Errors-In-Variables County Poverty and Income Models
Geof Gee and Robin Fisher$
U.S. Census Bureau
Key Words: Errors-in-variables, Small Area
Estimates, Hierarchical Bayes
1. Introduction
At present, the Small Area Income and
Poverty Estimates (SAIPE) program at the U.S.
Census Bureau estimates state, county, and
school district poverty and state and county
median household income (MHI). The current
county models of child poverty are Empirical
Bayes models where the direct survey estimates
of poverty and MHI are shrunk with weighted-
regression model-based estimates of poverty and
MHI, respectively. 1 These weighted regressions
assume that direct Annual Social and Economic
Supplement (ASEC) estimates of county poverty
and MHI are a function of administrative record
and survey data.2 We address a fundamental
assumption of regression models that is violated
in this application: that the predictors are
measured without error. Practical experience, as
well as past research (Gee, 2001) suggests that
the data for small areas like counties are often
measured with error for many reasons. Recent
developments in experimental SAIPE county-
level poverty models (Fisher, 2003) derive a
measure of “true” poverty as a function of
several independent measures of poverty, all of
which are assumed to possess non-negligible
variances; i.e., an “errors-in-variables” model.
We adapt the method in Fisher (2003) to
estimating the county number of related children
$ We have benefited from the comments of several people. In
particular we thank Elizabeth Huang, Don Luery, and
members of the Census Bureau Small Area Estimates Group.
This paper reports the results of research and analysis
undertaken by the U.S. Census Bureau staff. This report is
released to inform interested parties of ongoing research and
to encourage discussion of work in progress. The views
expressed on technical issues are those of the authors and not
necessarily