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17 November 2006

Bayesian brains?

Amy Perfors

Andrew Gelman has link to a study that just came out in Nature Neuroscience whose author, Alex Pouget at the University of Rochester, suggests that "the cortex appears wired at its foundation to run Bayesian computations as efficiently as can be possible." I haven't read the paper yet, so I don't have much in the way of intelligent commentary, but I'll try to take a look at it soon. In the meantime, here is a link to the press release so you can read something about it even if you don't have access to Nature Neuroscience. From the blurb, it sounds pretty neat, especially if you (like me) are at all interested in the psychological plausibility of Bayesian models as applied to human cognition.

Posted by Amy Perfors at 11:40 AM

The "Imperial Grip" of Instrumental Variables

The Economist is agog over the increasing prominence of instrumental variables in econometrics ("Winds of Change", November 4, 2006). While it is always nice to get some square inches in a publication with a circulation greater than a few thousand, I'm afraid that I tend to sympathize more with the "instrument police" than the "instrumentalists."

For a variable to be a valid instrument, it must be (a) correlated with the variable for which we are trying to estimate a causal effect, and (b) only affect the outcome through the proposed causal variable, such that an exclusion restriction is satisfied. This is true for every estimation in which a proposed instrument is used; one must make a separate case for the validity of the exclusion restriction with respect to each analysis. Leaving aside what should be the second-order problem of actually carrying out an IV analysis, which may be a first-order problem in practice ("what do you mean it has no mean?"), our inability to verify the exclusion restriction in the case of naturally occuring instruments forces us to move from the substance of the problem we are trying to investigate to a duel of "just-so stories" for or against the restriction, a debate that typically cannot be resolved by looking at the empirical evidence.

Consider the two papers desribed in the Economist article. The first attempts to estimate the effect of colonialism on current economic outcomes. The authors propose wind speed and direction as an instrument for colonization, arguing (plausibly) that Europeans were more likely to colonize an island if they were more likely to encounter it while sailing. So far so good. Then they argue that, while colonization in the past has an effect on economic outcomes in the present, being situated in a location favorable for sailing in the past (i.e., before steam-powered ships) does not. Is this really plausible? The authors think so, I don't, and it isn't obvious that there is a way to resolve the matter. In the second example, the failure of ruling dynasties to produce an heir in Indian princely states is used as an instrument for the imposition of direct rule by the British. Here the exclusion restriction may be more plausible (or - shameless plug - maybe not, if it is the shift from a hereditary to a non-hereditary regime rather than colonialism per se that affects outcomes). One way or the other, is this really what we should be arguing about?

None of this is to say that instrumental variable models can never be useful. When we can be more confident that the exclusion restriction is satisfied (usually because we designed the instrument ourselves), then IV approaches make a lot of sense. Unfortunately (or fortunately), we can't go back and randomly assign island discoveries using something like a coin flip rather than the trade winds. Despite this, nothing seems to slow down the pursuit of more and more tortured instruments. The observation that "the instrumental variable now enjoys an almost imperial grip on the imagination of economists" carries more irony that was perhaps intended.

Posted by Mike Kellermann at 11:03 AM