in retirement ages over a longer time. so, structural changes can happen. it is not the job of monetary policy to prevent such changes, but rather to ensure that they do not have negative consequences for monetary stability, such as dislodging inflation expectations. on this point, it is worth remembering that an important reason why we have a positive rather than zero inflation target is to enable such changes in relative earnings to happen in a world of downward nominal wage rigidities. i started by quoting friedman and schwartz, and so i will end by doing the same. they emphasised the need to distinguish a change in price ( or wage ) levels from a persistent increase in the rate of change [ 3 ]. in my view, drawing this distinction is a crucial issue that we will be dealing with for some time. and of course, since it involves predictions of the future, for policymakers the task will not be easy. in conclusion, the yards will be hard i ’ m afraid, and we must stick to the task. the hard yards ‐ speech by andrew bailey | bank of england i am grateful to nishat anjum, jamie bell, justin beresford, ben broadbent, alan castle, pavandeep dhami, jonathan haskel, andrew hauser, karen jude, catherine mann, dave ramsden, fergal shortall, sophie stone and silvana tenreyro for their assistance in helping me prepare these remarks. 1. milton friedman and anna jacobson schwartz, “ a monetary history of the united states, 1867 - 1960 ”, princeton university press, 1971, p. 493 2. the furlough scheme, meanwhile, has pulled down measured average wages. the scheme has helped workers stay attached to their jobs but generally at lower pay than usual. but the compositional effect has more than offset this. 3. milton friedman and anna jacobson schwartz, “ a monetary history of the united states, 1867 - 1960 ”, princeton university press, 1971, p. 498 andrew bailey governor, bank of england sign up for latest updates the hard yards ‐ speech by andrew bailey | bank of england

really works. to subscribe to our investment service please send £5000 by return ”. quite what our president, as the former deputy chairman of the financial services authority, would make of this scheme i do not know. but it illustrates vividly that the interpretation of ex post outcomes depends critically on understanding the ex ante process which generated those outturns. another example shows that it is not just lay people who find statistical inference difficult. experts of all kinds do too. the advent of dna profiling in the 1980s led to the use of match probabilities in criminal cases. the jury is told that the probability of finding a match between the sample taken from the scene of the crime and the dna of the defendant is, for example, only 1 in 500, 000. that is sometimes taken as evidence that the probability of the defendant being innocent is also only 1 in 500, 000. such an inference is incorrect. in a city such as london where there might be about 5 million people who could have committed the crime, around ten people would have dna that matched the relevant sample. hence, in the absence of any other evidence, the probability that the defendant is guilty, far from being overwhelming, is only one in 10. of course, in practice other evidence is usually available. but this incorrect statistical reasoning has swayed enough cases to be given its own name - the prosecutor ’ s fallacy. 11 the cases of sally clark and angela cannings, both convicted and imprisoned for the alleged murder of their own children, show the desperate consequences of the false use of statistics to create a presumption of guilt to resolve the cause of apparently inexplicable events. both women were convicted by juries which had in all likelihood been influenced by the assertion that the probability of two cot deaths in the same family was extraordinarily low. that assertion was based on the assumption that cot deaths in the same family were independent events, a view for which there was see, for example, thompson and schuman ( 1987 ). no scientific evidence and which is a priori implausible. 12 the assumption of independence was crucial to the prosecution evidence against sally clark that the odds of two cot deaths in a family such as hers were 1 in 73 million and so would be expected only once a century. given the complex and conflicting medical evidence, it would not be surprising if that striking and simple statistic had played a role in helping the jury come to its conclusion. in fact