## Keynes and the adding-up problem

31 March, 2015 at 12:26 | Posted in Economics | 3 CommentsThe 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) [h/t Robert Skidelsky]

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.

## 3 Comments

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Of course, the algebraic adding together of qualities makes little sense to anyone except neoclassical economists.

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Where addition does make perfect sense — in arithmetic — as when the money to make demand effective falls short in the aggregate of the amounts necessary to clear markets of labor, neoclassical economist blink uncomprehendingly.

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Wrong models are not nearly as obstinate as wrong economists.

Comment by Bruce Wilder— 31 March, 2015 #

In the Keynes quotation, “suppose f(x) is the goodness of x and f(y)”, obviously “is the goodness of y” has been dropped. A bit more than a typo.

Comment by Min— 3 April, 2015 #

Fixed. Thanks 🙂

Comment by Lars Syll— 3 April, 2015 #