The Black Swan Problem. Håkan Jankensgård

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The Black Swan Problem - Håkan Jankensgård


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      The ‘by a lot’ is actually an important qualifier of wild uncertainty. To see why, consider that whenever we have a dataset, some of the observations will represent the tail of the distribution. They are large but rare deviations from some more normal state. Let us say that we have, in a given dataset, a handful of observations that can be said to constitute the tail. There will be, by construction, a minimum and a maximum value, which are the most extreme values that history has had to offer so far.

      Unless we are talking about a truly truncated distribution, like income having zero as the lower limit, it is a potential mistake to think that the ‘true’ underlying data‐generating process is somehow capped by the observed minimum and maximum values. If we feed all the observations we have into a statistical software, we can ask it to analyse which random process that most plausibly generated the patterns in the data. Now, if we immediately take the process identified by the programme and draw random values based on it in a simulation, it will come up with a distribution that contains outcomes that go beyond the lowest/highest observed values in the dataset without the probability of that dropping to virtually zero. This will always happen as long as the approach is to assume that there is some underlying random process generating the data and use real data to approximate it. It is as if the software doing the fitting ‘gets it’ that if we have observed certain extreme values, even more extreme observations cannot be ruled out. If we have observed a drop in the S&P 500 of minus 58% over a certain period of time, who would say that a drop of minus 60% is outside the realm of possibilities? The simulated extremes will lie somewhere to the left (right) of the minimum (maximum) observed in the data. The tail we model in this way will encompass the observed tail and then some.

      In many cases, we lack data that we can explore for mapping out the tail of a random process. In this kind of setting, uncertainty tends to be wildly out of the gate. Technological innovation fits right into this picture, because it brings novelty and injects it into the existing, already volatile, world order. New dynamics are set in motion, triggering unintended consequences and side effects that ripple through the system in an unpredictable fashion. Because we keep innovating, we also keep changing the rules of the game, forever adding to the complexity. Two Black Swans that have sprung from the onward march of technology are the emergence of the internet and the more recent invasion of social media and mobile phones into our lives. There was no existing dataset that we could have studied prior to them that might have suggested that such transformations of our reality were about to happen. Or, more importantly, that they were even possibilities at all. To appreciate how technologies that we are completely immersed in today and take for granted are actually Black Swans, cases of wild uncertainty, consider the words of Professor Adam Alter of New York University:

      Alter's thought experiment of going back 20 years in time and imagining talking to people about something highly consequential that later happened is a useful one for deciding whether something is to be considered a Black Swan. If you imagine their reaction to what you describe would be that it is ridiculous or inconceivable, chances are that you have found one.


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