# Presentation: 448073

## A Quantitative Analysis of the Relative Effects of the Components of Change Used in Postcensal County Population Estimates 

**Sam T. Davis**
**Population Estimates Branch**
**Population Division**
**U.S. Census Bureau**

*This report is released to inform interested parties of ongoing research and to encourage discussion of work in progress. **The views expressed on methodological issues are those of the authors and not necessarily those of the U.S. Census Bureau.*

## The Component Method

*In general -*
- P1 = P0 + C
*where*
- P0 is the beginning population
- P1 is the estimated population, and
- C is a collection of **components of population change**

***This is what we use to produce annual county population estimates.***

## The Components

**Natural Change** – *Births minus Deaths*
**International Migration – *****Net International Movement, Emigration, Movement from Puerto Rico***
**Change in Group Quarters (GQ) Population**
**Net International Military Movement**

**The Components**

## The Questions

-  How much does each component influence the estimates?
- For how many counties is each component the most influential?
- How much more influential is the top component than the second component?
- How much decline in accuracy is there if you make estimates omitting a component?

## Measurement of Component Impact

- Component total April 1, 2000- July 1, 2003 as a percent of Census 2000 Population
- Use sum of annual **absolute** component
*(This is important for Internal Migration, Group Quarters Change, Natural Change, since positive and negative values are both common.)*

## Internal Migration is the largest county component.

- Internal Migration, 3.2%

- Natural Change, 1.4%

- International Migration, 0.5%

- GQ Change, 0.2%

***Percents are sum of absolute component, April 1, 2000-July 1, 2003 of Census 2000 Population***

## Internal Migration is the top component in most counties.

- Internal Migration, 2,517

- Natural Increase, 512

- International Migration, 70

- GQ Change, 42

*Number of Counties where Each Component is Top*

***Components are April 1, 2000-July 1, 2003 ***

## Internal Migration and Natural Change are first or second in most counties.

- Internal Migration, 3,003

- Natural Increase, 2,667

- International Migration, 436

- GQ Change, 164

*Number of Counties where Each Component is Either First or Second*

***Components are April 1, 2000-July 1, 2003 ***

## Internal Migration, GQ Change, are further ahead of the next component, when they are top.

- Internal Migration, 2.4%

- Natural Increase, 0.8%

- International Migration, 0.5%

- GQ Change, 2.2%

***Percents are the average difference between the top component and the second component***

***Components are April 1, 2000-July 1, 2003 ***

## Counties where International Migration is the top component are largest, where GQ change is top they are smallest.

*Military Movement is never the top component*

***Components are April 1, 2000-July 1, 2003 ***

## Evaluation – How does omitting a component affect the accuracy of the county estimates for April 1, 2000?

- Approach – Reproduce April 1, 2000 Postcensal Estimates five times – each set of estimates omits one of the components.
- Compare Mean Absolute Person Error (MAPE) for Each set with that for the original set of estimates
*All estimates are controlled to the existing national total estimate.** *

## Leaving out the Internal Migration has the most effect on the April 1, 2000 County Estimates.

***PostCensal April 1, 2000 Estimates vs. Census 2000 Results***

## Leaving out the Internal Migration has the most effect...	Increase in MAPE

***PostCensal April 1, 2000 Estimates vs. Census 2000 Results***

## When Internal Migration is omitted, increase in MAPE is largest for moderately large counties.

*6.3% Increase in MAPE!*

## Increases in MAPE by Size for Other Omitted Components

*Lack of Natural Change affects smaller counties*

*GQ Change affects these medium counties*

*International Migration affects large counties*

*Military Movement not shown since all values are 0*

## Leaving out Internal Migration affects the faster growing counties more...

## Increases in MAPE by Growth for Other Omitted Components

*Military Movement not shown since all values are 0*

## Conclusions

**Of the five components of population change, net internal migration is the largest average percentage of county population. Natural Change is second.**
**Net internal migration is the top component in over 80 percent of counties.**
**When internal migration is the top component, it is ahead of the second component by an average of 2.4 percentage points. When GQ Change is top, it is ahead by 2.2 percentage points.**
**When estimates are produced omitting net internal migration, the Mean Absolute Percent Error increases by over 5 percentage points. When other components are omitted, the increase is much less.**