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Title: Does Regression Produce Representative Estimates of Causal Effects?

Abstract:

It is well-known that, with an unrepresentative sample, the estimate

of a causal effect may fail to characterize how effects operate in the

population of interest. What is less well understood is that

conventional estimation practices for observational studies may

produce the same problem even with a representative sample.

Specifically, causal effects estimated via multiple regression

differentially weight each unit's contribution. The ``effective

sample'' that regression uses to generate the causal effect estimate

may bear little resemblance to the population of interest. The effects

that multiple regression estimate may be nonrepresentative in a

similar manner as are effects produced via quasi-experimental methods

such as instrumental variables, matching, or regression discontinuity

designs, implying there is no representativeness basis for preferring

multiple regression on representative samples over quasi-experimental

methods. We show how to estimate the implied ``multiple regression

weights'' for each unit, thus allowing researchers to visualize the

characteristics of the effective sample. Knowing the effective sample

is crucial, because it allows one to relate effect estimates to sample

characteristics. We then discuss alternative approaches that, under

certain conditions, recover representative average causal effects. The

requisite conditions cannot always be met.