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.

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”.

To Control Letting Fees or Not To Control Letting Fees ... Really Isn't the Question

The coalition has frequently trumpeted their “help to buy” policy where the government guarantees the mortgage of someone buying a new home.  Some fairly basic economic analysis will show you that all it really does is to push up prices and benefit the people who already own homes.  See my analysis here.  Now Labour have proposed some housing market reforms, claiming that they will help Generation Rent, but some relatively simple analysis shows that once again, this will only help home owners, in this case landlords.

The policy in question involves banning letting agent fees.  First of all, let’s look at the scale of the problem.  When renewing a lease (and maybe changing one or two terms in it), or getting a new lease, estate agents will charge the tenants for things like changing the contract, or credit reference agency checks.  Labour’s research (reported here) suggests that these fees average £902 across the country and £1,700 in London.  This may sound like a lot, but compared to the average cost of renting, is it?

Let’s take a somewhat unscientific approach to gauge the scale of this problem by looking at the rental prices of some 3 bedroom properties.  In order to do this, I am using Rightmove’s ability to look at properties on a map and selecting a property at random on the outskirts of a city.  On the outskirts here means just inside the Ring Road.  I’m not going to claim I have found the average rental price in these cities, but this will give us an idea

• Oxford: This 3 bed semi costs £1,500 pcm, so fees would be 5% of annual rental cost. 
• Bristol: This 3 bed flat costs £1,395 pcm, so fees would be 5% of annual rental cost.
• Southampton: This 3 bed semi costs £925 pcm, so fees would be 8% of annual rental cost.
• Manchester: This 3 bed house costs £1,495 pcm, so fees would be 5% of annual rental cost.
• Birmingham: This 3 bed house costs £1,000 pcm, so fees would be 8% of annual rental cost.

Overall, based on a quick but unscientific survey, we are talking about fees representing between 5% and 8% of the rental cost outside of London.  In London, this 3 bed flat is available for £2,275 pcm, so the fees would represent 6% of the annual rental cost, this is within the range for the rest of the country.

This is small, but could be significant, but it is all rather beside the point anyway, because the policy will not save tenants anywhere any money whatsoever.  The reasoning, once again, is the fixed supply of housing which cannot increase at anything like the rate at which it needs to because of the UK’s planning regime.  Tenants have no reason to distinguish between money spent on housing in the form of estate agent fees or money spent on housing in the form of rent.  So if the estate agent fees go down, the money they are willing to spend on rent will just go up by exactly the same amount.  From the perspective of the landlords, the abolition of estate agent fees is just like an increase in the quantity of housing demanded at any given price.  But the planning regime means that the supply of housing barely responds to changes in the price of housing, so we can think of the supply curve as being virtually vertical.  

The  result is an increase in prices and tenants are no better off.  The real beneficiaries will be the landlords who will start to see higher rents.  So just like the coalition's "help to buy" policy, this policy, which as advertised as being on the side of Generation Rent, actually benefits those who already own homes, rather than the people it is supposed to be helping.  Still at least this policy transfers resources from estate agents to home owners, rather than help to buy, which transfers the resources from the people it is supposed to be helping.

Is This a Tax or a Subsidy I See Before Me?

So Edward Samuel Miliband, the leader of the Labour Party, has finally promised to abolish the spare room tax, or should that be the spare room subsidy?  I’m not entirely clear.  Every Labour party politician assiduously refers to this as the spare room tax and every member of the Conservative party assiduously refers to the spare room subsidy. Their various supporters in the press follow suit, so which is it?  In essence, this is about the use of language to bias a debate.

• If it is a tax being imposed on poor people, then that is more evidence that the people imposing it are heartless Tories.
• If it is a subsidy being withdrawn, then that is further evidence that people who oppose the policy just want to spend money and would explode the deficit if they got power.

This kind of labelling is an old (and quite transparent) trick, and one that I have already used twice in this post alone (although you may have to know what my own political bias is in order to spot one of them).

Technically speaking, I have more sympathy with the Conservative description of the policy as what is happening is that a subsidy is reduced if the family living in subsidised accommodation is judged to have more than sufficient living space.  I suspect some quick witted Conservatives will start saying “there he goes again making promises he can’t keep: You can’t abolish a tax that doesn’t exist.” 

Although withdrawal of a subsidy can have effects similar to the imposition of a tax.  Indeed, a subsidy is simply a negative tax rate, and so there is a point that if a subsidy is reduced, that is mathematically the same as increasing a tax. This often leads some people to cast a reduction in tax rates, or a refusal to tax a good they think should be taxed as subsidising the good in question.

The problem with using this logic to cast the failure to impose taxes you like as a subsidy and the failure to give out a subsidy you like as a tax is that it is highly vulnerable to reductio ad absurdum.  A friend and I were once discussing an article which referred to the withdrawal of a tax on mortgages (which happened about 20 years ago) as a subsidy for private home owners. At the time we were sitting in Oxford’s economics department which is one of those buildings where all the external walls are made of floor to ceiling windows, so I had to point out that the abolition of the Window tax in 1851 meant we were in the most subsidised building in Oxford.  Indeed, under that view, the Shard of Glass in London is receiving an eye wateringly large subsidy (adjusting the taxes that were charged for inflation).

To go one step further into the absurd, before breakfast, I could claim that books have been heavily subsidised by the government’s failure to tax them at £1,000 per book. After breakfast, I can claim that books have been heavily taxed by the government’s failure to subsidise each book by £1,000. The only thing that has actually changed while I was having breakfast is my reference price, not the policy.

So there must be some reference where we can refer to the good as either being taxed or subsidised.  One extremely convenient one would simply be to look at whether the government is paying out money (in which case we should probably refer to a subsidy) or whether the government is taking in money (in which case we should probably refer to a tax).  The key advantage of this way of labelling things is simplicity, to know whether a policy is a subsidy or a tax, you just need to look at what happens to the government’s budget. Under this convention, the Conservatives are correct and the housing benefit changes constitute a reduction in subsidy rather than an increase in tax.

However there is another way of looking at this which allows us to be more sympathetic to Labour. We could say that a policy is a tax if it raises the price above the market price that would prevail if there were no market imperfections, and that it is a subsidy if it lowers the price below the one that would prevail if there were no market imperfections. One attractive property of this way of labelling policies is that we can refer to the refusal to tax petrol in a manner that takes the price of the carbon externality into account as a subsidy.  In this labelling scheme, any policy that involves any kind of subsidy or tax is per se inefficient. Since the price of housing in the UK is kept artificially high by imperfections in the housing market, this would allow us to cast the benefit changes as a tax and say that Mr. Miliband is correct to talk about abolishing the bedroom tax.

If this labelling scheme appeals to you, then I just have one question for you and Mr. Miliband: So you are going to be taxing those who are ineligible for housing benefit how much?

I thought so. It is probably best if we just stick with the definitions of tax and subsidy that refer to the effect on government spending and income. 

None of this makes any comment on whether reducing housing benefit in this way is the correct policy, it is just about whether we should call it a tax or a cut in subsidy. Now might be a good time to start openly discussing the merits of this particular subsidy and whether it should be reduced or not; and if it should be reduced, is this the right way to go about it?

Pampered or Rational?

So a recent post about why Generation Y is so miserable caused a bit of a fuss recently, and a response can be found here. I’m not going to try and endorse or deny the stuff about entitlement. For one thing I am of Generation Y myself, so if I bite on that bait, I will only be providing evidence for the other comment about Generation Y that they don’t respond well to negative feedback. My main point is simply as follows: The trends identified in the “waitbutwhy” article are actually rational responses to a changing work environment. In particular pensions used to provide incentives which dramatically increased the financial value of careers which would give rewards only after many years’ hard work. I don’t want to get drawn into too much of the institutional detail here, if for no other reason than that those details differ on different sides of the Atlantic, so I’m afraid it is going to be pretty broadbrush at this point.. 

While institutional details differ, the general pattern is similar.  In the immediate post-war years, with greater faith in what the state could achieve, many Western countries set up “pay as you go” pension systems, where each generation would pay the pensions (and other retirement benefits) of the one that preceded it through the tax system. A bit of nominal ring-fencing goes on, but ring-fencing like that is normally just window dressing.

There is nothing wrong in principle with a pay as you go system.  Indeed, it can be an important way to ensure that the generations alive and approaching retirement when the pension system is set up do not miss out.  However when there is a baby boom (as there was in the immediate post war years), the system can be put under a great deal of strain.  When the baby boomers reach working age, there are a lot of them to spread the burden of supporting the older generations. When they retire, there will be a lot of them who need to be supported by the subsequent generations.

But there has been another trend, which means that each retired baby boomer will be an even larger burden for subsequent generations than the pensioners they supported in their working life.  The baby boomers will live much longer, their lives being preserved by expensive medical treatments (courtesy of the tax payer again), but retire at virtually the same age. In the UK, the age at which people most commonly die has increased by 10 years for men and by 5 years for women since 1980. This means that the typical man enjoys twice as many retirement years today as the average baby boomer did. There is nothing wrong with extra longevity, but it does mean that there are more pensioners whose pensions and other benefits need to be paid for by a relatively smaller population of workers.  That means a larger burden for each worker to bear.

Most of the solutions to this problem amount to moving the stable door from wide open to ajar once the entire team of horses have got out into the wild and are well on the way to producing more horses. Broadly speaking, the plan among those countries that are planning to do anything is to slightly raise the retirement age long after the baby boomers have retired. As with any “solution” to a problem which fails to go far enough, this simply means that more drastic actions will be required later, probably just as Generation Y is nearing retirement age. That age will probably be substantially raised, and the retirement benefits they will enjoy have already been drastically reduced compared to those that will be enjoyed by the baby boomer generation.

However this offers some insight into one of the differences highlighted between generation Y and their parents. Their parents expected to work until they were 65 and then enjoy a good 20 years of retirement. In those circumstances it is rational to look for a career purely on financial criteria. Generation Y’s parents will also, for the most part, benefit from pension schemes based on their final salaries.  This dramatically increases the financial benefits of a career which sees very large salaries right at the end, because that has a huge effect on pension income.

Generation Y is probably expecting to live to about 90 and retire at 86 (yes I am exaggerating, but the point is they will work longer and enjoy fewer years of retirement). The closure of most final salary pension schemes also means that sudden salary rises at the end of their careers will not have such a dramatic effect on their lifetime incomes as it did for their parents.

All this adds up to two things:

• Rationally the early financial rewards to their careers are more important to Generation Y than they were to their parents; and

• Rationally their careers will be a much bigger part of their lives and so Generation Y should be looking for a career where they can follow their passion rather than one that merely provides a living.

So maybe the feelings of frustrated expectations and the desire for earlier rewards from their career, and a career that provides a lot more job satisfaction are more than simply the selfish demands of a pampered generation. They might simply be rational responses to the environment they face.