  Exposure mappings facilitate investigations of complex causal effects when
units interact in experiments. Current methods assume that the exposures are
correctly specified, but such an assumption cannot be verified, and its
validity is often questionable. This paper describes conditions under which one
can draw inferences about exposure effects when the exposures are misspecified.
The main result is a proof of consistency under mild conditions on the errors
introduced by the misspecification. The rate of convergence is determined by
the dependence between units' specification errors, and consistency is achieved
even if the errors are large as long as they are sufficiently weakly dependent.
In other words, exposure effects can be precisely estimated also under
misspecification as long as the units' exposures are not misspecified in the
same way. The limiting distribution of the estimator is discussed. Asymptotic
normality is achieved under stronger conditions than those needed for
consistency. Similar conditions also facilitate conservative variance
estimation.
