Finite-Sample Bias and Inconsistency in the Estimation of Poverty Maps
I argue that the estimation technique - widely used in the poverty mapping literature - introduced by Elbers, Lanjouw and Lanjouw, is highly sensitive to specification, severely biased in finite samples, and almost certain to fail to estimate the poverty headcount consistently. First, I show that the specification of the first-stage model of household expenditure strongly influences the estimated headcount; the range of obtainable estimates is on the order of 20% for many districts, and is as high as 48% for some areas. Further, some specifications imply province-level headcounts which diverge from the direct estimates by many as six standard deviations. Secondly, I construct bootstrap confidence intervals for the difference between the estimates under alternative specifications, which shows that (at a 2% level of significance) finite sample-bias is present in more than 42% of districts in even the best-performing regions. I calculate approximate lower bounds for the bias; I find it to be on the order of 3% for most areas, but the lower bounds range as high as 19.6% in some provinces. Finally, I argue that consistent estimation of the first stage model is necessary for consistent second-stage imputations and I decompose the difference between the true and estimated headcount into a sampling component and a specification component, the latter of which is asymptotically persistent. Given these results, it appears that the poverty maps estimated by this technique reflect primarily the arbitrary and unexamined methodological choices of their authors rather than robust features of the data.
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