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This paper evaluates the accuracy of county-level population estimates and forecasts under three different methods for estimating the domestic migration in a components-of-change framework. The first is a net-migration approach similar to that used by the U.S. Census Bureau and by many state data centers. While common, the net migration assumption has been widely criticized for not accurately reflecting the population ‘at risk’ of migrating into a county. The other two methods follow a gross migration approach whereby in- and out-migration are added separately into the population change equation. The simple gross migration approach estimates domestic in-migration to each county from the rest of the nation as a whole. The multiregional gross migration model examines flows between specific pairs of counties and adds these together to measure total in-migration. Otherwise, the population estimates models are identical – allowing us to isolate differences in population estimates due solely to how the domestic migration component is estimated.

We evaluate the accuracy of the three migration approaches against the county household population counts of the 2010 Decennial Census using a variety of common measures of predictive accuracy. We find that the simple gross migration model typically produces the smallest forecast errors. However, this is followed closely by the net migration approach, whose average forecast errors exceed the simple gross model by only .2 percentage points. Despite its far greater complexity the multiregional model produces the highest average errors of all three approaches with an average absolute error .7 percentage points higher than the net migration model. This is due largely to a higher proportion of extreme errors —counties where the model produces an average in excess of five or ten percent greater than the actual census counts. We suspect that this is due to measurement error in the Internal Revenue Service migration data, which may be more influential when calculated for specific pairs of counties but has less noticeable impact when distributed across the entire nation (i.e. the simple gross migration approach) or when in and out-migration are subtracted from one another (i.e. the net migration approach). Although producing higher errors when averaged over all counties, the multiregional model still produces the lowest errors for the greatest number of counties.

All three models produce their most reliable estimates for large counties and the greatest error for the smallest counties—places where even small differences can greatly influence year to year changes in migration rates. The simple gross migration approach is generally preferred among mid-sized and larger counties. The multiregional model is typically favored among counties with fewer than 20,000 persons. Counties experiencing rapid decline or growth are also notoriously difficult to estimate, regardless of method. Rapidly growing counties tend to be overestimated, most notably so in the case of the multiregional model which has a natural upward bias to begin with. However, the multiregional model tends to do a little better than the others at estimating population in cases of recent decline. The simple gross migration model is generally preferred for rapidly growing counties. The key exception is among fast growing small counties, which are favored by a multiregional approach.

This project was funded by:

The United States Census Bureau

For Services in Support of the U.S. Census Bureau’s 2010 Estimates Evaluation

Work Order: YA132310SE0381