OVERVIEW OF CALIFORNIA'S COUNTY POPULATION

ESTIMATING METHODS

by Melanie Martindale, Ph.D.

Demographic Research Unit

California Department of Finance

[Summary of Current Practice]{.underline}

In the 1990s California has estimated county population proportions
twice yearly, using three of four methods at each estimate date (January
1 and July 1). All estimates are benchmarked on 1990 decennial census
counts. The unweighted algebraic mean of the three estimated
distributions is calculated to produce a final proportionate
distribution that is applied to the independently estimated state
control to derive a final set of population estimates for the state's 58
counties. Multiple methods are used to estimate change in county
population, because no one method for estimating postcensal county
population has shown itself superior in terms of consistency, acceptable
accuracy and minimum bias, taking into account methods' requirements of
data type, availability, coverage and timeliness.

The four methods used are: (1) the Tax Return method; (2) the
Ratio-Correlation method; (3) the Household method; and (4) the Driver
License Address Change (DLAC) method. All four methods, with
modifications and in various incarnations, have been used in California
over many years. The DLAC and Ratio-Correlation methods are used for
county population proportion estimation biannually, while the Household
method is used in January and the Tax Return method, in July. It should
be emphasized that, regardless of the strengths and weaknesses of the
various county estimating methods, they produce remarkably similar
estimated proportions for most California counties for most estimating
periods. Estimated proportionate distributions, converted to percents,
for July, 1998 estimates and January, 1999 estimates are shown in Tables
1 and 2.

[Tax Return Method]{.underline}

This component method, formerly know as the Administrative Records
method, has been extensively described and evaluated in various
publications by the Census Bureau and other researchers and is familiar
to all of us here. A current description of it is available on the
Internet at the address cited in the attached list of references.
California uses the state and county population estimates generated by
this method to derive a proportionate distribution of county population.
This proportionate distribution is one of the three estimated
distributions of county proportions that are averaged and applied to the
independently estimated state population to produce the July 1 county
estimates.

In the July, 1998 estimates, the mean absolute difference between the
Tax Return method's estimated county proportions (converted to percents)
and those of the Ratio-Correlation method was about two hundredth's of
one percent. The same comparison between results of the Tax Return
method and the DLAC method shows a difference very close to eight
hundredth's of a percent. The mean absolute difference between estimates
of the Ratio-Correlation and DLAC methods also was an average absolute
percent difference of almost eight hundredths of a percent (see Table
1).

If one looks at July, 1998 results of each method county by county, one
finds that the county proportion estimated by the Tax Return method was
the highest of the three estimated proportions for 19 (33 pct.) of the
58 counties. For the same date, Ratio-Correlation estimated the highest
of the three proportions for over half (34, 59 pct.) of the counties,
while DLAC produced the highest estimated proportion for only five
counties --Glenn, Los Angeles, Monterey, San Francisco and Santa Clara.
In this decade, all of these counties but Glenn have experienced
relatively high annual estimates of net immigration, though other
counties also have relatively high levels (e.g., Fresno; Orange). As can
be seen in Table 1, the relatively high DLAC estimate for Los Angeles
county is the major factor accounting for the small number of counties
whose highest proportion was estimated by this method.

While a general assessment of the Tax Return proportions and
proportionate change over the last few years seems to indicate that the
method 'lags' in capturing relatively rapid population change (e.g.,
'turnaround' counties), this appears to result from differences in
timeliness of some of the data used in this method. However, extended
analyses of this impression have not yet been completed.

[Ratio-Correlation Method]{.underline}

Since its introduction in 1911, this method and its related versions
have come to be among those most widely used to estimate a variety of
demographic values. This methodology and its variants have also
stimulated some of the most diverse and interesting literature on
population estimation. Though at present California uses it to estimate
relative change in county household population share semiannually, in
the past we also used at least two versions of it to estimate net
civilian migration as a proportion of total civilian population.

Formally, the method is used to estimate observed intercensal change in
household population (e.g., proportionate change from 1980 to 1990) as
an hypothesized function of observed relative change in one or more
indicators. Several models may be tested to determine the indicators
that are most effective in 'explaining' the intercensal population
change. The final model's indicator change coefficients are then built
into the postcensal ratio-correlation model to be used. Clearly, the
assumption is that the multiple relationships between indicators and
dependent variable continue to hold throughout the postcensal estimating
period. In deriving a model for post-1990 use, California related 13
indicator variables to 1980-1990 household population change. These
variables included state income tax returns, driver licenses, registered
automobiles, residential electric customers, nonagricultural employment,
occupied housing units, births, deaths, births + deaths, school
enrollment grades 1-8, registered voters, taxable sales and civilian
labor force.

The quite familiar basic form of the multiple regression equation
estimated postcensally is:

> n

y= α + ∑ β~i~x~i~ + ε

i=1

As a result of our tests, a combination of three variables best
'explained' 1980-1990 relative change in household population. These
three indicators\-- driver licenses, school enrollment grades 1-8 and
civilian labor force \-- are used in a model that data availability
permits us to estimate twice yearly. The current realized estimating
equation is

∆ Propor HHPOP~90\ to\ 99~ = 0.122694 + 0.491381 \[99/90 ratio, Driver
License proportions\]

\+ 0.249044 \[99/90 ratio, Elem Enroll proportions\]

\+ 0.116426 \[99/90 ratio, Civ Labor Force proportions\]

We add in group quarters (residents of barracks and ships on military
installations; inmates and staff residents of state and federal prisons;
college dorm residents and other local group quarters counts) in
deriving the final county proportions of total state population.

Calculations from our July, 1998 estimates show that the mean absolute
difference between county proportions (converted to percents) estimated
by the Ratio-Correlation method compared to the Tax Return method was
two hundredths of a percent, and compared to the DLAC method, about
eight hundredths of a percent (Table 1). In January, 1999 the mean
absolute percent difference between Ratio-Correlation and DLAC method
estimates was slightly over eight hundredths of a percent, while that
between Ratio-Correlation and Household methods was slightly over two
hundredths of a percent (Table 2).

Other researchers have used the difference-correlation version of this
method with varying degrees of success. In the past, California's final
county estimating equation for changes in household population contained
more than three variables of those tested (as noted above). In contrast,
our past versions for estimating net civilian migration as a percent of
civilian population included only two variables each: (a) one model used
percent change in occupied housing units and percent change in school
enrollment grades 3-8 compared to the prior year's grades 2-7
enrollment, while (b) the other version used percent change in
residential electric customers and the enrollment change variable of
(a).

For the future, California is considering averaging the results of
simple linear estimates that relate indicators individually to
proportionate change in both total and household population, and
comparing these results to various multiple regression models. We also
are exploring testing a couple of models that use information on 10-year
estimated change transformed into annual change factors that
hypothetically apply postcensally.

Though the strengths and weaknesses of the various forms of this model
are generally well known, there is a need for more states to test
various versions of these models using proposed corrections and
modifications already identified in the research literature (for some
titles, see the appended bibliography). Of as much concern to California
as assumptions inherent in applying this version of a multiple
regression model (e.g., temporal stability in the relationships among
the model variables) is the continued availability of good quality and
timely candidate indicator variables for testing and estimation. Partly
this results from researchers' greater ability to devise adjustments for
model, as opposed to model input, flaws (e.g., Swanson and Tedrow's
correction for temporal inconsistency), and partly from our inability to
stem erosion in administrative and other records we need to measure
population change. For example, our ability to obtain high-quality
school enrollment data can be compromised by presence of known but
uncountable overcovered elements (e.g., starting in 1999, incarcerated
persons bused to school programs are now included in both reported
district-level enrollment and in prison counts in California) or
inflated/deflated county counts due to computer ghosts (enrollment that
is inflated/deflated by *computer commuters*: those who actually live in
other counties but are counted as enrolled in one or more counties
providing computer-based education under a state-approved contract).

Other concerns, many technical, surround candidate indicator variables.
For example, though using annual averages of civilian labor force
estimates softens error effects somewhat, there is no question that
estimates for some of the counties would appear to be rather
problematic. However, continuing improvements in BLS techniques for
producing substate estimates and the fact that DRU uses both a relative
change model and annual averages somewhat mitigates the problems of
using monthly substate survey estimates. Driver license data in
California continue to improve, though occasional problems with lags in
the return and processing of surrendered licenses from out of state
arise. However, note that this model uses total driver licenses by
county, not driver license address change data. We will return to this
later.

[Household Method]{.underline}

This method is based in the Housing Unit method, probably the most
frequently used method for population estimation. California uses a
county model each January that features estimated proportionate change
in household population plus current group quarters to derive a final
proportionate distribution for total county population. The input data
for the county model are current estimated households (occupied housing
units), derived separately for cities and for unincorporated parts of
counties using the Housing Unit method approach to estimating number of
households. Proportionate change in these estimated occupied housing
units since the 1990 census is used to estimate change in the county
distribution of household population in the county model, which is
benchmarked to the 1990 census distribution of household population and
uses an independent current estimate of the state's household
population.

For each jurisdiction in each county, households=occupied housing units
are determined as follows:

> HH~t~ = HU occup~t~ = (HU~c~ + lagged BP~t~ - D~t~ +/-
> Conversions~t~ + Final inspections~t~ + Annexed units ~t~ - Deannexed
> units~t~) OCC~t~

where HU~c~ are housing units counted in the census, BP~t~ are permits
appropriately lagged for single- versus multi-unit structures and
including mobile unit placements since the last census, D~t~ are
demolitions since the last census, conversions are units both gained and
lost through structural modification since the last census, final
inspections are reported and verified new units in place since the last
census, annexed and deannexed units are those added to or taken from a
jurisdiction since the last census, and OCC~t~,~.~ the most recent
occupancy rate. As a practical matter, DRU completes this assessment
each year for each jurisdiction. No adjustment is made for permitted
construction that is not built (this contrasts with the Bureau's
distributive housing unit method that assumes 2 percent of permitted
units are not built). Also, the Demographic Research Unit undertakes an
annual data collection to obtain information on the status and occupancy
of residential housing stock on military installations.

As is well established, Housing Unit method results are a direct
function of the accuracy and completeness of the data used. Though DRU
annually collects information from all cities and unincorporated county
jurisdictions on demolitions, conversions, annexations, deannexations
and group quarters change, our impression is that the quality of
demolition information we receive has deteriorated since the Census
Bureau's C-404 monthly data collection program ceased collecting
information on demolitions. The local areas appear to have gotten out of
the habit of tracking this information since they no longer are required
to report it monthly. We have not yet quantified the suspected affects
of this on the Housing Unit method estimates.

As noted above, the Household method yielded the highest of the three
proportions estimated for half the counties (29; 50 pct.) in the last
January estimates series (see Table 2). The mean absolute difference
between this method's estimated county proportions (in percents) and
those produced by the Ratio-Correlation method was slightly over two
hundredths of a percent, and by the DLAC method, slightly over seven
hundredths of a percent.

[DLAC Method]{.underline}

The Driver License Address Change (DLAC) method was developed in the
1970s as a cohort-component model to estimate state population, then
modified for counties. The current model accounts for both interstate
and intrastate migration. In broad outline, the method estimates changes
in county population proportion as a function of changes in various data
series for three age groups: population under 18, population ages 18-64
and population 65 and over.

[Population 65 and Over.]{.underline} The change in the population 65
and over is indicated by changes in Medicare enrollees. Note that
theoretically this change comprehends migration change. However,
practical aspects (information availability, affordability of monthly
costs for nonqualifying enrollees) of Medicare enrollment for an
increasing number of the foreign-born population aged 65 and over makes
reliance on Medicare data for this population group potentially
problematic. We in California feel that Medicare enrollee change
underestimates change in the population 65 and over. Comparisons of
Medicare counts to estimated and projected population 65 and over appear
to indicate a coverage problem for the California Medicare file
concerning its utility to estimate the population 65 and over (in the
last two years in particular).

[Population Under 18.]{.underline} The population under 18 is estimated
using information on the survived school-age cohort from the 1990
census, school enrollment change benchmarked on the 1990 census
school-age population, and appropriate cohorts of births since 1990
survived from birth to grade 1, and survived into successive grades each
succeeding year, and adding a new cohort survived from birth to grade 1
each year beginning in 1996. Deaths under age 18 are included. As noted
in the section on the Ratio-Correlation method, we will be monitoring
California school enrollment data closely. More research is needed on
identifying flaws in secondary enrollment data and methods to improve
their utility.

[Population 18-64.]{.underline} The non-group quarters population aged
18-64 is separately estimated from the group quarters population in
military installations, state and federal institutions, college dorms
and other types of group quarters. The non-GQ portion of this cohort is
survived since the decennial, deaths are taken out and the several types
of migration are estimated. These include domestic interstate and
intrastate migration, legal immigration, undocumented migration and
emigration. Interstate and intrastate flows using driver license address
change data by county for ages 18-64 are derived from information
provided by the California Department of Motor Vehicles monthly. Because
of lags in the return of surrendered California licenses to our DMV by
other states, DRU ratio adjusts DLAC outflow data to IRS-based outflow
data after both sets of data have been adjusted up to correct for
persons without licenses who move and persons underrepresented in
exemptions data, respectively. Any bias is in the direction of
overstating domestic outmigrants as represented by the actual data.
Backlog of unprocessed surrendered licenses at our DMV is reported to
DRU monthly. Our assessment of the system is that it functions
reasonably well, though periodic administrative communications among
state compact members is required to keep the surrendered licenses
flowing back to the origin states.

Other migration data used are annual INS data by county for legal
immigrants aged 18-64, a statistical estimate of emigration by county
that is a fraction of legal immigration into the county over the last
five years, and a fixed value for each county of the state's total
undocumented population (given the most recent INS estimate) based on
research showing the estimated distribution of undocumented migrants by
California county.

We feel that both strengths and weaknesses of this method of estimating
county population proportion resides in the timeliness and quality of
the input data, as is usually the case for a component method. Because
the state's vital statistics data are quite reliable as to coverage
(totals) and geographical coding of vital events, most attention has
focused on data used to estimate the types of migration. For legal and
other immigration events, California relies on INS information and the
best research on undocumented stocks. The statistical estimate of
emigration is based on Social Security Administration research on rate
of return and other emigration by previous legal immigrants over
successive 5-year periods. The county proportion of emigrants is a
fraction of its prior legal immigrants.

Our experience in estimating domestic migration using DLAC data has been
reasonably good in the 1990s, a particularly difficult period for
estimating domestic migration events in California. We have integrated
net intrastate migration into the model using the DLAC data but plan to
do more research to refine this aspect of it. As is generally known,
licenses in the state are up for renewal every four years. Though data
processing turn-around has improved since the DLAC model was first put
in place, it remains true that people moving within the state have no
strong incentive to report address changes, though previous research
indicates that about 85 percent do so within a year of moving. We will
be exploring the need for updated research on time lags in
address-change notifications by intrastate migrants and local movers. We
anticipate no changes in the interstate compact of agencies that have
agreed to return surrendered licenses to the issuing state and a
continuation of research to monitor coverage and the need for
adjustments such as those currently used.

The great strength of the DLAC model is its ability to capture an
important subset of very recently occurring migration events, though
with obvious coverage flaws. The method depends upon administrative
records and other data that have excellent coverage, high quality, and
timeliness. We plan to expand efforts to identify changes in coverage
and quality in some of the data used (for example, as noted in the
section on the population 65 and over).

[Conclusion]{.underline}

Overall, we feel that the performance of our county estimating models
has been reasonably good and generally predictable year to year during
the 1990s, though we have noticed that during the mid-decade period of
rapid population change, where a heavy outflow was followed fairly
rapidly by a reversal of flow, all based on economic changes, even
'current' models may not pick up distributional change as quickly as one
would like. This is probably in the nature of the beast, but certainly
our research plans will include not only evaluations of the quality and
coverage of all major data used, but also reassessments of indicators
used in the past but discarded for one or another reason. We also are
working to locate new data types and sources as well as assessing
alternative uses for existing data (this would include new ways of
evaluating data as well as using them directly in an estimating model).
For example, California state income tax exemptions changes are
fruitfully being used in background analyses though no longer used
directly in the ratio-correlation model.

In anticipation of continued use of both the DLAC and Ratio-Correlation
models to estimate county population proportions, we have plans to test
several indicator variables that have been used currently or in the past
and whose quality and availability make them candidates, as already
noted. Our final plans will certainly include promising new methods and
ideas for data use that come from this conference and the continued work
of the Post-2000 Estimates Committee.

**Current and Historical County Population Estimation: Selected
Bibliography**

**[Tax Return Method]{.underline}**

Judson, D.H., C.L. Popoff, and M.J. Batutis. "An Administrative Records
Approach to Evaluating the Accuracy of Census Estimation Methods." Paper
presented at the 6^th^ International Conference on Applied and Business
Demography, Bowling Green State University, Bowling Green, Ohio,
September 19-21, 1996.

US Bureau of the Census. "Methodology for Estimates of State and County
Total Population." Revised 1/10/97. Available at
h*ttp://www.census/gov/population/methods/stco.txt.*

**[Ratio-Correlation Method]{.underline}**

Ericksen, Eugene P. "A Regression Method for Estimating Population
Changes of Local Areas." [Journal of the American Statistical
Association]{.underline} 69(348) (December 1974): 867-879.

Mandell, Marylou and Jeff Tayman. "Measuring Temporal Stability in
Regression Models of Population Estimation." [Demography]{.underline} 19
(1982): 135-146.

Namboodiri, N.K. "On the Ratio-Correlation and Related Methods of
Subnational Population Estimation." [Demography]{.underline} 9 (1972):
443-453.

Namboodiri, N.K. and N.M. Lalu. "The Average of Several Simple
Regression Estimates an Alternative to the Multiple Regression Estimate
in Post Censal and Intercensal Population Estimation: A Case Study."
[Rural Sociology]{.underline} 36 (1971):187-194.

Schmitt, R.C. and A.H. Croscetti. "Accuracy of the Ratio-Correlation
Method for Estimating Postcensal Population." [Land
Economics]{.underline} 30 (1954): 279-281.

Snow, E.C. "The Application of the Method of Multiple Correlation to the
Estimation of Post-Censal Populations." [Journal of the Royal
Statistical Society]{.underline} 74 (May 1911): 575-620.

Swanson, D.A. and L.M. Tedrow. "Improving the Measurement of Temporal
Change in Regression Models Used for County Population Estimates."
[Demography]{.underline} 21(3)(August 1984): 373-381).

Zitter, Meyer and H.S. Shryock. "Accuracy of Methods of Preparing
Postcensal Population Estimates for Local Areas."
[Demography]{.underline} 1 (1964): 227-241.

9

**[Household/Housing Unit Method]{.underline}**

Smith, Stanley K. "A Review and Evaluation of the Housing Unit Method of
Population Estimation." [Journal of the American Statistical
Association]{.underline} 81(394) (June, 1986): 287-296.

Smith, Stanley K. and Scott Cody. "Evaluating the Housing Unit Method: A
Case Study of 1990 Population Estimates in Florida." [APA
Journal]{.underline} (Spring, 1994): 209-221.

**[Evolution of DLAC Method]{.underline}**

Rasmussen, W.N. "The Use of Driver License Address Change Records for
Estimating Interstate and Intercounty Migration." in I[ntercensal
Estimates for Small Areas and Public Data Files for
Research,]{.underline} Small Area Statistics Papers Series GE-41, No. 1.
Washington, DC: U.S. Bureau of the Census, May, 1975, pp. 16-22.

**[Multiple Methods]{.underline}**

Hollman, Walter and W.N. Rasmussen. "A Comparison of Four Methods of
Estimating County Population with Mid-Decade Census Results, Selected
California Counties." Paper presented at the Annual Meeting of the
Population Association of America, Montreal, Quebec, April, 1976.

Lee, Everett S. and Harold F. Goldsmith (eds,). [Population Estimates:
Methods for Small Area Analysis.]{.underline} Beverly Hills: Sage, Inc.,
1982.

National Research Council. [Estimating Population and Income for Small
Areas.]{.underline} Washington, DC: National Academy Press, 1980.

Office of Management and Budget. Statistical Policy Office. Federal
Committee on Statistical Methodology. Subcommittee on Small Area
Estimation. [Indirect Estimators in Federal Programs.]{.underline}
Statistical Policy Working Paper 21. Washington, DC: OMB, July 1993.

Smith, Stanley K. and Marylou Mandell. "A Comparison of Local Population
Estimates: the Housing Unit Method vs Component II, Ratio Correlation
and Administrative Records." Paper presented at the Annual Meeting of
the Population Association of America, San Diego, California, April
29-May 1, 1982. Also published in [Journal of the American Statistical
Association]{.underline} 79(386)(June 1984): 282-289.

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