Thursday, December 17, 2009

Samuelson And The Sons Of Samuelson On The Random Walk

The point I made in an earlier post about Paul Samuelson has become clearer due to debates on other blogs, most notably on Marginal Revolution, with the paper, "Proof that properly anticipated prices fluctuate randomly," Industrial Management Review, 1965, available at This famous paper, cited by Krugman recently as presenting one of Samuelson's eight (nine really) most important original ideas, has been widely misinterpreted by his followers, a case of the "sins of the Sons of Samuelson." It has been interpreted as an early example of showing that markets follow random walks, which in turn are examples of market efficiency in conformance with rational expectations. Pretty much of this is either a misinterpretation or just plain outright false.

This latter argument depends on very strong assumptions such as Gaussian distributions of noise. Samuelson's proof is very general, allowing for probability distributions to drift over time (ultimate skewness) as well as to have varying variance (fat tails), and even not to rule out speculative trading by agents. He explicitly states in the conclusions that his theorem does not establish any sort of efficiency outcome to such trading.

Many, including most textbooks (such as Campbell, Lo, and MacKinlay) have simply missed the boat on this, identifying Samuelson with an efficiency result, and then proclaiming him to be wrong because such things as technical trading can make money sometimes. The problem arises from confusing "properly anticipated" with "rational expectations" or at least ratex in a simplistic formulation. Samuelson's result implies that agents are anticipating even the endogenous influence of other traders as well as the usual gaggle of exogenous shocks, and is very general to the form of the probability distribution, thus being perfectly consistent with such outcomes as the peso problem identified in an MIT Ph.D. thesis by Ken Rogoff in 1979. Indeed, Samuelson himself declares his result to be so general as to border on being empirically untestable, and lmost "vacuous," his term. It has been his "sinful sons" who have narrowed it down by making stronger assumptions to claim for it things Samuelson himself never claimed for it (indeed, explicitly denied, such as an implied market efficiency result).

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