Additivity — a dangerous assumption

21 Jan, 2016 at 20:28 | Posted in Economics | 1 Comment

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.

1 Comment

  1. Sure. But this does invite the (inevitable) “We already have non-linear and non-additive models” line. “And … interaction terms!”

    I propose something more radical. How about?:

    “Algorithmic Composition — An Arbitrary Assumption”

    Why on earth should causes in the social world necessarily combine according to some mathematical function?

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