Friday, 16 August 2013

Signalling games and giving to charity

In recent work with Amrish Patel we model giving to charity using a signalling game. With this approach a person is assumed to give to charity in order to signal some desirable trait about herself such as generosity or wealth. To many this approach seems quite a cynical one. It seemingly paints a picture of very strategic giving. Do people not give to charity because they want to make the world a better place?
      What I want to try and convince you of here is that a signalling game approach actually paints a nice picture of giving - strategic, but not overly cynical.
      Here is how a simple signalling game works: There are two types of people - generous and not-generous. The generous want to make the world a better place. The not-generous do not care. Society likes generous people. It likes them enough that it is willing to reward them in same way. This could be through esteem, status, or a greater willingness to help them when they need help, etc.
      Notice the 'nice' story being told here. There are generous people who want to give to make the world a better place. And society likes such people and wants to reward them.
      Now for the strategic bit. The not-generous do not deserve any esteem or status. The trouble is society cannot know a-priori who is a generous type and who is a not-generous type. There is, therefore, an incentive for the not-generous to appear generous and get some undeserved esteem. This is where signalling comes in. The generous type somehow needs to signal her generosity. How can she do that? She can give such a large amount to charity that no not-generous type would ever match her. This results in a separating equilibrium. Society can tell who the generous and not-generous types are. The only cynical part of this story is that some not-generous people exist. But, that's clearly true!
      A separating equilibrium is not the only possible outcome. Another possibility is a pooling equilibrium where the generous and not-generous are indistinguishable. In the work I did with Amrish Patel we argue that charities might want to set things up so as to get this outcome. The basic logic goes something like this: With a separating equilibrium the generous type gives more than she would like to signal her generosity and the not-generous types give nothing. In a pooling equilibrium the generous type gives what she wants and the not-generous types gives something. By forcing a pooling equilibrium the charity, therefore, loses out on the generous type but gains on the not-generous type. Overall, the gain will likely offset the loss. I also think there is something nice about the not-generous type being incentivized to give something! 

Friday, 2 August 2013

Jane Austen's ring and valuing the future

A ring that once belonged to Jane Austen came up for auction recently and was bought by US singer Kelly Clarkson for £150,000. The UK government has, however, subsequently put a ban on the singer taking the ring out of the country. The Culture Minister said 'I hope that a UK buyer comes forward so this simple but elegant ring can be saved for the nation.'
      This is clearly the kind of policy that will split opinion. Some are going to think its important to save our heritage, and some will think it stupid to stop the sale of a ring worn by an author who died nearly 200 years ago. What does amuse me, however, is that just about every spokesperson I have heard criticising the policy appeals to economic theory to back up their case. Listening to them talk you could easily get the impression that hard-headed economic logic leads to only one conclusion - sell the ring. This is wrong!
      The basic argument I heard more than once goes something like this. Kelly Clarkson paid £150,000 for the ring. If the UK populous really value the ring at more than £150,000 then they would do something to buy the ring, e.g. every member of the Jane Austen fan club could contribute £50 each. The fact that this has not happened shows the populous of the UK does not value the ring at £150,000. So it should be sold. This logic is flawed on at least three counts.
       First, keeping the ring in the UK is, in large part, a public good. Which means that individuals will try to free-ride on paying for it. Or equivalently individuals will wait and hope that someone else pays the money. The collective willingness to pay could easily exceed £150,000 and yet the money not be forthcoming because  everyone is waiting for everyone else. Indeed, measuring the willingness to pay for a public good is incredibly difficult - something called the preference revelation problem. Because of this, government intervention is justified in providing public goods.
       Second, there are large transaction costs in organizing lots of people to contribute towards the ring. That means raising the £150,000 needed to buy the ring is going to cost a lot more than £150,000. This will exasperate the public good problems. Again, government intervention is justified when transaction costs are high.
        Both the reasons above justify intervention on behalf of the current population of the UK. The ring, however, is to be saved for the nation. That presumably means future generations should count too. But we have a problem: future generations are not born yet and so cannot contribute towards keeping the ring! When valuing the ring we should estimate the value that future generations will put on it. This amount should be discounted a little, because, for instance, an asteroid might kill us all in 50 years time. But, the discount rate should be relatively small, because it is unlikely an asteroid will kill us all in 50 years time. Yet again, government intervention is justified to protect the interests of future generations.
       I'm not saying that the UK should keep the ring. But, I am saying that economic theory can go either way on this one. Hard-headed economic theory does not inevitably mean selling the ring. This is an important point to understand because the principle is very general. Many things are analogous to Jane Austen's ring. The natural environment probably being top of the list. For the same reasons economic theory may back saving Jane Austen's ring it also backs saving the environment (despite what many would have you believe).