16 June 2012

Bank jobs

'Robbing Banks: Crime Does Pay - But Not Very Much' by Barry Reilly, Neil Rickman and Robert Witt in 9(3) Significance (2012) 17-21 argues that bank robbers would be better off in another occupation, with a UK 'career' bank robber being likely to be in prison after only four attempts and the average per-person return amounting to US$19,750.

The authors are Chicago-School economists who claim that
we have been given rare, perhaps unique, access to a normally confidential data set [from the British Bankers' Association]. This has let us construct, for perhaps the first time, a model of the economics of robbing banks. ...
our research was concerned with the various factors that determine the proceeds from bank robberies; hence, we could work out (among other things) the economics (to the criminal) of attempting one, and the economics (to the banks) of trying to thwart it. How much should banks spend on such security precautions as fast-rising screens in order to deter robbery attempts and to foil those attempts that do take place?
we cannot share all the raw data with you; we can, however, share our analysis and conclusions. They give a remarkable picture of the profitability of bank robberies – a picture that is rather different from the popular imagination or from the depictions in big-budget movies.
They comment that -
Figures for the UK show that there were 106 bank robberies or attempted robberies in 2007; there are approximately 10,500 high-street bank branches. This gives us one important factor in analysing the economics, to banks, of security measures: relatively few of their branches – one in a hundred – are likely to suffer a raid or an attempted raid.
In the same year there were 80000 robberies recorded by the police, of which 7500 were committed against businesses; so clearly even among the criminal fraternity robbing banks is a minority occupation. ...
what kind of banks are most targeted? Does the size of the branch, or its location, or how busy it is make a difference? We used distance from the nearest police station as a proxy for location. A small distance would imply a city; a larger distance, a smaller country town. The number of staff present during the raid was our indicator for the size of the branch, and the number of customers in the bank was our guide to how busy it was.
We found that none of these factors had any significant effect on whether the branch was targeted. There seems no favourite type of branch to rob. Of all the branches that were subject to robbery attempts in 2007, only 13 were targeted twice, and only one three times. The choice would seem random. Nor does the size of the haul depend on the type of branch. If larger floats of cash are held in bigger branches, or if smaller branches have less security, this does not seem to enter the calculations of the robbers in selecting their targets. 
What is the return? The authors comment that -
the average haul from a bank raid in the UK between 2005 and 2008 is £20,330.50. The standard deviation is £53,510.20. The sample size of 364 raids includes those that were foiled; as the table shows, one-third of raids were unsuccessful, meaning that the robbers got way with no money at all. The average haul per successful robbery is therefore around £30,000. But again, some “successful” raids – around 20% in both the UK and the USA – are detected and the perpetrators caught and sentenced, and in some cases the money is recovered; this reduces the expected gain to the robbers.
The average US bank robbery nets considerably less: some $4,330, compared to an average of $1589 for all commercial robberies. (There is a sector low of $769 for robberies from convenience stores.)
They argue that -
A bank robbery can be thought of as a production process. It has “inputs”, which the potential robber has to supply; and “outputs” – the money, if any, that he gets away with. The nature and size of the inputs affect the output. As with any commercial enterprise, the inputs include both labour and capital, as well as factors that affect productivity – the efficiency of your factory or the ease or difficulty of your raid. 
For the potential robber, the main “inputs” are the number involved in his gang (which we can think of as the labour input), whether firearms were displayed in the course of the crime (which is part of the capital input), and a raft or vector of what you could call difficulty or deterrent factors that may influence the effectiveness of the inputs: bank security measures (such as the presence of a fast-rising screen), whether the alarm was activated during the robbery, the number of staff and customers present during the robbery, and so on. The “output” is a function of all of these and is the value of the money that is stolen. In an unsuccessful raid of course this is zero. The output might also include capture and a lengthy term in jail. Our equations let us model the effect of varying one or more of the inputs on the expected output. 
As we have seen, the “average” proceeds from the “average” robbery is £20331, but about one-third of robberies yield nothing at all. The average number of raiders is 1.6 ..., though a sole raider was involved in 60% of cases. The average number of customers present was 2 and an alarm was activated in 85% of cases. A firearm was displayed in over one-third of robberies, and just over 10% of banks raided had a fast-rising security screen system in place. 
As we have also seen, neither the numbers of customers nor of staff in the bank at the time of the robbery affects the output. How- ever, the number of raiders involved most definitely does. It yields a positive well-determined coefficient. The bigger the gang, the greater the take. We were able to use maximum likelihood estimates to quantify it. Every extra member of the gang raises the expected value of the robbery proceeds by £9,033.20, on average and other things being equal. 
This may well reflect the effect of criminal organisation. More experienced robbers operate in teams. It is advantageous to divide tasks – monitoring the bank lobby, accompanying staff to vaults to ensure maximum takings, driving the getaway car and so on. A larger gang may have spent more time on planning and reconnoitring – in short, it may be more professional, and the larger returns may reflect that. Even so, if the gang splits the proceeds equally, although the total haul goes up the haul per person goes down.
From there it's a short jump to algebra city ... v[qR – (1–q)P] + (1–v)[q×0 – (1–q) P]* ... and conclusions such as -
A robber will attempt a raid if and only if the expected benefit outweighs the expected costs – both costs and benefits being as perceived by the robber. This assumes, of course, that potential robbers behave rationally and self-interestedly. That people behave thus is a central assumption in all economics and is no more true, and no more false, for bank robbers than for anyone else.
The expected benefits are, of course, the haul multiplied by the probability of getting it and keeping it; the probability of getting it is the probability that the raid is successful, that of keeping it is the probability of not subsequently getting caught. The expected costs are the lengthy term in jail – converted into monetary terms at the robber’s own conversion rate – times the probability of serving that term – that is, of being caught and convicted. The balance between these costs and probabilities can be expressed as an equation, as in the box at top left. 
Expressing the main deterrent – the potential prison sentence – in terms of money is of course problematic. It does not include the psychological effects of prison but treats in- carceration in purely financial terms as merely a period of non-earning. The fear of jail may well outweigh calculations of lost earnings as a deterrent. On the other hand, in certain subcultures serving time in jail is a “badge of honour” or rite of passage, a perverse incentive if you like. Similar considerations apply to the expected gain: the kudos from planning and executing a raid may be a greater incentive than the financial reward. Attempts to quantify this we leave to others. 
It is here that we can answer our original question of why, statistically speaking, robbing banks is a bad idea. The return on an average bank robbery is, frankly, rubbish. It is not unimaginable wealth. It is a very modest £12,706.60 per person per raid. Indeed, it is so low that it is not worth the banks’ while to spend as little as £4,500 per cashier position at every branch on rising screens to deter them. 
A single bank raid, even a successful one, is not going to keep our would-be robber in a life of luxury. It is not going to keep him long in a life of any kind. Given that the average UK wage for those in full-time employment is around £26,000, it will give him a modest life-style for no more than 6 months. If he decides to make a career of it, and robs two banks a year to make a sub-average income, his chances of eventually getting caught will increase: at 0.8 probability per raid, after three raids or a year and a half his odds of remaining at large are 0.8 × 0.8 × 0.8 = 0.512; after four raids he is more likely than not to be inside. As a profit-able occupation, bank robbery leaves a lot to be desired.
* R is the proceeds from the robbery, v is the probability of a successful raid (i.e., leaving with R > 0), q is the probability of not subsequently being arrested (i.e. retaining the proceeds), and P is the penalty perceived by the robbers when planning the raid should they be apprehended and punished.