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Detail specificity depends on context: exs – arithmetic & GDP vs GNP September 12, 2011

Posted by larry (Hobbes) in economics, Logic.
Tags: , ,

When it comes to applied contexts in some sciences such as economics, there is sometimes a feeling that a discussion is overly detailed.  This is sometimes true. But I would like to use an example from arithmetic to show that this is ultimately the case.  The principle I am working with is the one that stipulates that one should be as simple as one can be but no simpler, a principle that dates at least back to Ockham.

When one sets out the fundamental principles of arithmetic, say those of addition and multiplication, you find statements like these:

x + y = y + x


x + 0 = x.

The first says that addition is commutative, that is, that it doesn’t matter in what order you add two numbers together. The second principle says that zero is the identity element for addition – any number added to zero equals itself.

Now, it may be thought that these are obvious and therefore need no explicit representation.  But this would be a misunderstanding of the context these principles operate in.  For example, multiplication is commutative, that is, x * y = y * x.  But division is not commutative, that is, x ÷ y does not equal y ÷ x.  Neither is subtraction commutative.

And zero is not an identity element for multiplication, for x * 0 ≠ x.  The identity element for multiplication is 1.

The reason such strict distinctions must be made is that it is easy to extrapolate incorrectly from one arithmetic operation to another where it won’t work correctly.

Something similar could be said about certain distinctions between certain chemical elements, say U235 and U238. While the difference could be said to be small, it is nevertheless a momentous one. You can make a bomb with one but not the other.

The same goes for a theoretical and applied social science* like economics.  Take the distinction between GDP, Gross Domestic Product, and GNP, Gross National Product, which are two distinct measures of a nation’s economic productivity.  States used to use GNP but changed over time to GDP.

These measures are very similar but in certain contexts one may be preferable to the other.  GNP measures productivity in terms of ownership regardless of where the ownership lies.  For instance, it counts income made overseas as part of the nation’s income.  GDP, on the other hand, measures a nation’s productivity that takes place within its territorial border whether produced by a foreign firm or not.  These two measures can produce different accountings of total output.

The reason given by the Bureau of Economic Analysis for making the change from GNP to GDP, which took place in the early 1990s, was that it made international comparisons more direct and facilitated comparisons among different kinds of economic activities.  Some economists deplore the change from GNP to GDP, contending that the latter is a misleading indicator of actual productivity.  Whether it is or not depends on the context, even if the measures do not differ much in value. US GDP in 2009 was estimated by the BEA at $14.119 trillion and its GNP at $14.265 trillion.  Whether the value itself or the method by which it was obtained is considered significant/meaningful will be largely determined by the context, including the theoretical framework where the interpretation of these and related measures are embedded.

As William James once wrote: in order for a difference to be a difference, it must make a difference. Sometimes the context is all.

For a detailed discussion of various alternatives from one economic perspective, see ALTERNATIVES TO GROSS NATIONAL PRODUCT: A Critical Survey (1998) by Richard England & Jonathan Harris. Whether GDP or GNP are adequate measures of a nation’s economic well-being is another matter.


* The social sciences are sciences although they are not identical to physics, nor should physics be pursued as an ideal, as happens in the pseudo-field of econophysics.


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