Burning down the house

Untitled
The purpose of this post

Readers living in South West London may have seen the opposite poster featuring prominently in a real estate agency’s (Acquire Estate Agents not to mention any names) shop front. It was probably designed with the best intent, but this is actually a very bad promotional mechanism.

Let us dissect the proposal. At first sight, the offer seems appealing. The poster indeed advertises a “flat fee of £700” which “includes VAT, EPC, floorplans and pictures” for home owners willing to sell their property. With the average London house costing as much as £531,000, a £700 fee is equivalent to 0.1% of the average transaction value, whereas other major real estate agencies typically charge around 3% of the priceIn that case, why should the prospective seller think twice before walking into the lion’s den?

The reasoning is detailed in-depth and supported by empirical evidence in Levitt’s and Dubner’s Freakonomics  – a book I have already had the chance to write about – and relates to the role of incentives. In a nutshell, with a flat fee, especially a low one, the real estate agent is not incentivised to maximise the transaction value on behalf of the seller but to complete the transaction as quickly as possible, even if it means making sacrifices on price. Quantity prevails over quality.

For the seller, the ‘great offer’ may thus backfire and leave him worse-off overall after the transaction. He will save an average of £15,230 in agency fees (3% * £531,000 – £700), but this saving can be easily more than offset by performing a marginally higher number of visits or by spending a little bit more time negotiating the buyers’ offers – especially given the fever surrounding the London housing market.

A good alternative mechanism could have consisted in offering lower fees as a percentage of the transaction value, which would have maintained the agent’s incentive – albeit at a lower scale.

Daniel-Kahneman-008
Daniel Kahneman

I have not been able to assess whether this marketing campaign ultimately proved successful for the agency or not. In any case, and to paraphrase Daniel Kahneman (2002 Nobel Memorial Prize in Economic Sciences) in Thinking: Fast and Slow, this is a perfect example of our ‘rational’ System 2 overriding the gut feels emitted by our ‘impulsive’ System 1.

P.S.: More on Kahneman and behavioural economics will be covered more in-depth in a later post.
P.S. 2: To finish with music…

Catch me if you can (afford to pay)

Catch_Me_If_You_Can_2002_movie
Theatrical release poster for the movie “Catch me if you can” (2002).

In an earlier post I discussed the benefits that shoplifting could have on inflation. In a nutshell, my thesis defended the (theoretical) use of ‘moderate’ shoplifting as a way to fight against inflation. Indeed, if the share of stolen goods grows, retailers have to anticipate this behaviour by increasing their prices in order to offset the losses incurred because of theft. I nonetheless ended up moderating my remark by underlining the fact that ‘too much theft could kill theft’. The topic of this post is actually to prove this latter assertion. To do so, I will rely on a powerful and widespread microeconomics tool called ‘game theory’.

According to Wikipedia, game theory is “the study of mathematical models of conflict and cooperation between intelligent rational decision-makers”. Although historians can find traces of rudimentary game theory dating back to the 18th century, this theory started to be properly formalised appeared in the 1920s, championed by brilliant economists such as von Neumann and later John Nash – made famous in the eyes of the general public through the movie A Beautiful Mind. Although the framework sometimes requires ample simplification to be quantitatively workable, it yields satisfactory results in our case.

Note: The following paragraphs may repel non-scientific readers. Those readers may prefer to jump directly to the conclusion, which is signalled by cropped-Untitled.png.

Let us represent today’s problem as a game between two players, namely the shoplifter community and the shop – we use one representative shop and we similarly consider that the shoplifting community can be considered as a relatively homogeneous group. We assume that both players are risk-neutral, i.e. all they care about is their utility at the end of the game, irrespective of the degree of uncertainty surrounding this outcome. The ‘sequential game’ is the following:

  • First, the shop decides whether to set-up a surveillance system (CCTV, security guards etc. at total cost C>0) or not (at no cost).
  • Having observed this choice, the shoplifter decides whether to try to steal or not. The shoplifter’s probability of success depends on the presence of a surveillance system. If there is none, this probability is pmax. If there is one, this probability falls to pmin, where pmin<pmax.
  • Finally, we distribute the rewards. If the shoplifter is successful, he enjoys the product of his theft, assumed to be equivalent to $ in dollars – the same amount is withdrawn from the shop’s utility. If he is caught, he has to face a penalty equivalent to a cost of F – although the penalty may be made of non-monetary items e.g. prison sentences.

We assume F, pmin, pmax and C to be known and constant throughout the problem. The question we try to answer is: to which extent does the outcome of this problem depend on $?

To solve sequential games, game theory uses the principle of ‘backward induction’. We start by deducting the optimal solution for the agent playing last, and we move backward to anticipate each player’s move given the subsequent decisions made by the other players. Here, the shoplifter plays last, so we will pay attention to him first.

The shoplifter will try to steal only if his expected utility is greater than the utility he gets by staying home, which we assume to be equal to 0. Mathematically speaking, this translates into:

  • 4if the shop is equipped or
  • 5if the shop is not.

We can rewrite the previous two equations as follows: 6and 7. In proper English, these equations illustrate the fact that the shoplifter will only try to steal if the reward is high enough compared with the potential punishment.

If we plot the shoplifter’s decision as a function of $, we come up with the following strategy:

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We now turn our attention to the shop, which can perform the same reasoning as the one we just did and is therefore able to predict the shoplifter’s behaviour depending on all the problem’s variables. We can distinguish three cases:

  • If the shoplifter does not try in all cases because the reward is not worth the effort, then it is optimal for the shop not to buy protection.

    "They're fake. Part of the new false sense of security system."
    Credit: www.cartoonstock.com.
  • If the shoplifter tries only if the shop is not equipped, it is optimal for the shop to protect itself if the expected savings of protecting the shop against theft are greater than the cost of the equipment itself. If the equipment is indeed prohibitively expensive, the shop may be financially better-off letting the theft unmonitored. Mathematically this can be written as: 8or 9. Note that the boundary does not depend on F, i.e. the shop makes his decision irrespective of the legal framework.
  • If the shoplifter tries in all cases, then there is a possibility that the shop pays for the equipment and gets stolen from. The related equation is therefore 10or 11.

Although we could continue to solve the game using abstract variables, the conclusion is more powerful if we now switch to a numerical illustration.

Let us set the fine F to £500, the cost of equipment C to £200, the probability of successful theft without any equipment to pmax=80% and the probability of successful theft with equipment to pmin=5%. We can now replace the formulaic boundaries driving the shoplifter’s behaviour in the axis above by their numerical values, respectively £125 and £9,500. The latter value can appear as very high, but is only due to the fact that the shoplifter has a very high chance of being detected and will therefore only try his luck if the reward significantly outgrows the (almost certain) penalty.

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For the shop, the reasoning is as follows:

  • “If the expected reward is less than £125, the theft will not even try so I do not spend any money on surveillance”.
  • “If the reward is between £125 and £9,500, then the theft will only try if I am unprotected. On my side, I am better-off on average by setting up a surveillance system only if the expected take is greater than .”
  • “If the reward is greater than £9,500, then the theft will always try. On my side, I am better-off on average by setting up a surveillance system only if the expected take is greater than . This condition is always verified given that we are only considering takes greater than £9,500 in this third case.

idea-light-bulb-clip-art-black-and-white-MTLEnkBTaNote: The non-scientific reader may resume from here. That makes the article quite shorter I must admit.

As a summary, if we put the decision of the theft and the decision of the shop together as functions of $, our conclusion is the following:

3

How can we interpret those results?

  • If the expected take is too small (smaller than £125 in our example), the fine is relatively too high for the shoplifter to take the risk. In this first case, the shop is actually protected by the legislation around shoplifting.
  • If the expected take is high enough, i.e. in our example between £125 and £250, then the law does not provide a strong enough deterrent while the equipment is relatively too costly for the shop given the expected loss it faces. Within this ‘window of opportunity’ the optimal choice for the shoplifter is actually to try his luck.
  • If the expected take is between £250 and £9,500 the shoplifter will not try: his probability of success is too low given the implementation of the surveillance system.
  • Finally, if the expected take is greater than £9,500, the shoplifter is willing to take all possible risks – but, realistically, how likely is the shoplifter to manage to steal £9,500 worth of goods with only a 5% chance of being detected?

Game theory here shows us that, provided that the shop can perfectly anticipate the value of $ and both players are rational and risk-neutral, there is indeed a gap where attempted shoplifting makes rational sense for everyone. Nonetheless, as already pointed out in my earlier post, economists have managed to translate rationality in their models, but morality has been so far largely left behind.

Million Dollar Baby

Note: This post had been in my ‘draft’ basket for a while, but Michael Skapinker’s remarkable column in yesterday’s Financial Times put it back at the top of my pile.

Housing has become a real issue for British inhabitants in general, and Londoners in particular. LSE Professor Paul Cheshire has made a new contribution in this debate through a widely echoed report which concludes that one of four London homes will cost more than £1m by 2020, with the Financial Times concluding in the same article that “‘not just having a mum and dad who bought a house, but a grandparent too’ would be needed to get on the [property] ladder in the future”. So far, the latest data seem to prove him right.

The fact that owner occupiers and renters are not in the same boat is not news. The latest English Housing Survey supports that assertion in many respects. The share of overcrowded dwellings is almost four times higher in rented places (5-6% compared with 1-2%) and the gap is increasing. Conversely, the share of owned dwellings which are under-occupied has been soaring over the last two decades and now concerns more than 50% of the properties – partly due to the fact that almost all houses larger than 110 sq. m. are owned – compared with 9% and 13% for socially and privately rented dwellings, respectively. The share of non-decent homes has been decreasing across all types of occupations, but more than one out of four privately rented dwellings is still affected by ‘decency’ issues, primarily damp. For all those reasons, owner occupiers understandably report a higher satisfaction level than all types of renters (both social & private).

Share of non-decent homes, by tenure. Source: English Housing Survey 2014-15.
Share of non-decent homes, by tenure.
Source: English Housing Survey 2014-15.

Although the benefit of home ownership in terms of life satisfaction is indisputable, and despite the low interest rates and the numerous government schemes aimed at favouring ‘prime ownership’, UK inhabitants remain negative about their chances to ever get on the property ladder. Only 60% of private renters expect to buy one day, although the age for first time buyers has been continuously rising. For the youngest (25 to 34 years old), the mirage of ownership is vanishing at fast pace.

Split of households with a HRP aged 25-34, by tenure. Source: English Housing Survey 2014-15.
Split of households with a HRP aged 25-34, by tenure.
Source: English Housing Survey 2014-15.

In his report, Prof. Cheshire adds to the pessimism. Analysing the historical evolution of house prices in the UK, Prof. Cheshire concludes that “the key variables we have found have influenced house prices are real incomes, changes in population and house construction and interest rates”, with the former being “by far the most influential”. That being said, the relationship is clearly not 1:1, since real incomes have gone up by a factor of more than 3 since the early 1950s and the price of houses in London has been multiplied by 10 in half the time according to the Halifax House Price Index.

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Quarterly evolution of house prices in London. Indexed at 100 for the average of 1983 prices. Source: Halifax House Price Index.

Government schemes or massive foreign capital inflows are not part of the list. In one hand, this is reassuring, as this means that house prices are directly linked to the income UK workers receive. On the other hand, this also means that an increase in inequalities between the richest and the poorest will leave more and more people on the side of the property ladder.

Source: http://thecrownblogspot.blogspot.co.uk/.
Source: http://thecrownblogspot.blogspot.co.uk/.

Prof. Cheshire’s quantitative forecast adds further colour. His econometric model, calibrated using historical data, forecasts an average house price increase of 23% by 2020 and 97% by 2030, with significant disparities between areas. London will be most heavily hit, with 25% of houses being priced at £1m or more by 2030 and the price of a house in the lowest quartile of all prices representing 17 times the income of a person earning the lowest quartile wage at that time, compared with 11.5 times today.

House Prices Observed and Predicted 1961 to 2030 – in logs. Source: Future Britain: Housing Millionaires and housing paupers.
House Prices Observed and Predicted 1961 to 2030 – in logs.
Source: Future Britain: Housing Millionaires and housing paupers.

Experts agree to say that the price surge we have been witnessing is also due to an imbalance between supply and demand. On that front, the Financial Times recently highlighted that new house building was still apathetic, leading the government’s ‘1m homes built by 2020’ target to be considered as increasingly unrealistic. The root causes of this supply shortage are subject to debate, but the UK regulatory and planning systems surrounding the building industry are often pointed out as major roadblocks – at least this is an area where the British and the French converge. There is however an urgent need for action: as rightly pointed out by Skapinker, at that pace, London will become unaffordable for the next wave of young talents it used to attract.