21.7.03

SPELLING OUT YOUR LOSS FUNCTION. There is more to statistical inference than reporting coefficients with suitably many asterisks on the "significant" coefficients. Although many economists -- not always students -- have yet to grasp this point, Prime Minister Blair apparently does. Consider the following passage (via Andrew Sullivan) from his speech to a joint session of Congress:

"Can we be sure that terrorism and WMD will join together? If we are wrong, we will have destroyed a threat that, at its least is responsible for inhuman carnage and suffering. That is something I am confident history will forgive. But if our critics are wrong and we do not act, then we will have hesitated in face of this menace, when we should have given leadership. That is something history will not forgive."

The first couple of lines spell out his loss function in the case of a false positive (Saddam neither has nuclear, chemical, nor biological weapons, nor provided them to terrorists, despite what Intelligence concludes) and his argument that the consequences of removing Saddam are still to be preferred to leaving Saddam alone. The remainder of the passage spells out his loss function in the case of a false negative (Saddam deceives enough people into believing that he has no such weapons, then uses them himself or finds an agent to do so). His loss function is not symmetric with respect to false positives (small consequences from acting anyway) and false negatives (large consequence from failure to act.) No two-tailed t-test here.

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