It is an area-level model, meaning some input data are associated with sub-aggregates such as regions, jurisdictions, or industries.
The model is applied in the context of small area estimation in which there is a lot of data overall, but not much for each subgroup.
In random effects models like the Fay–Herriot, estimation is built on the assumption that the effects associated with subgroups are drawn independently from a normal (Gaussian) distribution, whose variance is estimated from the data on each subgroup.
[1] Often fixed effects are included, making it a mixed model, with auxiliary data and economic or probability assumptions that make it possible to identify these effects separately from one another and from sampling variation
[2] The parameters of interest including the random effects are estimated together iteratively.
The test may not reject the hypothesis of no-correlation even when it is false, a Type II error, so that it cannot be definitively concluded that random effects estimation is unbiased even if the Hausman test fails to reject.
Robert Fay and Roger Herriot of the U.S. Census Bureau developed the model to make estimates for populations in each of many geographic regions.
[6][13] Rao and Molina's small area estimation text is sometimes characterized of as a definitive source about the FH model.
[14] The FH model is used extensively in the Small Area Income and Poverty Estimates (SAIPE) program of the U.S. Census Bureau.