Identification of Expected Outcomes in a Data Error Mixing Model with Multiplicative Mean Independence

Brent Kreider, Iowa State University
John V. Pepper, University of Virginia

Abstract: We consider the problem of identifying a mean outcome in corrupt sampling where the observed outcome is
drawn from a mixture of the distribution of interest and some other distribution. We make two contributions to this literature.
First, the statistical independence assumption maintained under contaminated sampling is relaxed to the weaker assumption
that the outcome is mean independent of the mixing process. We then generalize this restriction to allow the two conditional
means to differ by a known or bounded factor of proportionality. Second, in the special case of a binary outcome, we
consider the possibility that draws from the alternative distribution are known to be erroneous, as might be the case in a
mixture model of response error. We illustrate how these assumptions can be used to inform researchers about the
population's use of illicit drugs in the presence of nonrandom reporting errors. In this application, we find that a response
error model with multiplicative mean independence is easy to motivate and can have substantial identifying power.

Keywords: measurement error, identification, contaminated sampling, corrupt sampling, nonparametric bounds
JEL classification: C14, C25