less than 4 %. forecasts have been consistently over - optimistic by ½ percentage point per year. the evidence so far during 2015 suggests this pattern may continue. caution is a plausible explanation for this dragging anchor. bis central bankers ’ speeches the household sector has undertaken significant balance sheet repair since the crisis, dragging on spending. 8 this can be seen in the proportionately greater belt - tightening exhibited among highly - indebted consumers ( chart 15 ) ). these debt - induced adjustments in spending have also been important among us consumers ( mian and sufi ( 2014 ) ). several other features of household decision - making over recent years might also plausibly reflect the effects of insecurity : weak transactions in the housing market, which are 20 % lower than their pre - crisis average ; subdued job - to - job flows in the labour market, which remain below their pre - crisis average ; and real wages which remain lower than historical relationships can explain, as workers ’ bargaining power has been sapped. over the past year, this cautious behaviour has been evident in households ’ response to the income windfall arising from the fall in oil prices. this has boosted real incomes by perhaps 0. 4 %. and it appears also to have boosted consumer confidence. what it appears not to have translated into, or at least not yet, is higher consumption : retail spending growth is little different than before the oil price fall ( chart 16 ). one interpretation is that consumers are simply waiting to see if the fall in oil prices persists. my preferred interpretation is that it reflects instead the asymmetric response of a cautious consumer : good news has been banked, not blown. consumers are pleased their glass is now less than half empty. but they are no more willing to drink it. this cautious behaviour is, to a degree, also mirrored among companies. this can be seen in the weakness of global investment since the crisis, despite the cost of company borrowing being at its lowest - ever levels ( chart 17 ). uncertainty - induced weakness in investment has provided a continuing drag on recovery, globally if not nationally. this uncertainty can be seen, too, in how companies are reinvesting their earnings. the trend over the past 20 years has been for companies to invest more in passive assets such as cash, than active ones such as physical capital. but this trend has been accentuated since the crisis. table 2 looks at the ratio of liquid assets to investment by the corporate sectors in the uk, us,

, the historical distribution of growth is fat - tailed and negatively skewed ( haldane ( 2012 ) ). large recessions are significantly more likely than, for example, the normal ( or bell ) curve might lead us to expect. based on historical data, the probability of a recession ( defined here as a negative rate of annual gdp growth ) over the following year lies between 17 % ( taking cross - country evidence since 1870 ) and 30 % ( if we take the uk since 1700 ). in other words, a recession should be expected one in roughly every 3 to 6 years. of course, the distant past might be a poor guide to the future. but even if we took the period since 1945, the probability of recession would only fall to 12 %, or one year in around every 10. these are probabilities over a one year horizon. in practice, what matters for spending and saving are people ’ s risk perceptions over a longer - term horizon. by making some assumptions about how these probabilities evolve over time, it is possible to construct cumulative probabilities of recession. chart 11 shows the cumulative probabilities of recession over a ten year horizon using two long - run cross - country gdp samples. 5 over the course of a decade, the risk of experiencing at least one recession rises steadily, reaching between 85 – 90 % after ten years. using post - war data, this cumulative probability is just less than 80 %. so over any plausible sample period, a recession remains considerably more likely than not over the course of a decade. 6 that is not to say longer periods of interrupted growth are impossible. the world has in the past experienced lengthy periods of continuously positive annual growth : in the uk, for a remarkable 26 years after the second world war and for 16 years during the great moderation starting in the late 1990s. as chart 12 shows, however, these are extreme outliers in the distribution of expansions. the probability of an expansion lasting for longer than 10 years is, on past evidence, less than 10 %. assuming these probabilities evolve according to a bernoulli distribution – that is to say, the probability of a recession triggering shock occurring in one year is independent of the probability of a shock occurring in another year. this probability is calculated by looking at data on the frequency of negative annual growth rates. the cumulative probability is the probability that there will be at least one such shock over a given horizon. using conditional probabilities