Category Mostly Harmless Econometrics: An Empiricist’s Companion

The Experimental Ideal

It is an important and popular fact that things are not always what they seem. For instance, on the planet Earth, man had always assumed that he was more intelligent than dolphins because he had achieved so much—the wheel, New York, wars and so on—while all the dolphins had ever done was muck about in the water having a good time. But conversely, the dolphins had always believed that they were far more intelligent than man-for precisely the same reasons. In fact there was only one species on the planet more intelligent than dolphins, and they spent a lot of their time in behavioral research laboratories running round inside wheels and conducting frighteningly elegant and subtle experiments on man...

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The Selection Problem

We take a brief time-out for a more formal discussion of the role experiments play in uncovering causal effects. Suppose you are interested in a causal “if-then” question. To be concrete, consider a simple example: Do hospitals make people healthier? For our purposes, this question is allegorical, but it is surprisingly close to the sort of causal question health economists care about. To make this question more realistic, imagine we’re studying a poor elderly population that uses hospital emergency rooms for primary care. Some of these patients are admitted to the hospital. This sort of care is expensive, crowds hospital facilities, and is, perhaps, not very effective (see, e. g., Grumbach, Keane, and Bindman, 1993)...

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Random Assignment Solves the Selection Problem

Random assignment of Dj solves the selection problem because random assignment makes Dj independent of potential outcomes. To see this, note that

E[yj |dj = 1] – E[Yj|Dj =0] = E[yli IDj = 1] – E[Yoj|Dj =0]

= E[yij |Dj = 1] – E[Yoj|Dj = 1],

where the independence of Yoj and Dj allows us to swap E[Yoj|Dj = 1] for E[Yoj|Dj = 0] in the second line. In fact, given random assignment, this simplifies further to

E [Yij|Dj = 1] – E [Yo j | D j = 1] = E [y ij – Yoj|Dj = 1]

= E [yij – Yoj] .

The effect of randomly-assigned hospitalization on the hospitalized is the same as the effect of hospitalization on a randomly chosen patient. The main thing, however, is that random assignment of Dj eliminates selection bias...

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