A variety of identification strategies have a common cell structure, in which the observed heterogeneity of the regression defines a partition of the sample into cells. Typically in the presence of exogenous covariates that define the cell structure, identification assumptions are imposed conditional on each value of the covariate, or cell by cell. Treatment effects across cells are typically heterogeneous. Researchers might be interested in unconditional parameters which are the averaged treatment effects across the cells. Alternatively, treatment effects can be estimated more efficiently if researchers are willing to impose additional parametric and semiparametric structures on the heterogeneous treatment effects across cells.