Sunday, January 08, 2006

is income distributed according to the second law?

the second law states that energy in a system is distributed in the most probable way, which is exponentially decreasing if its like an ideal gas (composed of parts which do not interact except by random exchanges of energy). Most parts of the system have low energy and fewer and fewer have higher energies.
(it should be noted that this is not a 'normal' distribution which arrives for different circumstances: essentially if money is not distributed in 'packets' but instead 'piecewise' (dollar by dollar) ).

a current claim is that this applies to income, though with the stipulation that this applies only to about 90% of the population which lives in a 'thermal equilibrium' with respect to the distribution of 'social energy' (income). the top 10% gets its income a different way, from investment, which does not obey the equilibrium dynamics governed by the maximization of entropy.

theoretically then, 'wage' income follows the random exchange model. One problem with this is that of total national income of around 10 billion $ in 2000 only about 5.6 billion is wage income. 2.1 billion is from forms of ownership or investment, and 2.1 from transfers (ie taxes). in fact, in an 11 billion $ economy (called GDP), there is really only about 7 billion dollars. 1 billion is depreciated away, and 2 billion arrives by redistributing to the have-nots from the haves. theoretically the wage income is subject to the randomness distribution, but transfers at least are tied partly to investment income through taxes. (There may be even less since foreign trade introduces a lien (debt) owed to foreign lenders, though this is only realized at a later time.)

another problem is that an exponential distribution can arise in many ways, non-randomly. one study suggests that sectors of the economy each have a particular income and only when one lumps the sectors together does the exponential form arise. in other words, the apparent exponential is actually a mixture of distributions of different incomes. one discussion of the 'entropy' model also shows it can arise when there is a hierarchical wage system (ie bosses and lower level employees). this makes exchanges assymetric.

the random theory also essentially claims that, by the ergodic hypothesis that time averages equal ensemble averages, the lifetime income of everyone in the society should be equal to the same average. every individual would have the exact same mobility pattern, spending some time in every income bracket. in addition it implies there are no correlations among individuals, no segmentation of society based on classifications like 'hereditary descent', race, gender, or any other factor . (while the randomness assumption is compatible with different average wages for different occupations, it then implies that people switch occupations randomly, so on average they get the same averages as everyone else----from dishwasher to brain surgeon, etc.). most studies show high correlations in income among families, races, genders, etc. so the theory fails here. even educational status is inherited in part. (affirmative action plays the role of progressive taxation here, leveling the distribution of opportunities a bit.)

another strange feature of the 'entropy' model is that it shows a different temperature characteristic for different states. If the wage market is at equilibrium, as the exponential model suggests, all subsystems should have the same temperature. If they don't they should all fluctuate around an average.
( in the model, the 'temperature' is simply per capita income. possibly it has been normalized to exlude investment income earners, and their income. conceivably if this is done, and done state by state, the differences would dissapear. i tend to dought it however. states tend to cluster.)
the model also would claim that all state level Gini coefficients, or inequalities, are identical. this is not true (though again corrections are possible if investment income and investors are left out, and family structure is accounted for.)

authors of these studies do a fair amount of travel, typically on the taxpayer dime, it appears. this suggests that the standard theories of inequality are more in play, having to do with income hoarding and distortion of social spending towards maintaining inequality. other variants of this theory would call it the effect of bounded rationality, so that inequality is socially constructed through ignorance and guile. from this view a sociological interpretation of these theories is they simply serve to justify a 'do nothing' ideology about inequality, basing them on 'the laws of physics'.

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