Tuesday, 12 June 2007

Errors in Cost Benefit Analysis

A recent Bloomberg article referring to the AEI-Brookings Institute paper Has Economic Analysis Improved Regulatory Decisions? made me think again about cost benefit analysis.

The paper condemns both the quality of cost benefit analysis used in determining the impact of regulation and the `tenuous' use made by policy makers of that analysis. Undoubtedly that is partly for political or hegemonic reasons - cost benefit analysis sometimes comes to the `wrong' conclusions - but I suspect it is also partly because the conclusions of a cost benefit analysis are sometimes not believed. The analyst may be at fault here for not stating the margin of error?

Error bars are common in experimental science: the fine structure constant, for instance, is known to roughly one part in a billion, and in any precise discussion we would state not 1/alpha = 137.035999710 but rather 1/alpha = 137.035999710(96) meaning that the reciprocal of alpha could be as high as 137.035999796 or as low as 137.035999624.

In cost benefit analysis this could be a very useful tool, especially as the error bars are much larger. To take the first example that google coughed up, an amusing cost benefit analysis of different law schools (where the cost is the fees and the benefit is the increase in expected salary after going to the school), the problem is that while the costs are fixed, the benefits aren't. Not only do different individuals earn different amounts despite having the same education, speciality counts so that (in the perverse world in which we live) a tax lawyer earns more than a criminal defender. Moreover the reputation of various law schools will change over time effecting not just the earnings of current graduate but also those of past ones.

An even better example is one of the next hits, a discussion of the cost benefit analysis of rebuilding New Orleans after Katrina given its obvious hurricane risk. Here not only is the benefit uncertain, but so too is the cost. Any analysis with error bars would suggest at best 'case not proven': that, rather than 'cost > benefit' or 'cost < benefit' is often the best that we can conclude since it will often be the case that the intervals [cost - possible error in cost, cost + possible error in cost] and [benefit - possible
error in benefit, benefit + possible error in benefit] intersect.

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