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There has been substantial recent interest in record linkage, attempting togroup the records pertaining to the same entities from a large database lackingunique identifiers. This can be viewed as a type of "microclustering," with fewobservations per cluster and a very large number of clusters. A variety ofmethods have been proposed, but there is a lack of literature providingtheoretical guarantees on performance. We show that the problem isfundamentally hard from a theoretical perspective, and even in idealized cases,accurate entity resolution is effectively impossible when the number ofentities is small relative to the number of records and/or the separation amongrecords from different entities is not extremely large. To characterize thefundamental difficulty, we focus on entity resolution based on multivariateGaussian mixture models, but our conclusions apply broadly and are supported bysimulation studies inspired by human rights applications. These results suggestconservatism in interpretation of the results of record linkage, supportcollection of additional data to more accurately disambiguate the entities, andmotivate a focus on coarser inference. For example, results from a simulationstudy suggest that sometimes one may obtain accurate results for populationsize estimation even when fine scale entity resolution is inaccurate.

Theoretical Limits of Record Linkage and Microclustering