Why precision matters

iangunn May 17th, 2019

Here’s a startling real example from “Humble Pi” by mathematician Matt Parker. It concerns a BA aircraft in for routine maintenance: its windscreen was due for replacement. The screen is held in by bolts, part number A2117D. It turned out there were not enough of these in the workshop, so the fitter drove to another location to get some more. Unfortunately, the parts bins did not actually contain what was on the labels. As a result, he picked up some A2118C bolts. Although they looked the same, these were 0.026 inches wider and 0.1 inches shorter than the A2117Ds. As an additional safety check, each bolt has a specific wrench, which only fits exactly on the correct part. To add to the chain of unfortunate events, the fitter had forgotten his glasses, and so failed to detect the miniscule difference in size. When the aircraft reached cruising altitude, the screen blew out, almost taking the pilot with it. The one bit of good luck was that the steward had just walked into the cockpit and the crew were able to grab the pilot by the legs, saving him. Between them, they managed to safely land the aircraft.

Here’s another from the 5th Report of the House of Lords Economic Affairs Committee “Measuring Inflation”, published January 2019. The report is highly critical of the RPI as a measure of inflation. It has been well known for many years that the statistical method used to average prices in the RPI produces upward bias. Irving Fisher, an American economist of some note, pointed out the flaw in the method in 1922 and warned against its use. The fault was first identified even earlier, by William Stanley Jevons in 1863. He gave the example of an index measuring the price of just two commodities, cocoa and cloves. If the price of cocoa is doubled and the price of cloves is halved, there has been no overall alteration in the level of prices, but the (Carli) formula used in the RPI will show that prices have increased by 25%.

Index-linked gilts have historically been the measure of risk-free return used in setting the personal injury discount rate and are linked to the RPI. Owners of them know about the defect in the index, and the market priced-in an expected change in methodology by the ONS. However, on 10th January 2013, the ONS announced its decision not to change. On that day, the value of index-linked gilts rose by £25billion – what amounted to a one-off transfer to investors who held them at that time. This is one of the market distortions giving rise to negative real yields on index-linked stocks.

Under the new methodology prescribed by the Civil Liability Act, the Lord Chancellor will not be bound to use the RPI as the reference measure of inflation in setting the discount rate, although it remains the default measure of indexation for PPOs under the Damages Act. When thinking about where the new discount rate might be set, bear in mind that choosing the CPI as the reference measure of inflation in place of the RPI would, on its own, add around 0.8% to the discount rate.

Good job the ONS is not responsible for aircraft safety.