Truth — not unbiasedness — is what we should aim for

5 January, 2017 at 10:59 | Posted in Statistics & Econometrics | Leave a comment

notes7-2Econometricians usually aim for unbiased estimates. And in econometrics textbooks you learn that if it’s not BLUE, it’s not good.

But if you really think about it, there is no real unbiased estimates. As soon as you weigh in the fact that in all econometric applications you always get your ‘unbiased’ estimates based on non-ideal randomized samples, measurement errors, non-additive and non-linear relationships, and so forth — well, then you realize there is no such a thing as ‘unbiasedness’ in the real-world.

And it’s even worse than this! ‘Randomistas’ are usually very keen to point out that their RCTs give results based on ‘unbiased’ estimator. But that doesn’t take us very far …

One should not jump to the conclusion that there is necessarily a substantive difference between drawing inferences from experimental as opposed to nonexperimental data …

In the experimental setting, the fertilizer treatment is “randomly” assigned to plots of land, whereas in the other case nature did the assignment … “Random” does not mean adequately mixed in every sample. It only means that on the average, the fertilizer treatments are adequately mixed …

abRandomization implies that the least squares estimator is “unbiased,” but that definitely does not mean that for each sample the estimate is correct. Sometimes the estimate is too high, sometimes too low …

In particular, it is possible for the randomization to lead to exactly the same allocation as the nonrandom assignment … Many econometricians would insist that there is a difference, because the randomized experiment generates “unbiased” estimates. But all this means is that, if this particular experiment yields a gross overestimate, some other experiment yields a gross underestimate.

Ed Leamer

So — as soon as we realise that ‘unbiasedness’ is not the Holy Grail of econometrics, it’s easier to accept that it’s better get close to the truth with a biased estimator, than to be stuck with an ‘unbiased’ estimator that is typically not even close to truth.

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