Compatible Trends for ACS Data
Tucker McElroy
U.S. Census Bureau
American Community Survey (ACS)
• ACS replaces Census Long Form
• Sampling error is reduced through rolling samples (pooling over time)
• This induces a time lag in the reported Multi-Year Estimates (MYEs)
• Lag makes diverse ACS data incompatible
ACS
• Data is pooled in 1-year, 3-year, or 5-year windows, according to
population size in the region
• Sample is equally weighted over the years in the rolling sample
• Time lag property: 3y MYE is centered at previous year; 5y MYE is
centered two years back
ACS Stylized Example
• Say a sample is collected for 3001 through 3005.
• In 3005, the 5y MYE consists of an estimate computed over all past five
years
• In 3005, the 3y MYE consists of an estimate computed over years 3003,
3004, 3005
• The 1y MYE is an estimate just based on sample over 3005
• For many types of estimates, the 5y MYE is centered at 3003 value, and
the 3y MYE is centered at a 3004 value. Generally true of locally linear
MYEs.
ACS Stylized Example
• Suppose we are measuring an increasing quantity (e.g., a population) in
two different counties A and B
• A 1y 3005 MYE for county A may be spuriously larger than a 5y 3005
MYE for county B
• We should compare the 1y 3003 MYE for county A to the 5y 3005 MYE
for county B
• Drawback: we throw away the 3004 and 3005 1y MYEs for county A.
These should be used somehow
Compatible Trends
We propose using trend filters to match up different MYEs such that:
1. The 1y, 3y, and 5y trends are compatible (close to identical)
2. Linear dynamics in the time series are treated appropriately
3. The filters are concurrent
4. Filter length is minimal
Compatible Trends
Let the ky MYE be denoted Y
(k)
t
, and use the representation for k = 3, 5
Y
(k)
t = Θ
(k)(B)Xt
with B the backshift operator, Xt the 1y MYE, and Θ(k)(z) is the Simple
Moving Average (SMA) polynomial of order k given by
Θ(k)(z) =
1
k
(
1 + z + · · · + zk−1
)
.
This representation is approximately true for many types of estimates.
Compatible Trend