{"id":65692,"date":"2014-06-05T11:24:16","date_gmt":"2014-06-05T09:24:16","guid":{"rendered":"http:\/\/www.pauljorion.com\/blog\/?p=65692"},"modified":"2014-06-05T11:24:16","modified_gmt":"2014-06-05T09:24:16","slug":"medical-breakthrough-low-dosage-piketty-prevents-ft-fits-iii-by-h-benisty-co-author-with-timiota","status":"publish","type":"post","link":"https:\/\/www.pauljorion.com\/blog\/2014\/06\/05\/medical-breakthrough-low-dosage-piketty-prevents-ft-fits-iii-by-h-benisty-co-author-with-timiota\/","title":{"rendered":"Medical Breakthrough: Low Dosage \u201cPiketty\u201d Prevents \u201cFT\u201d Fits (I\/II)<\/b>, by H. Benisty (co-author with Timiota)"},"content":{"rendered":"

Billet invit\u00e9. La version fran\u00e7aise se trouve ici<\/a>. Un grand merci \u00e0 Serge Boucher pour la traduction.<\/p><\/blockquote>\n

On the subject of wealth concentration and rising inequalities, Thomas Piketty tells us that there is indeed a growing rift, and that the fifties were only an exception. One can always pretend that the Gilded Age gave us several decades of only occasionally rusty capitalism, hence reviving those levels of inequality is nothing to scoff at, especially if millions of people concurrently rise out of poverty.<\/p>\n

Entertaining that view requires that we ignore many aspects of the Great Depression, which is highly difficult to understand, having taken place between two world wars, and in a period mixing technical progress, colonisation and then decolonisation. In any case, one can conceivably believe that history as a whole is so chaotic that what we\u2019ll get at the end of the current rise in inequality need not be exceptionally bad.<\/p>\n

Many reasons, which one might wish to file under \u201cour planet\u2019s survival\u201d, suggest that now is a horrible time for deadlocking a system already made rusty by wealth concentration and the mass poverty that it implies: even though a sizeable and growing middle-class manages to get by, a world where even in rich countries 30% of inhabitants are poor, with poor countries doing much worse, can\u2019t be expected to make the right choices regarding our planet\u2019s resources.<\/p>\n

I\u2019ve come up with a model, which suggests that even a rather slight Piketty-esque reduction of inequality is enough to bring about enormous gains in stability. The fundamental reason is that, in this model \u2013 which is intentionally simplistic and intended only as inspiration \u2013 there\u2019s \u201ccoupling\u201d between the fluctuations among the fortune of the hyper-rich and the irreversible downfall of the more modest into survival-level misery. Moderating hyper-wealth is thus a need, not just a societal choice among others.<\/p>\n

In this model, you\u2019ll only find very simple things: the \u201cwealth\u201d of individuals, who will be lucky or unlucky in their daily exchanges, and end up after a while with more or less \u201cfortune\u201d.<\/p>\n

There\u2019s also a poverty level, because one can only risk what lies above that threshold: the poor won\u2019t risk any more than a few euros, the rich only a few millions.<\/p>\n

Global wealth evolves with those exchanges, but I\u2019ve chosen to put that aside, to \u201cnormalise\u201d it as the mathematically-inclined say. This circumvents much more complex debates on demography, technology, sociology, \u201cvalue creation\u201d, etc. This only affirms that each society defines financial well-being locally, that one is only rich or poor in comparison with his neighbours.<\/p>\n

Every day, one risks a part of his surplus (in every form, including time and effort) with varying success. This will be described as an independent random process. In principle, he exchanged with other people, and some form of compensation should exist, but that can only be true on average \u2013 and sometimes not even so, as an especially bad bet involving a huge sum of money can make everyone poorer. In contrast, one who invents something especially useful but only extracts a fraction of the societal gain (this being springtime, I\u2019m hoping for a silent lawnmower) can make everybody substantially richer.<\/p>\n

I\u2019ll now give you the maths, but if this disturbs you feel free to jump ahead:<\/code><\/p>\n

Let K be the wealth of an individual and Kp the poverty level. Wealth will change from day to day according to a bounded random value:<\/p>\n

K\u2019=K+alpha*(K-Kp)*RAND<\/p>\n

Where K_extra=alpha*(K-Kp) is that day\u2019s \u201cbet\u201d, and RAND is a random number between -1 and 1. (Computationally, it\u2019s -1+2*rand, where \u2018rand\u2019 is the usual random function in [0,1]).<\/p>\n

With a fixed population of N actors (numbered i from 1 to N), we do this independently for each i:<\/p>\n

K(i,D+1)=K(i,D)+alpha*(K(i,D)-Kp)*RAND_i \u00a0\u00a0\u00a0\u00a0(N bets are made every day).<\/p>\n

This gives us N temporal series or \u201crandom walks\u201d, which will all eventually slow down as they approach Kp, which is a lower bound. (We start with K=1000 \u201ceuros\u201d for all K_i on the first day, and Kp=400 \u201ceuros\u201d).<\/p>\n

We see that in this model total wealth varies, and that there is no higher bound for K. This lack of a higher bound is what I\u2019ll call the \u201cFT effect\u201d, as financial journalists have shown very little concern over the rising gap between the wealthy and the ones they employ, and it is this single fact that leads to paralysis, as we\u2019ll see, despite the independence between random trajectories.<\/p>\n

I\u2019ve chosen alpha=0.06, for a simple reason: nobody really risks 6% of his surplus every single day, but maybe 50% over three months, which is about the same.<\/p>\n

As for global wealth, in the beginning (where there is no \u201csuper-rich\u201d making huge bets), evolution is slow. With many actors (N>>1), the winners nearly compensate for the losers. We\u2019ve chosen to normalise this anyway, for reasons explained above. After each day, each actor\u2019s wealth is slightly adjusted so that the mean remains 1000, using an elementary and proportional operation (K\u2019_norm = K\u2019*mean\/1000 for each actor)<\/p>\n

This ends most of the maths.<\/code><\/p>\n

In this first post, I\u2019ll simply show that a few \u201crather rich\u201d appear far quicker than one would intuitively assume, and mostly familiarise the reader with the color histograms I use to present the results. I\u2019ll also talk about the \u201cGini coefficient\u201d, often used as a \u201csynthetic\u201d measure of wealth inequality. An Appendix at the end of the second post explains the movie in detail using selected frames, 6 of them, from chosen movies. It tells you \u201cwhat it means and what you should and can see\u201d, hoping to train you to feel what the model may tell us on inequality, and what weapons it could help us design. These 6 commented frames will be labelled: ((1)), ((2)),\u2026((6)). For those unwilling to browse between two html windows, a pdf version of the Appendix is here<\/a><\/strong>.<\/p>\n

In the second section, I\u2019ll explain the \u201cPiketty vs FT\u201d remedy, showing how paralysis occurs, and how a slight bias can counterbalance the \u201crich-gets-richer\u201d syndrome and avoid deadlock. This is a mathematical version of an ill condition that the Greeks already wanted to cure, \u201cpleonexia\u201d, or immoderate appetite for wealth. Non-western anthropology is full of examples where, every time wealth is accrued by a member of society, it is then \u201csocialised\u201d to avoid the lucky rich ending up gravely hurt. (See \u00ab\u00a0Conversation sur la naissance des in\u00e9galit\u00e9s\u00a0\u00bb, by Christophe Darmangeat.)<\/p>\n

Here\u2019s the first movie:<\/p>\n