Alternative formulas for synthetic dual system estimation in the 2000 census

TL;DR

This paper introduces three alternative formulas for dual system estimation in the 2000 U.S. Census, analyzing how different treatments of imputation counts affect local population estimates and the assumptions involved.

Contribution

It proposes new formulas for dual system estimation and examines their impact on population estimates, focusing on the treatment of imputation counts.

Findings

Different formulas lead to varying population estimates for local areas.

Treatment of imputation counts significantly influences the estimates.

Understanding assumptions helps improve accuracy of census-based estimates.

Abstract

The U.S. Census Bureau provides an estimate of the true population as a supplement to the basic census numbers. This estimate is constructed from data in a post-censal survey. The overall procedure is referred to as dual system estimation. Dual system estimation is designed to produce revised estimates at all levels of geography, via a synthetic estimation procedure. We design three alternative formulas for dual system estimation and investigate the differences in area estimates produced as a result of using those formulas. The primary target of this exercise is to better understand the nature of the homogeneity assumptions involved in dual system estimation and their consequences when used for the enumeration data that occurs in an actual large scale application like the Census. (Assumptions of this nature are sometimes collectively referred to as the ``synthetic assumption'' for dual system estimation.) The specific focus of our study is the treatment of the category of census counts referred to as imputations in dual system estimation. Our results show the degree to which varying treatment of these imputation counts can result in differences in population estimates for local areas such as states or counties.