on the multiyear period estimates, assuming no change in population size and demographic composition, geographic boundaries, or question wording over the applicable period. The complications associated with population changes are addressed in Section 6-D. Other changes that potentially affect multiyear period estimates, such as changes in geographic boundaries or question wording, and the problem of discontinuities in population and housing controls around the time of the 2010 census are addressed elsewhere in the report.
During the panel’s early deliberations, various alternative estimands based on 3- and 5-years of ACS data were under consideration. The discussions focused on three main forms of estimand. For the majority of applications, the most attractive estimand is the population parameter for the most recent year of the multiyear period (provided that it can be estimated with adequate precision). A second estimand is the population parameter for the middle year. The third estimand is a multiyear period parameter comparable to the 1-year period parameter. The choice between these and other parameters needs to be based not only on which is preferred from a user perspective, but also on how well the parameters can be estimated. The paper by Jay Breidt in Appendix C, commissioned by the panel, discusses methods for comparing these and other estimands.
The rationale behind the use of multiyear data for producing estimates for any single year—such as the middle year or the end year—is that the estimation can “borrow strength” from the ACS data collected in other years. The process requires a statistical model that relates the estimands across time.
Some simplifying assumptions are made in order to illustrate the key issues in developing model-dependent estimates of single-year estimands from multiyear data. It is assumed that the population of the area for which the estimate is required remains constant over the multiyear period, that the sample size is the same for each year in that period, and that the standard error of each of the 1-year estimates in the period is the same, say σ.
Let the multiyear estimate be a simple weighted combination of the 1-year estimates, denoted by , where yi is the 1-year estimate for year i and wi is a weight such that ∑wi = 1. Under the above assumptions, the variance of is then σ2∑wi2.
The optimum choice of the wi depends on which estimand is selected and on the way in which the 1-year parameters are assumed to vary across