now and the future, and a discount rate, would be sub-optimal.
2) Is it true that when their current-selves makes a choice, they recognise that their future self will be unable to commit and make their decision in a corresponding fashion. This is required for sub-game perfection isn’t it.
Ultimately, your future-self should be valued in your utility function, so any externalities between your current-self and future-self should be internalised. The only problems should come from market-failure (eg asymmetric information), or if your discount method/rate and the social discount method/rate between yourself and your future-self are different.
This is just how I currently see these problems. Would you be able to tell me how I am wrong so I can be enlightened 🙂
I don’t think you’re wrong: I just didn’t really explain anything about time inconsistency in the post 🙂
1) Papers usually tend to take the person’s current preferred choice as the optimal one. They calculate the choices that the agent would make if they had full precommitment power and take that as the welfare maximising trajectory. Obviously future selves would disagree but that’s the cause of the welfare loss so their disagreement is essentially disregarded. From the point of view of the current period the precommitment outcome can be regarded as first best.
2) There are two ways of modelling inconsistent agents: as self-aware agents who recognise that they’re inconsistent or as naive agents who don’t. Naive agents will exhibit inconsistency in their decisions, while self-aware agents will take into account the consequences of future incentives to deviate when they choose their current action. As you say, the sophisticated agents will be sub-game perfect in their decision making. However, compensating for future incentives to deviate acts as a constraint upon their utility maximisation and means they can only achieve a second best outcome. Depending upon the payoffs it can sometimes be the case that the naive agent is better off than the sophisticated one! In either case, availing the agents of precommitment power can improve their overall welfare.
3) Inconsistency usually arises as a result of either inter-temporal, intra-personal externalities or as a result of a non-exponential discount rate. In the first case, a sophisticated agent will compensate for the externalities in order to be time consistent but, thus constrained, will not be able to achieve first best outcomes. This type of inconsistency is usually caused by the current payoff depending upon an expected future action. In the latter case the cause of inconsistency is obvious, as you say.
Does that make any sense or did I fail to really explain it all over again?
Ahhhh I see. The welfare comparison is between the case when the person maximises their utility subject to the choice of their future-selves, and the case when the person can choice both their current and future choice right now. Thanks 🙂
If I mangled together two different causes of dynamic inconsistency as often as you did, I would be embarassed to show my face at the pub.
PS. I thought dynamic inconsistency was brought on by drinking too much beer.
PPS. My mistake, I was thinking of dynamic incontinency.
That’s how I understand it, Matt. Although, as Kimble points out, sloppy analysis like that is probably the reason that you get paid to do economics and I pay to do it 😉
Hey hey, I get paid to do the ‘astrology’ of economics, you do the beautiful astronomy part.
Thats what you get when you have Tarot card reading on your CV 😉