Thursday, 3 September 2015

Bayes' Rule and Political Inference

Consider a question such as: Would politician A be a good leader or not?  Now consider some information that might arrive that might inform our answer to that question in the form of the recommendation of an opinion former, maybe a newspaper makes a decision as to whether to endorse A or not.
Suppose an individual’s prior belief that A is a good leader is p, and their prior belief that the newspaper endorses a politician who is a good leader is q.  Once the news arrives, the newspaper will either endorse A or not.  If they do not endorse A, then the individual’s posterior probability that A is a good leader will be:
p'= p(1-q)/[p(1-q)+q(1-p)]
But the posterior belief about the accuracy of the newspaper’s endorsements will also have changed, and will indeed be the complement of the probability above:
q'= q(1-p)/[p(1-q)+q(1-p)]
Afterall, once the newspaper does not endorse A, either A is not a good leader or the newspaper does not make good endorsements. 
Suppose that the newspaper is a source that we would normally trust reasonably well, q=0.75.  It might, for example, be The Economist. But suppose that we are convinced on a level approaching religious fervour that politician A would be a good leader, and p=0.99.  Then as a result of the newspaper’s lack of endorsement for A, a bit of doubt will creep in, and  p'=0.97, but by far the biggest movement is in the probability that the newspaper endorses good candidates and doesn’t endorse bad ones as q'=0.03.
What if the newspaper endorses the politician?  Then the posterior probabilities in this case will be:
p''= pq/[pq+(1-p)(1-q)]
q''= pq/[pq+(1-p)(1-q)]
Similar results obtain if the individual detests the politician in question, and believes, with semi-religious fervour, that they are not a good leader.  Suppose that q=0.75, and p=0.01, and the newspaper endorses the politician.  Then the posterior probabilities will be p''= q''= 0.03.  So, once again, by far the biggest update  from the news of the recommendation is on the reliability of the recommender, rather than the subject of the recommendation.

The lesson?  When a group of people are absolutely convinced that a politician is the right/wrong person to lead, endorsements, or failures to endorse will be treated more as evidence of the accuracy of the person giving the endorsements rather than as evidence about the potential leader in question.  This offers some explanation as to why "marmite politicians" people who are either really liked or really hated, are able to maintain their core support in the face of such ferocious attacks as they frequently receive.  To their supporters, the attacks contain more information about the attackers than about their target.  To their detractors, any defence of them contains more information about the defenders than about the subject of  the defence.

Friday, 29 May 2015

Can Tax Avoidance Save Housing Associations From "Right to Buy"?

So the Conservatives are pressing ahead with their plans to extend the right to buy to tenants of Housing Associations.  There is almost unanimous agreement among everyone who knows anything about Housing policy or even just basic economics, that this is a monumentally bad idea.  The right to buy your council house was part of what led local councils to stop building council houses.

With the resultant drop off in the overall UK housing supply that has led to the dramatic increase in prices with all the consequences I have written about elsewhere.

Essentially, the Right to Buy is a tax on Housing Associations, raiding their assets and transferring them, at a hefty discount, to the most privileged social housing tenants.  Others have already written eloquently about how Housing Associations fund their home building activities by borrowing against their existing asset base (see Martin Wolf in the FT in particular).  If that asset base is now subject to state confiscation, it will not provide banks with sufficient surety against the loans they need to fund house building. 

State confiscation of this sort is essentially little different from a tax.  Let’s not dwell too long on the absurdity of a Conservative government, which purportedly believes in the “Big Society”, having found a way to tax charities, and simply ask a different question.  Who has been particularly good at avoiding tax, and is there anything that Housing Associations might be able to learn from them?

The essential point here is that the “Right to Buy” will never to extended to the tenants of private landlords.  So Housing Associations should find some way to make sure that their tenants are not actually, on paper, the tenants of the Housing Association, but the tenants of some private landlord.  The same tenants should still be paying the same rent to live in the same properties, but the assets themselves would not be liable to seizure.

One way to do this would be to transfer all the houses owned by the Housing Associations to some private company.  The Housing Association would then lease the properties from this company and sub-let them to their tenants.  All of these rental agreements would, of course be happening at sub-market rents.  Right to Buy would not then apply as the Housing Association cannot sell to the tenant what they do not own.  The downside of this solution would of course be that the Housing Association would not own the properties and so would not be able to borrow against them in order to build more homes - though this could be done by the entity into which ownership of the homes was transferred.  

Of course, elaborate legal arrangements would be needed between the Housing Association and the firm that owns the houses.  Ideally the Housing Association would own all of the shares in the house owning firm, but this might make things a bit legally tricky in claiming that the Housing Association does not own the house.  

One solution might be to turn the  Housing Association itself into a private company, which owns houses and rents them out, nominally for a profit, they just agree not to make a profit.  The loss of charitable status might lead to an increase in costs because of taxes they would now be liable for, but this would be a small price to pay for securing the assets.  This solution might present legal problems because of the nominal duty of a management board of a private company to make profits for their shareholders.  Some structure would have to be constructed where the firm was effectively owner-managed.

My purpose here is not to suggest the precise legal structure through which Housing Associations might protect their assets from “Right to Buy”, I’m an economist, not a lawyer dammit!  I merely wish to suggest that such an arrangement should be possible.  Afterall, since the “Right to Buy” is effectively an asset tax, it should be as liable to tax avoidance as any other tax.  Maybe that army of lawyers and accountants employed by large multinationals to avoid taxes could be directed towards some socially useful activity in helping Housing Associations to re-jig their legal structure to avoid the “Right to Buy”.