Keynes on the additivity fallacy

8 Aug, 2020 at 09:42 | Posted in Statistics & Econometrics | 2 Comments

2014+22keynes%20illo2The unpopularity of the principle of organic unities shows very clearly how great is the danger of the assumption of unproved additive formulas. The fallacy, of which ignorance of organic unity is a particular instance, may perhaps be mathematically represented thus: suppose f(x) is the goodness of x and f(y) is the goodness of y. It is then assumed that the goodness of x and y together is f(x) + f(y) when it is clearly f(x + y) and only in special cases will it be true that f(x + y) = f(x) + f(y). It is plain that it is never legitimate to assume this property in the case of any given function without proof.

J. M. Keynes “Ethics in Relation to Conduct (1903)

Since econometrics doesn’t content itself with only making optimal predictions, but also aspires to explain things in terms of causes and effects, econometricians need loads of assumptions — most important of these are additivity and linearity. Important, simply because if they are not true, your model is invalid and descriptively incorrect. It’s like calling your house a bicycle. No matter how you try, it won’t move you an inch. When the model is wrong — well, then it’s wrong.

2 Comments

  1. This is connected to flaws in economists’ assumption of transitive utility preference functions. Both additivity and transitivity depend on assumption that all goods can be reduced to monetary equivalent. That f(x+y)=f(x)+f(y) is only true if x and y can be measured in some common property, ie money value. Non reductive multiple evaluative criteria is the root cause of Arrow’s Impossibility Theorem, and applies not just to voting but any preference order where there are multiple criteria, or where value of goods cannot be reduced to monetary value.

    Comment by Karey— 8 Aug, 2020 #

    • We need a common denominator of a measure of additive utility which may (i.e. can-) not be money but some “util” since we can not simply add apples and houses…. and fx(x), fy(y) may be such ones… (be it they may be logarithmic, linear, inverse quadratic or so on, in addition to being “normalising”). Thus, fx(x)+ fy(y) can never be =f(x+y) since the latter is impossible, (that is, unless x and y are already normalised values of “utils” ). Considering money is linearly additive, and knowing utility is diminishing, money can not be adequate measure of utility either… only a non-linear e.g. a log(x$) may be an adequate, approximate model for the “util”

      Comment by Leandroff Perendia George— 8 Aug, 2020 #


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