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DEMOGRAPHICS HOME > POPULATION ESTIMATES
Methodology
The Demographics & Workforce Section of the University of
Virginia’s Weldon Cooper Center is the agency responsible for producing
the Commonwealth’s official population estimates for its counties and
independent cities.
The population estimates are produced annually for each non-census
year. This document explains the data required to make the estimates
and the methodology used to generate them.
What is a Population Estimate?
Although population estimates and population projections are both
attempts to measure the size of a population, they are actually quite
different.
Population projections look to the future. They aim to produce a number
that represents the population size one, five, ten, or twenty years
from now. As a result, projected quantities like births, deaths, and
net migration are an integral part of making a projection.
Population estimates look to the present or the recent past. They are
usually much more accurate than projections because they make use of
current indicators of population growth and change—data like births or
licensed drivers—that are direct measurements, usually derived from
government agency records. The range of statistical methods that can be
used to make estimates is consequently greater than the methods
available to produce projections.
The three most widely used estimating methods are the tax return
method, the housing unit method, and ratio-correlation. The Census
Bureau uses the tax return method to develop its county/city series and
the housing unit method to develop its town series. (In the process of
generating the town estimates, the Bureau also generates
housing-unit-method estimates for counties and independent cities.
These were released to the public for the first time in 2003.) The
Weldon Cooper Center uses the third method, ratio-correlation, since
this method has proven to be more accurate than the other two in
estimating the population of Virginia localities.
Data Requirements
1. The sum of personal and dependent exemptions on state tax returns in
the estimating and base years (the base year is the most recent census
year), obtained from the Virginia Department of Taxation.
2. A sum of births in the estimating and base year and the two years
preceding each, obtained from the Virginia Department of Health, Center
for Health Statistics. A multi-year sum of births is used because
births vary from year to year, and a three-year sum tends to even out
some of this random variation.
3. Public school enrollment in grades 1–8 in the fall of the year
preceding the estimating and base years. Public school figures are for
fall (September 30) membership and are obtained from the Virginia
Department of Education.
4. The number of licensed drivers in the estimating and base years, obtained from the Department of Motor Vehicles.
5. The housing stock in the estimating year. The housing stock is
estimated by adding cumulative building permits together with an
estimate of the number of mobile homes to the base year housing unit
counts. Building permits are obtained from the Bureau of the Census’
Construction Division and, in the case of missing data, from the
localities themselves. Mobile home data are derived from 2000 Census
counts and Division of Motor Vehicle figures.
6. The civilian group quarters population. The group quarters
population is made up of persons permanently or quasi-permanently
residing in institutions with populations of approximately 50 or more.
Included are long-term health care facilities, correctional
institutions, and residents of college and university dormitories The
data are obtained from a variety of sources, including the Virginia
Department of Corrections (prisons), the State Compensation Board
(jails), the Department of Juvenile Justice (juvenile detention
facilities), and the institutions themselves (dormitory populations).
The Ratio–Correlation Method
The ratio-correlation method uses a prediction equation generated by
multiple-regression analysis, a statistical technique that measures the
relationship between one or more indicator variables (X’s, or
independent variables, or exogenous variables) and a dependent variable
(Y). For use in estimating the population, a new equation is generated
once every ten years, using the Census Bureau's decennial census
population count as the dependent variable. This equation takes the
form:
Estimated Y = b1(X1) + . . . + bn(Xn) + C
where each b is a regression coefficient, each X is an indicator
variable, C is a constant, and Estimated Y is the dependent variable.
These variables are used in the equation in a double ratio form, in
which each locality's share of the state total in the estimating year
is compared to its share of the state total in the base year (the year
in which the equation was developed). For example, in producing an
estimate for 2006, the form of the births indicator is:
[(2006 locality births) / (2006 state births)]
divided by
[(2000 locality births) / (2000 state births)]
where "births" in the numerator are the sum of 2004-2006 and "births"
in the denominator are the sum of 1998-2000. It is because all the
variables in the multiple-regression equation are expressed as ratios
of ratios that the method is called the "ratio" correlation.
These double ratios actually measure change in the locality’s share of
the state total for the indicator and are the major diagnostic
indicator when a question about why an estimate has risen or fallen
arises. A double ratio under 1.0 indicates that the locality’s share of
the state total for that variable has fallen; a double ratio over 1.0
indicates growth in that variable.
The double ratios are also a major diagnostic tool for evaluating
errors, either in procedure or, more often, in the data. Each time the
estimates are produced, the 134 series of five ratios (one set for
every county and city) is reviewed for any instance where one or more
of the double ratios seem out of line with the others. In each such
case the input data is checked, first against the Cooper Center’s own
records, then with the data provider. If neither yields a satisfactory
answer, Weldon Cooper staff contact the locality for clarification.
The current indicator variables and their coefficients are:
Estimated housing stock
State tax return exemptions
Three-year sum of births
Public school enrollment
Licensed drivers
Constant (intercept)
| 0.429
0.172
0.083
0.214
0.163
-0.064
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After multiplying each of the double ratios by its coefficient and
adding the constant, mathematical adjustments are made to allow for the
time elapsed between the base year and the estimating year. The
resulting estimate is not a population figure; rather it is the
percentage of the state's total non-institutional population that will
be allocated to the locality. These percentages are adjusted to equal
100%, and the adjusted percentages are applied to the state’s total
population to yield a non-group quarters, or household, population
estimate.
The final step in producing an estimate is the addition of the
institutional population to the estimated household population to
obtain an estimate of the total population.
It is extremely important to understand that ratio-correlation does not
involve a one-to-one correspondence between each indicator variable and
the population estimate. That is, a coefficient of 0.214 in no sense
indicates that for every student in grades 1-8, 0.214 of a person will
be added to the estimate. Similarly, although it may seem that each
person in the institutional population constitutes one person in the
estimate, this is not the case. Because the equation is derived using
the base year non-institutional population, the amount of change in the
institutional population between the base and estimating years is
actually more important than the numbers themselves.
The Housing Unit Method
The Cooper Center's 2006 final and 2007 provisional estimates, as well
as onward estimates up to 2010, are prepared by combining
ratio-correlation estimates with a new series of estimates derived from
the housing unit method. This approach incorporates the Cooper Center’s
newest research on estimates methodology, which was funded by the U.S.
Census Bureau in 2007.
The housing unit method of estimating post-census population is
straightforward. In order to make a current population estimate, four
data items are required, each of which is estimated for July 1 of the
estimate year: (1) the current housing stock, (2) the occupancy rate
(3) the average number of people living in each occupied unit, and (4)
the number of people living in group quarters. The household population
is derived by multiplying total housing stock by the occupancy rate and
by population per occupied housing unit. An estimate of the group
quarter population living in the locality is added to the household
population estimate to produce the estimate of the total population.
The housing unit estimates for all Virginia localities are then summed,
and raked to the state control total. Finally, ratio-correlation
based estimates and housing unit based estimates are evaluated and
averaged to produce the most accurate population estimate series.
The State Control
The state control is an estimate of the entire state’s population in
the estimating year. The current model uses the most recent Census
Bureau estimate available at the time the locality estimates are
produced.
Census Bureau Estimates and Weldon Cooper Center Estimates
The Census Bureau’s population estimates are currently produced by a
method that in some cases yields very different results from those
produced by the Weldon Cooper Center. The Census Bureau uses a
component estimating methodology. It involves updating the population
from the date of the last census with births, deaths, and an estimate
of net migration derived from a matched sample of federal income tax
returns. Due to federal confidentiality requirements these tax data are
administratively restricted to use by Census Bureau personnel.
Provisional vs. Final Estimates
Ordinarily the difference between provisional and final estimates for a
given year are produced by differences in both the data inputs and the
state total. First, at the time the estimates are generated, final
figures for births, housing permits, and state tax returns are
unavailable and must themselves be estimated. Thus, provisional
estimates are just that—population estimates that are made from several
estimated data series. Second, the Bureau of the Census periodically
revises the state total, and each of the estimates uses the most recent
total. As a result, the state totals used for provisional and final
estimates almost always differ.
As a result of both these factors, the provisional estimates, though more timely than the final ones, are less accurate.
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