EVALUATING THE HOUSING UNIT METHOD:

A CASE STUDY OF 1990 POPULATION ESTIMATES IN FLORIDA

Stanley K. Smith

and

Scott Cody

Bureau of Economic and Business Research

University of Florida

Gainesville, Florida 32611

BIOGRAPHICAL SKETCH

Stanley K. Smith is a Professor of Economics and Director of the Bureau
of Economic and Business Research at the University of Florida. Scott
Cody is a research demographer at the Bureau. Smith and Cody produce the
official state and local population estimates used by the State of
Florida for revenue-sharing, planning, and budgeting.

**ABSTRACT**

The housing unit (HU) method is the most commonly used approach to
making small-area population estimates in the United States. This study
evaluates the accuracy and bias of HU population estimates produced for
counties and subcounty areas in Florida for April 1, 1990. The major
findings are that population size has a negative effect on estimation
errors (disregarding sign) but no effect on bias; growth rates have a
U-shaped effect on estimation errors (disregarding sign) and a negative
effect on bias; electricity customer data provide more accurate
household estimates than do building permit data; errors in household
estimates contribute more to population estimation error than do errors
in estimates of average household size or group quarters population; and
the application of professional judgment improves the accuracy of purely
mechanical techniques. We believe the HU method offers a number of
advantages over other population estimation methods and provides
planners and demographers with a powerful tool for small-area analysis.

**EVALUATING THE HOUSING UNIT METHOD:**

**A CASE STUDY OF 1990 POPULATION ESTIMATES IN FLORIDA**

**Introduction**

Postcensal population estimates for states and local areas are used for
a wide variety of purposes in the United States. They form the basis for
the distribution of billions of dollars of federal, state, and local
government funds. They determine boundaries and representation for city
councils, county commissions, school boards, and other political
entities. They are used for planning when and where to build new
schools, roads, hospitals, banks, electric power plants, and shopping
centers. They provide an important tool for marketing a wide variety of
goods and services, and even determine the salaries of some public
officials. Clearly, there is a profound need for accurate and timely
postcensal population estimates.

Several different methods can be used to make population estimates (see
Murdock and Ellis 1991; National Research Council 1980; and Rives,
Serow, Lee, and Goldsmith 1989). At the substate level, the HU method is
by far the most commonly used (U.S. Bureau of the Census 1983, 1990).
This method is widely accepted because it can use a variety of data
sources and estimation techniques, can be applied virtually everywhere,
and can produce reasonably accurate estimates. Given its widespread use
and the importance of population estimates for many types of planning
and budgeting, it is essential to evaluate the performance of the HU
method from time to time.

This article provides such a critical evaluation. It focuses on April 1,
1990 population estimates for counties and subcounty areas in
Florida.[^1] It evaluates estimation errors by size of place and rate of
growth, by component (i.e. households, persons per household, and group
quarters population), and by technique. It calculates the contribution
of each component to overall estimation error, considers the role of
judgment in producing population estimates, and compares the performance
of 1990 estimates with that of 1980 estimates. It confirms some results
that have been found before and reports others that are new. Although
this study focuses on Florida, it provides insights into the HU method
that will be useful in a much broader context.

Many planners have used the HU method to produce small-area population
estimates; others have used similar concepts, data sources, and
techniques for analyses of fiscal impacts (e.g., Burchell and Listokin
1978), residential mobility (e.g., Varady 1984), age structure (e.g.,
Myers and Doyle 1990), household size (e.g., Gober 1990), and housing
demand (e.g., Myers 1987). Planners have thus been intimately involved
in developing the HU method and extending its application into new
areas. We believe the present study will help both planners and
demographers make more effective use of this increasingly important tool
for small area analysis.

Demographers typically distinguish between population estimates and
population projections (or forecasts). Estimates refer to the present or
some time in the past, whereas projections refer to the future. In terms
of methodology, the primary difference between estimates and projections
is that estimates can be based on symptomatic data corresponding to the
date of the estimate, whereas projections cannot be based on such data;
rather, projections must be based on the extrapolation of past trends or
assumptions about future demographic change. In this article we focus
solely on population estimates.

**Brief Description of Methodology**[^2]

The foundation of the HU method is the fact that almost everyone lives
in some type of housing structure, whether a traditional single family
unit, an apartment, a mobile home, a college dormitory, or the state
penitentiary. The population of any geographic area can therefore be
calculated as the number of occupied housing units (households) times
the average number of persons per household (PPH), plus the number of
persons living in group quarters facilities (e.g., college dormitories,
prisons, military barracks) or without traditional housing (e.g., the
homeless):

P~t~ = (H~t~ PPH~t~) + GQ~t~ (1)

where P~t~ = total population at time t, H~t~ = occupied housing units
at time t,

PPH~t~ = average number of persons per household at time t, and GQ~t~ =
group quarters population at time t (including the homeless population).

This is an identity, not an estimate. If these three components were
known exactly, the total population would also be known. The problem, of
course, is that these components are almost never known exactly. They
must rather be estimated from various data sources, using one or more of
several possible techniques. In this section we provide a brief
description of the data and techniques used to estimate these three
components for counties and subcounty areas in Florida. More detailed
descriptions of the HU method can be found in Smith and Lewis (1980),
Rives and Serow (1984), and Smith (1986).

[Households]{.underline}. A number of different types of data can be
used to estimate households, such as building permits, certificates of
occupancy, electricity customers, telephone customers, property tax
records, and aerial photographs. The most commonly used types of data
are building permits and electricity customers (U.S. Bureau of the
Census 1983), since they are widely available and correlate closely with
population change. These are the data sources we use in Florida.

The housing inventory for a city or county can be estimated by adding
building permits issued since the most recent census (net of
demolitions) to the units counted in that census. Building permit data
are available from the U.S. Department of Commerce, which collects them
directly from cities and counties throughout the United States.[^3] The
time lag between issuance of permit and completion of unit is assumed to
be three months for single family units and ten months for multifamily
units; these assumptions are based on surveys of developers in Florida.
For mobile home units, there is no time lag. Although building permit
data are not available everywhere, it has been estimated that
approximately 90 percent of new housing units in the United States are
built in areas requiring building permits (Siskind 1980). In Florida,
building permit data are available in 82 percent of the subcounty areas
for which we produce population estimates; these areas contain 90
percent of the state\'s population.

Combining building permit data with housing data from the decennial
census provides an estimate of the current housing stock. The next step
in the process is to estimate the proportion of housing units occupied
by permanent residents. The most effective way to determine current
occupancy rates is to conduct a special census or sample survey. Given
their high costs, however, such censuses or surveys are rarely
conducted. A common procedure is simply to use the occupancy rates from
the most recent census (U.S. Bureau of the Census 1983). This is the
procedure we follow in Florida.

The product of the housing stock and the occupancy rate (preferably
performed separately for each type of housing unit) gives an estimate of
the number of households. There are several problems with this estimate.
Time lags between issuance of permit and completion of unit may vary
from place to place and from year to year. The proportion of permits
resulting in completed units is generally unknown. Occupancy rates may
be going up or down. Data for mobile homes may be non-existent or of
poor quality. Certificate-of-occupancy data can eliminate problems of
estimating time lags and completion rates, but not problems of
estimating current occupancy rates, demolitions, or conversions from one
use to another.

Our second source of data avoids some of those problems. Active
residential electricity customer data are available for all cities and
counties in Florida and are often of better quality than building permit
data. More important, households can be estimated [directly]{.underline}
from electricity customer data, avoiding the intermediate steps of
estimating time lags, completion rates, demolitions, conversions, and
occupancy rates. A number of studies have concluded that household
estimates based on electricity customer data are generally more accurate
than those based on building permit data (e.g., Starsinic and Zitter
1968; Smith and Lewis 1980, 1983; Rives and Serow 1984). We collect
electricity customer data from 54 electric power companies in Florida;
the five largest companies serve 81 percent of the state\'s population.

There are several ways to estimate the number of households from active
residential electricity customer data. One uses the net change in
customers as a measure of the net change in households (Starsinic and
Zitter 1968). However, a number of factors may prevent a perfect
one-to-one relationship between permanent households and residential
electricity customers: housing units occupied by seasonal and other
non-permanent residents; master meters serving more than one household;
separate meters for pumps, barns, and other non-housing uses; geographic
boundaries for utility companies that do not correspond exactly to those
used by the Census Bureau; and the bookkeeping practices of individual
utility companies. These differences can be accounted for by forming a
ratio of the number of households counted in the most recent census to
the number of customers reported for the same date, and applying this
ratio to the current number of customers. This approach has been found
to produce more accurate household estimates than the first approach
does (Smith and Lewis 1980, 1983). The ratio approach is the one we
follow in Florida.[^4]

Our final estimates of households are not based on the same data sources
and techniques for all places, however. Rather, we use our professional
judgment to decide which sources and techniques are likely to be most
reliable for each individual place. In a majority of places we use only
electricity customer data, but we occasionally adjust the
household/customer ratio to account for evidence of changes in seasonal
populations (e.g., shifts in the composition of the housing stock;
seasonal fluctuations in the number of active residential electricity
customers). When electricity customer data are of dubious quality and
building permit data appear to be good, we use only building permit
data. When the data sources differ substantially and it is not clear
which is better, we average the two. Our choices of data and techniques
are determined primarily by the consistency of the data series over
time, the presence (or absence) of gaps in the data series, and the
availability of additional evidence about data quality or demographic
trends. We believe the application of professional judgment provides
better household estimates than does the mechanical application of the
same data and techniques for all places. The next section offers some
evidence supporting this belief.

**[Persons per household]{.underline}**. The second component of the HU
method is the average number of persons per household (PPH). Although
trends nationally and in Florida have been toward steadily smaller PPH,
trends for local areas vary considerably from one place to another.
Between 1980 and 1990, PPH declined in all but two of Florida\'s 67
counties, with declines ranging from 0.9 percent to 11.4 percent. Values
of PPH for Florida counties in 1990 ranged from 2.18 to 3.00. Variation
in PPH levels and changes over time are even greater for cities than for
counties.

To estimate PPH for cities and counties, we developed a formula that
combines the local PPH calculated in the most recent census, the
national change in PPH since that census (as measured by the Current
Population Survey), and the local change in the mix of housing units
(single family, multifamily, mobile home) since the most recent census.
We base local changes in PPH on national changes, but adjust them up or
down depending on whether the initial PPH was higher or lower locally
than nationally; on the average, declines are greater when initial
levels are higher.[^5] We further adjust the estimates to account for
changes in the local mix of housing units and the PPH for each type of
unit calculated in the most recent census. (Multifamily units typically
have lower PPH than do single family units do).[^6] This formula is
described more fully in Smith and Lewis (1980). Again, we make some
adjustments to the formula\'s estimates according to our professional
judgment about factors affecting PPH (e.g., increases in the Hispanic
population, which has a relatively large PPH). PPH could also be
estimated by extrapolating past trends or holding values constant at
levels found in the most recent census (e.g., Starsinic and Zitter
1968). The formula described above, however, has been found to produce
more accurate estimates of PPH than either of these alternatives (e.g.,
Smith and Lewis 1980, 1983). We test several alternative estimation
techniques for PPH in the next section.

**[Group quarters population]{.underline}**. Population in households is
estimated by multiplying the number of households times the PPH.
Population in households accounted for 97.3 percent of total population
in the United States in 1990 (97.6 percent in Florida). To obtain an
estimate of total population, persons living in group quarters or
without traditional housing must also be estimated. We do this in three
steps. The first is to collect group quarters data from prisons,
colleges, military bases, and long-term health care facilities, for the
same date as in the most recent census. The second step is to subtract
these numbers from the total non-household population counted in that
census, and then to form a ratio of the residual to population in
households; we call this ratio the GQ multiplier. In the third step, the
current group quarters population is estimated by applying the GQ
multiplier to the current estimate of the household population, and
adding a direct count of the current number of persons residing in
prisons, college dormitories, military barracks, and long-term health
care facilities.[^7]

**Evaluating Accuracy and Bias**

The obvious question to ask of any estimation methodology is \"How
accurate are the estimates?\" We provide an answer to this question by
comparing April 1, 1990 population estimates with April 1, 1990 census
counts for counties and subcounty areas in Florida. This comparison
doesn\'t provide a perfect measure of accuracy and bias, because census
counts themselves are subject to error. Differences between estimates
and census counts may therefore reflect errors in the decennial census
as well as errors in the estimates. The decennial census is believed to
be quite accurate for most places, however, and provides a widely used
standard for evaluating population estimates. We refer to differences
between estimates and census counts as estimation errors, but the reader
is cautioned that they may have been caused by enumeration error as well
as by estimation error.

Five measures of accuracy and bias are used. Mean absolute percent error
(MAPE) is the average error when the direction of error is ignored. The
proportion of errors less than 5 percent and greater than 10 percent
indicates the frequency of relatively small and of large errors,
respectively. These are measures of accuracy, or how close estimates
were to census counts, regardless of whether the estimates were high or
low. Mean algebraic percent error (MALPE) is the average error when the
direction of error is included. This is a measure of bias: a positive
error indicates a tendency to overestimate, a negative error indicates a
tendency to underestimate. Since a few extreme errors in one direction
can change the sign of MALPE, the proportion of estimates that were
above the census count (%POS) is used as another measure of bias.

**[Errors by Population Size and Growth Rate.]{.underline}** Table 1
shows the results for Florida\'s 67 counties. The average error
(regardless of sign) was 5.4 percent. Weighted by population size, the
average error was only 3.0 percent, reflecting an inverse relationship
between size of place and size of error. The MAPE for counties with
fewer than 50,000 population was almost three times larger than the MAPE
for counties with more than 250,000 population. The proportion of small
errors generally increased with population size, and the proportion of
large errors generally declined. A negative relationship between
estimation errors and population size is a common empirical finding
(e.g., Kitigawa and Spencer 1981; Smith 1986; U.S. Bureau of the Census
1985).

**\[Table 1 about here\]**

The estimates had an upward bias. Almost three-quarters of the county
estimates were higher than the census counts, and the MALPE was 3.3
percent. The MALPE weighted by population size was 1.6 percent, the same
as the error for the state as a whole. There was no apparent
relationship between bias and size of place, however; the tendency to
overestimate was about the same for large and for small counties. An
explanation for the overall upward bias in the 1990 estimates will be
given later in this article.

Differences in county growth rates had a major impact on both accuracy
and bias. There was a U-shaped relationship between MAPEs and the growth
rate: errors declined with increases in growth rates through the first
five categories, but increased for the last category. Differences were
not large after the first two categories, perhaps because of small
sample sizes. There was also a strong relationship between growth rates
and the direction of errors: both the MALPE and %POS declined steadily
as the growth rate increased. Every county that lost population or grew
by less than 15 percent was overestimated, whereas every county that
grew by more than 100 percent was underestimated.

Table 2 shows the results for subcounty areas, which include 386
incorporated cities and the unincorporated balances of 66 counties. (One
county in Florida has no unincorporated area.)[^8] The average error
(regardless of sign) was 11.9 percent; weighted by population size, the
average error was 4.5 percent. There was again a strong negative
relationship between accuracy and population size; the MAPE for places
with fewer than 250 residents was 10 times larger than the MAPE for
places with more than 100,000 residents. The proportion of small errors
increased steadily with population size, and the proportion of large
errors declined.

**\[Table 2 about here\]**

Errors for subcounty areas were considerably larger than errors for
counties, primarily because of differences in population size. Only
eight counties had fewer than 10,000 residents in 1980, and none had
fewer than 5,000, whereas 304 subcounty areas had fewer than 10,000
residents and 101 had fewer than 1,000. For size categories greater than
10,000, errors for subcounty areas were very similar to errors for
counties.

As for counties, estimates for subcounty areas had a substantial upward
bias. The MALPE was 6.0 percent, and more than two-thirds of the
estimates were higher than the census counts. Again, there was no
distinct relationship between bias and size of place; rather, the
proportion of positive errors fluctuated inconsistently with population
size. Although the MALPE became smaller as population size increased,
this was due to smaller absolute percent errors, not to a declining
tendency to overestimate.

Errors were strongly affected by differences in growth rates. The MAPE
had a clear U-shaped relationship with the growth rate: errors were
large for places with negative growth rates, became smaller as growth
rates increased to 25-50 percent, and became larger as growth rates
increased further. Similar results were found for the proportion of
errors less than 5 percent and greater than 10 percent. Estimates were
thus most accurate for places with positive, moderate growth rates and
became less accurate as growth rates deviated in either direction from
these moderate levels.

This U-shaped relationship between errors and growth rates has been
reported before, both for population estimates (U.S. Bureau of the
Census 1985) and projections (Smith 1987). There are several possible
explanations for this finding: 1) Places losing population or growing
very rapidly are undergoing large compositional changes that are not
picked up in the data; 2) There is greater opportunity for estimates to
deviate from the actual population in places with very high (or
negative) growth rates; and 3) Errors in census coverage may be greatest
for places showing very high or negative growth rates. If so, the large
errors observed for those places would be due in part to
larger-than-average enumeration errors.

Bias was also strongly related to the growth rate: MALPE and %POS each
declined steadily as the growth rate increased. This reflects a strong
tendency to overestimate declining or slowly growing places and to
underestimate very rapidly growing places. It appears that the HU method
has difficulty picking up both the full extent of population decline for
places losing population and the full extent of population growth for
places growing very rapidly. Research on other methods is needed to
determine whether this is a general characteristic of population
estimates; we suspect that it is.

To account for possible interactions between population size and growth
rates, we divided subcounty areas into nine groups based on three size
categories and three growth rate categories. The results are shown in
Table 3. We again found accuracy to increase with population size:
within all three growth categories, MAPEs and the proportion of large
errors declined steadily as population size increased, while the
proportion of small errors increased. Differences in growth rates
affected accuracy primarily for smaller places: for each of the two
smallest size categories, both the MAPE and the proportion of large
errors had a strong U-shaped relationship with growth rates. For places
with more than 10,000 population, however, there was only a weak
relationship between growth rates and accuracy.

Differences in population size had little effect on bias, but
differences in growth rates had a substantial effect: within all three
size categories, MALPE and %POS each declined steadily as the growth
rate increased. The results found when population size and growth rates
were considered separately (Table 2) are thus confirmed when the two are
considered jointly.

**\[Table 3 about here\]**

**[Errors by Component]{.underline}**. Which component of the HU method
can be estimated most accurately? Table 4 shows that persons per
household (PPH) had the smallest errors, group quarters population (GQ)
the largest. For counties, MAPEs were 2.3 percent for PPH, 5.1 percent
for households and 32.5 percent for GQ; for subcounty areas, MAPES were
5.0 percent for PPH, 11.2 percent for households and 67.2 percent for
GQ. Small errors were common for PPH and large errors were common for
GQ. Percentage errors for GQ were so large because they were often based
on very small numbers of people. As shown in the bottom panel of Table
4, differences in population size affected estimation accuracy for all
three components, but the effect was considerably greater for households
than for PPH. **\[Table 4 about here\]**

Several studies have found errors for households to be greater than
errors for PPH (e.g., Smith and Lewis 1983; Starsinic and Zitter 1968).
This probably reflects the much more rapid rate of growth for households
than for PPH: the number of households grew by more than 50 percent
between 1980 and 1990 for many places in Florida, whereas PPH usually
changed by less than 10 percent. There was simply more potential for
error in estimates of households than in estimates of PPH.

The household estimates were also the major cause of the upward bias in
the population estimates. For counties, MALPEs were 2.7 percent for
households and 1.1 percent for PPH. Seventy-two percent of the household
estimates were above the census counts for counties, compared to 66
percent for estimates of PPH. For subcounty areas, MALPEs were 6.6
percent for households and only 0.5 percent for PPH. Seventy-two percent
of the household estimates were above the census counts for subcounty
areas, compared to only 59 percent of the estimates of PPH. The weighted
MALPE was actually negative for PPH, reflecting a small downward bias in
the PPH estimate for the state as a whole.

In both counties and subcounty areas, errors for GQ were much larger
than errors for households and PPH. Does this mean that GQ errors
contributed the most to overall estimation error? One way to answer this
question is to construct synthetic population estimates using a
combination of estimated values and census enumeration values. We made
synthetic population estimates for counties and subcounty areas under
three scenarios. The first combined our estimates of households with
1990 census counts for PPH and GQ; the second combined our estimates of
PPH with 1990 census counts for households and GQ; and the third
combined our estimates of GQ with 1990 census counts for households and
PPH. For each scenario, then, errors in the resulting population
estimates were due solely to errors in the single estimated component.
The results are shown in Table 5.

**\[Table 5 about here\]**

It is clear that errors in household estimates contributed the most to
overall estimation error, and that errors in GQ estimates contributed
the least. For both counties and subcounty areas, Scenario 1 had a MAPE
more than twice as large as the MAPE under Scenario 2 and about five
times larger than the MAPE under Scenario 3. It also had the greatest
degree of bias, the most large errors, and the fewest small errors. Even
with perfect estimates of PPH and GQ, errors in household estimates
would have created population estimation errors averaging 4.8 percent
for counties and 10.8 percent for subcounty areas. Although errors were
much larger for GQ than for households and PPH, those errors contributed
relatively little to overall estimation error because in most places the
group quarters population accounts for a very small proportion of total
population.

Since the household estimates were based on symptomatic data
(electricity customers, building permits), why were their errors so
large? Part of the problem is data quality: data may be incomplete,
erroneous, or contain errors in geographic allocation. We believe a more
important source of error, however, is the changing relationship between
symptomatic data and households. Changes in completion rates, time lags,
and occupancy rates may affect the accuracy of household estimates from
building permit data; changes in nonpermanent residents may affect the
accuracy of household estimates from electricity customer data. The
latter is particularly a problem in Florida, where a substantial
proportion of the housing stock is occupied by nonpermanent residents
(e.g., tourists, winter residents). New techniques for monitoring these
changes over time could lead to better household estimates.

[Errors by Technique: Households]{.underline}. A number of different
data sources and techniques can be used to estimate each component of
the HU method. Which are more accurate? For households we tested the
following estimates:

1\) **FINAL** - estimate actually used for counties and subcounty areas
in Florida. This estimate was based on electricity customer and/or
building permit data, but included our judgment regarding which data
sources, techniques, and assumptions should be used in each specific
place.

2\) **EC** - estimate based solely on electricity customer data, using
the ratio of households to active residential electricity customers,
calculated at the time of the most recent census.

3\) **BP** - estimate based solely on building permit data by type of
unit, using the techniques described in the previous section.

4\) **CONSTANT** - estimate that assumes that the number of households
has not changed since the previous census (1980).

5\) **TREND** - estimate that assumes that the linear change in the
number of households between 1980 and 1990 was identical to the change
between 1970 and 1980.

The results for households are summarized in Table 6.[^9] Estimates
based solely on electricity customers were clearly more accurate than
those based solely on building permits. For both counties and subcounty
areas, the **EC** estimates had smaller MAPEs, more small errors, and
fewer large errors than the **BP** estimates. The same result was found
in a test of 1980 estimates in Florida (Smith and Lewis, 1983).

Both **EC** and **BP** estimates performed much better than **CONSTANT**
and **TREND** estimates in subcounty areas: **CONSTANT** had very large
errors and a strong downward bias, whereas **TREND** had large errors
and a strong upward bias. **CONSTANT** also performed poorly at the
county level, but **TREND** performed almost as well as **BP** in terms
of accuracy and displayed very little bias, indicating that algebraic
errors at the subcounty level tended to offset each other when
aggregated. These results show that symptomatic data generally provided
much more accurate household estimates than simply extrapolating past
trends or assuming that no change has occurred.

**\[Table 6 about here\]**

The **FINAL** household estimates performed better than all the others,
with the smallest MAPEs, the most small errors, and the fewest large
errors, for both counties and subcounty areas. They had an upward bias,
but in most instances the degree of bias was less than for the other
estimates. Differences in errors were not always large, but they
consistently favored the **FINAL** estimates. In these estimates, then,
incorporating professional judgment led to better household estimates
than did the mechanical application of any single technique.

[Errors by Technique: PPH]{.underline}. For estimates of PPH we tested
the following techniques:

1\) **FINAL** - estimate actually used for counties and subcounty areas
in Florida. This estimate was based primarily on the mathematical
formula described in the previous section, but was occasionally adjusted
to account for other factors expected to affect local PPH.

2\) **FORMULA** - estimate based solely on the mathematical formula
described in the previous section (see Smith and Lewis, 1980, for a more
detailed description).

3\) **CONSTANT** - estimate which assumes that PPH has not changed since
the most recent census (1980).

4\) **TREND** - estimate which assumes that the linear change in PPH
between 1980 and 1990 was identical to the change between 1970 and 1980.

The results for PPH are summarized in Table 7. **FINAL** and **FORMULA**
produced much better estimates than either **CONSTANT** or **TREND**.
They had lower MAPEs, more small errors, and fewer large errors for both
counties and subcounty areas. They also exhibited relatively little
bias, whereas **CONSTANT** had a strong upward bias and **TREND** had a
strong downward bias. Similar results were found in a test of 1980
estimates in Florida (Smith and Lewis 1983). Results for **FINAL** were
only slightly better than those for **FORMULA**; on the average, the
application of professional judgment had very little effect on the
accuracy and bias of PPH estimates.

**\[Table 7 about here\]**

A number of other techniques could be used for estimating PPH. Special
censuses have been widely used by the State of Washington (Lowe et al.
1977). Sample surveys have been used in a few places, but to provide
accurate estimates the samples must be carefully drawn and quite large.
Roe, Carlson, and Swanson (1992) have developed an approach based on
sampling and interviews with local experts. Several researchers have
used regression analysis to relate changes in PPH to changes in
variables such as births, school enrollment, exemptions per income tax
return, and shifts in the composition of the housing stock (e.g., Voss
and Krebs, 1979). Advances in housing demography could also lead to new
techniques for estimating PPH by focusing research on the demographic
characteristics of occupants of various types of housing (e.g., Myers
and Doyle 1990). There are numerous opportunities for improving the
accuracy of PPH estimates.

**Discussion**

[Role of Judgment]{.underline}. Estimates of households which
incorporated professional judgment performed considerably better than
estimates based on the mechanical application of mathematical techniques
(Table 6). What about estimates of total population? For counties, MAPEs
were 5.4 percent for population estimates incorporating judgment and 6.5
percent for estimates derived from our most accurate mathematical
formula; for subcounty areas, MAPEs were 11.9 and 13.3 percent,
respectively. Population estimates incorporating judgment also had less
bias, more small errors, and fewer large errors than estimates based
solely on formulas. As professional demographers, we find this result to
be quite gratifying. Accurate data and sound methodologies are essential
for producing accurate population estimates, of course, but informed
judgment regarding demographic trends, changing local conditions, and
data idiosyncracies can improve the quality of population estimates as
well.^1^[^10]

It is difficult to draw general conclusions regarding the application of
professional judgment. Whose judgment should be heeded and whose
ignored? Will professional judgment always improve estimates, or only
under certain conditions? Will the application of professional judgment
improve accuracy for other population estimation methods? Can the
factors that affect professional judgment themselves be quantified and
incorporated into the formal estimation model? Very few studies have
empirically investigated the effects of judgment on the accuracy of
population estimates; we believe this is a research area deserving
further attention. (See Isserman 1984, for a discussion of the
application of judgment in the production of population projections and
forecasts).

[Comparison with 1980 Results]{.underline}. How do the results for 1990
compare with those found in 1980? Table 8 summarizes the results for
both years. In terms of accuracy, 1990 errors were generally smaller
than 1980 errors, especially for subcounty areas. At the county level
MAPEs were 5.4 percent in both years; weighted by population size, MAPEs
were 3.0 percent in 1990 and 3.9 percent in 1980. Surprisingly, for
counties there were more errors less than 5 percent [and]{.underline}
more errors greater than 10 percent in 1990 than 1980. At the subcounty
level, MAPEs were 11.9 percent in 1990 and 14.4 percent in 1980;
weighted by population size they were 4.5 and 5.6 percent, respectively.
The 1990 subcounty estimates had slightly more small errors and fewer
large errors than the 1980 estimates. For the state as a whole, the
absolute error was 1.6 percent in 1990 compared to 2.7 percent in 1980.

**\[Table 8 about here\]**

In terms of bias, the results for 1990 were completely different from
those for 1980: the 1990 estimates had a strong upward bias whereas the
1980 estimates had a strong downward bias. A majority of counties and
subcounty areas had positive errors in 1990, whereas a majority had
negative errors in 1980. The state estimate was 1.6 percent
[above]{.underline} the census count in 1990, 2.7 percent
[below]{.underline} the census count in 1980.

How can these differences in bias be explained? One possible explanation
is that the HU method is inherently unbiased and that these differences
simply reflect random fluctuations: errors tend to be predominantly high
one year and predominantly low another, balancing out over time. We
believe this is part of the explanation, but that another factor also
played a role; namely, changes in census undercount. Nationally, net
census undercount was estimated from demographic analysis as 2.7 percent
in 1970, 1.2 percent in 1980 and 1.8 percent in 1990 (U.S. Bureau of the
Census, 1991). Since the population estimates were based on data from
the previous census, an improvement in census coverage between 1970 and
1980 led to census counts that were generally above the 1980 estimates.
Conversely, a decline in coverage between 1980 and 1990 led to census
counts that were generally below the 1990 estimates. We believe that
changes in the coverage of the 1970, 1980, and 1990 censuses affected
the bias found in the 1980 and 1990 estimates.

Why were the 1990 estimates somewhat more accurate than the 1980
estimates? This may have been due to more reliable base data in 1980
than 1970; a larger change in net undercount from 1970 to 1980 than from
1980 to 1990; higher growth rates in Florida during the 1970s than
during the 1980s; or to improved judgment due to additional years of
experience in producing population estimates. Perhaps it was simply the
result of randomness. Whatever the cause of these improvements, they
were relatively small, and there is a striking similarity between 1990
and 1980 results with respect to accuracy characteristics by population
size, growth rate, component, and technique. We believe these
similarities strengthen the generalizability of the results presented in
this paper.

[Comparison to Other Methods]{.underline}. How do HU population
estimation errors compare with those produced by other methods? We
don\'t yet have results for other methods in 1990, but in 1980 the HU
estimates for counties in Florida were found to be more accurate and
less biased than estimates produced by the Administrative Records,
Component II, and Ratio Correlation methods (Smith and Mandell 1984).
For subcounty areas, HU estimates were found to be more accurate and
less biased than Administrative Records estimates in Florida,
California, Washington, and New Jersey (Smith 1986).^1^[^11] To our
knowledge, no study has found HU population estimates to be less
accurate than estimates produced by other methods. We believe the
evidence clearly shows that HU population estimates perform at least as
well as those produced by other methods, when proper data and techniques
are applied.

[Generalizability of Results]{.underline}. We cannot say, of course,
that all HU population estimates will have errors similar to those
reported here for Florida. Errors are affected by the specific data and
techniques used in applying the HU method; by differences in growth
rates and population size; and by changes in seasonal population,
racial/ethnic make-up, age distribution, and socioeconomic
characteristics. Errors will vary from one set of estimates to another.

From this and other studies, however, we believe we can draw the
following conclusions about the HU method: 1) Population size has a
strong negative effect on average estimation errors (disregarding sign),
but no effect on bias; 2) Growth rates have a U-shaped effect on average
estimation errors (disregarding sign) and a strong negative effect on
bias; 3) Symptomatic data generally provide more accurate and less
biased estimates of households and PPH than do historical values or the
extrapolation of historical trends; 4) Electricity customer data
generally provide more accurate household estimates than do building
permit data; 5) Errors in household estimates generally contribute more
to population estimation error than do errors in estimates of PPH and
GQ; 6) The application of professional judgment can improve the
performance of purely mechanical estimation techniques; and 7) The
accuracy of population estimates from the HU method is similar to (or
greater than) the accuracy of estimates from other methods, if proper
data and techniques are applied. Future research may eventually cause us
to change some of these conclusions, but we believe they accurately
reflect the current state of the art.

\"Generalizability\" refers not only to the universality of error
characteristics, but also to whether the method can be applied in all
states and for different levels of geography (e.g., counties, cities,
census tracts). In the latter sense, the HU method is extremely
generalizable. It is currently used by public and private agencies in
many states, for estimates from the state level down to small subcounty
areas (U.S. Bureau of the Census, 1990). We believe the HU method is an
ideal candidate for population estimates in many different settings.

[Further Research]{.underline}. \"Housing demography\" refers to the
union of population and housing analysis (Myers 1990). In recent years
housing analysts have become increasingly aware of the importance of
demographic characteristics in determining housing dynamics, and
demographers have become increasingly aware of the impact of housing on
the distribution and characteristics of local populations. These
population-housing connections can be approached from either direction,
focusing on the housing characteristics of different subgroups of the
population or on the demographic characteristics of occupants of
different types of housing. Both approaches lead to many interesting and
useful types of research.

Research on the HU method falls squarely within this emerging field.
Housing demography provides a theoretical foundation for the HU method
and promises to enhance its usefulness in several ways. For example,
Sweet (1990) studied family life cycle events (e.g., marriage, divorce,
childbearing) and how those events affect the demand for various types
of housing. Sweet and Bumpass (1987) studied the relationship between
stages in the family life cycle and average household size; they also
looked at differences in the household characteristics of various social
and ethnic groups. Myers and Doyle (1990) focused on relationships among
type of housing unit, age of unit, number of bedrooms, turnover, and the
age composition of households. Gober (1990) studied relationships
between residential location and household composition, including the
effects of distance from city center on average household size.
Morrow-Jones (1989) studied the relationship between changes in
owner-renter status and the age, sex, race, marital status, income, and
size characteristics of households. Burchell and Listokin (1978) used
the HU method to project age groups and the demographic impact of new
development. All these studies suggest ways to improve the accuracy of
the HU method or to extend its application into new areas.

We believe the development of Geographic Information Systems (GIS) will
also enhance the usefulness of the HU method. These systems have become
increasingly important in the planning profession in recent years (e.g.,
Levin and Landis 1990). Vast computerized databases containing
information on building permits, electricity customers, property tax
records, income tax returns, vehicle registrations, address lists, and
other types of data can be used in conjunction with the HU method to
produce housing and population estimates. There is a tremendous demand
for such estimates from state and local governments, planning agencies,
and private businesses, especially for estimates of very small areas
(e.g., zip codes, census tracts). A few analysts are already working on
the integration of demographic and GIS techniques to produce small-area
estimates (e.g., Batutis and Prevost 1991; Tayman 1991); we believe the
HU method will play a central role in this continuing development.

**Conclusion**

The HU method is an accurate, comprehensive, and extremely flexible form
of population estimation. It has a number of characteristics that make
it very useful for producing population estimates. First, it is
conceptually clear and can be explained to and understood by people with
little or no background in planning or demography; this is an important
characteristic when population estimates must be described and defended
in public forums. Second, it is not confined to a single technique or
source of data; rather, it can incorporate a number of different
techniques and unique data sources available only in a small number of
places. Third, it can be applied virtually everywhere and at any level
of geography, from states down to counties, cities, census tracts, zip
code areas, and even individual blocks. (This is a striking advantage
over most population estimation methods, for which data are often not
available for small areas.) Fourth, it can be customized to produce
estimates for unique geographic entities such as school districts,
voting districts, traffic analysis zones, and customer service areas.
Finally, it can produce estimates of population change that are at least
as accurate as those produced by any other method. We believe the HU
method is an extremely powerful tool for planners and demographers
engaged in small-area analysis.

**NOTES**

1\. The population estimates evaluated in this study were the official
estimates used for revenue-sharing, budgeting, and planning by the State
of Florida. They were produced by the Bureau of Economic and Business
Research at the University of Florida under the terms of a contract with
The Florida Legislature. The estimates refer solely to permanent
residents of Florida, thereby excluding tourists, snowbirds, and other
seasonal or part-time residents.

2\. This section is based on Smith 1986. Readers already familiar with
the HU method and its application in Florida may want to skip to the
next section.

3\. The reports issued by the U.S. Department of Commerce provide data
on both single family and multifamily units. Prior to 1987, they also
provided data on mobile homes. Since 1987, however, mobile home data
have not been included in these reports. Mobile home data can be
collected directly from city and county building departments, vehicle
registration systems, and surveys of mobile home parks. These are the
sources we use in Florida. Data for mobile homes are often less reliable
than data for single family and multifamily units.

4\. For the state of Florida as a whole, the ratio of permanent
households to active residential electricity customers was .873 in 1990,
down from .919 in 1980. Thirteen counties had ratios between 0.9 and 1.0
in 1990; 31, between 0.8 and 0.9; 19, between 0.7 and 0.8; and four,
between 0.6 and 0.7. These ratios are probably lower in Florida than in
most states because of the large number of seasonal housing units found
in many Florida counties.

5\. In Florida, PPH declined by 8.1 percent between 1980 and 1990 for
places with 1980 PPH values greater than 3.0; by 5.4 percent for places
with 1980 PPH values between 2.5 and 3.0; and by 0.9 percent for places
with 1980 PPH values less than 2.5.

6\. 1990 PPH values for the state of Florida were 2.72 for single family
units and 1.99 for multifamily units.

7\. The homeless population is included in the estimate of total
population only to the extent that it was included in the most recent
census. Given the very small number of homeless persons counted in the
1990 census, it is unlikely that changes in the homeless population will
have much effect on total population estimates for most places. For a
few places, however, the numerical impact of the homeless population may
be substantial. This creates an estimation problem not only for the HU
method, but for other methods as well.

8\. Estimates were made directly for the unincorporated balance of each
county, using the same techniques used for cities; in other words,
unincorporated areas were [not]{.underline} calculated simply as
residuals when city estimates were subtracted from county estimates.

9\. For estimates of subcounty areas, we analyzed only the 370 places
that had complete building permit data for the entire decade. The other
82 places (mostly small towns) either did not issue building permits or
were missing substantial amounts of data.

10\. Every estimation and projection methodology requires the
application of judgment in choosing models, techniques, variables, and
data sources. What we refer to as \"judgment\" in this article goes
beyond these decisions to cover adjustments made to estimates for
specific places [after]{.underline} the basic methodology has been
chosen.

11\. The Component II and Ratio Correlation methods were not used for
subcounty estimates in these states.

**TABLE 1. Population estimation errors by population size and growth
rate: Counties, 1990**

Percent of

[Absolute Errors]{.underline}

[Size - 1980]{.underline} [N]{.underline} [MAPE]{.underline}
[MALPE]{.underline} [%POS]{.underline} [\<5%]{.underline}
[10%]{.underline}

\<10,000 8 5.3 0.3 62.5 62.5 12.5

10,000 - 24,999 19 7.8 6.7 84.2 36.8 26.3

25,000 - 49,999 7 7.6 5.4 71.4 28.6 42.9

50,000 - 99,999 12 3.8 0.5 66.7 75.0 8.3

100,000 - 249,999 11 4.3 2.4 63.6 63.6 9.1

250,000+ 10 2.5 2.2 90.0 90.0 0.0

Total 67 5.4 3.3 74.6 58.2 16.4

Wtd. Total\* - 3.0 1.6 \-- \-- \--

1980 - 1990

[Growth Rate]{.underline}

\<0% 2 16.0 16.0 100.0 0.0 100.0

0 - 15% 6 11.9 11.9 100.0 16.7 83.3

15 - 25% 16 4.5 3.5 75.0 56.3 0.0

25 - 50% 28 4.7 2.7 75.0 64.3 10.7

50 - 99% 12 3.4 -0.1 75.0 83.3 8.3

100%+ 3 5.1 -5.1 0.0 33.3 0.0

TOTAL 67 5.4 3.3 74.6 58.2 16.4

\*Weighted by population size in 1990

**TABLE 2. Population estimation errors by population size and growth
rate: subcounty areas, 1990**

Percent of

[Absolute Errors]{.underline}

[Size - 1980]{.underline} [N]{.underline} [MAPE]{.underline}
[MALPE]{.underline} [%POS]{.underline} [\<5%]{.underline}
[10%]{.underline}

\<250 25 36.6 6.2 52.0 8.0 84.0

250 - 499 27 22.6 14.5 74.1 11.1 77.8

500 - 999 49 16.6 9.7 71.4 16.3 65.3

1,000 - 2,499 73 14.2 8.9 74.0 27.4 57.5

2,500 - 9,999 130 9.1 4.6 66.2 42.3 34.6

10,000 - 24,999 64 6.6 4.2 78.1 40.6 18.8

25,000 - 49,999 43 5.7 1.5 60.5 53.5 16.3

50,000 - 99,999 21 5.0 2.7 57.1 57.1 14.3

100,000+ 20 3.4 1.4 65.0 80.0 0.0

Total 452 11.9 6.0 68.4 36.5 40.5

Weighted Total\* - 4.5 1.6 \-- \-- \--

1980 - 1990

[Growth Rate]{.underline}

\<-10% 53 32.0 28.5 96.2 1.9 90.6

-10 - 0% 58 11.6 11.3 96.6 29.3 55.2

0 - 10% 89 8.8 5.3 74.2 36.0 34.8

10 - 25% 78 7.3 2.9 67.9 44.9 25.6

25 - 50% 83 6.8 1.7 54.2 45.8 20.5

50 - 100% 55 9.1 1.9 54.5 50.9 30.9

100%+ 36 17.1 -11.4 22.2 38.9 50.0

TOTAL 452 11.9 6.0 68.4 36.5 40.5

\*Weighted by population size in 1990

**TABLE 3. Population estimation errors by size-growth category:
subcounty areas, 1990**

Percent of

GROWTH [Absolute Errors]{.underline}

[SIZE]{.underline} [RATE]{.underline} [N]{.underline} [MAPE]{.underline}
[MALPE]{.underline} [%POS]{.underline} [\<5%]{.underline}
[\>10%]{.underline}

\<1,000 \<0% 47 28.7 24.4 93.6 6.4 83.0

\<1,000 0-50% 38 12.6 2.9 50.0 23.7 52.6

\<1,000 \>50% 16 32.1 -14.6 31.3 6.3 93.7

1,000 - 9,999 \<0% 48 19.0 18.9 97.9 12.5 77.1

1,000 - 9,999 0-50% 115 7.7 3.6 65.2 43.5 30.4

1,000 - 9,999 \>50% 40 10.4 -1.9 45.0 47.5 37.5

10,000 \<0% 16 6.9 6.9 100.0 56.3 25.0

10,000 0-50% 97 5.6 3.2 72.2 47.4 13.4

10,000 \>50% 35 5.3 0.0 42.9 62.9 14.3

Total 452 11.9 6.0 68.4 36.5 40.5

**TABLE 4. Estimation errors by component: counties and subcounty areas,
1990**

Percent of

[Absolute Errors]{.underline}

[Component]{.underline} [MAPE]{.underline} [MALPE]{.underline}
[%POS]{.underline} [\<5%]{.underline} [10%]{.underline}

[Counties]{.underline} Households 5.1 2.7 71.6 65.7 14.9

PPH 2.3 1.1 65.7 92.5 0.0

GQ 32.5 -12.3 25.4 10.4 79.1

Subcounty

[Areas]{.underline} Households 11.2 6.6 71.9 43.8 33.6

PPH 5.0 0.5 58.8 65.7 10.2

GQ 67.2 8.9 50.4 32.3 63.7

Errors weighted by population size in 1990:

[Component]{.underline} [MAPE]{.underline} [MALPE]{.underline}

[Counties]{.underline} Households 3.5 2.7

PPH 2.2 -0.8

GQ 27.2 -15.0

Subcounty

[Areas]{.underline} Households 4.6 2.7

PPH 2.9 -0.7

GQ 35.5 -13.0

**TABLE 5. Population estimation errors under alternate scenarios**

Percent of

[Absolute Errors]{.underline}

[Scenario]{.underline} [MAPE]{.underline} [MALPE]{.underline}
[%POS]{.underline} [\<5%]{.underline} [10%]{.underline}

[Counties]{.underline} 1 4.8 2.5 71.6 68.7 13.4

2 2.2 1.0 64.2 92.5 0.0

3 1.0 -0.4 25.4 100.0 0.0

Subcounty

[Areas]{.underline} 1 10.8 6.5 71.9 44.7 33.0

2 5.0 0.5 58.8 66.8 10.0

3 1.8 -0.3 50.2 93.4 3.1

**Note**: Scenario 1: Estimates for households, counts for PPH and GQ.

Scenario 2: Estimates for PPH, counts for households and GQ.

Scenario 3: Estimates for GQ, counts for households and PPH.

**TABLE 6. Errors by technique for household estimates: counties and
subcounty areas, 1990**

Percent of

[Absolute Errors]{.underline}

[Technique]{.underline} [MAPE]{.underline} [MALPE]{.underline}
[%POS]{.underline} [\<5%]{.underline} [10%]{.underline}

[Counties]{.underline} FINAL 5.1 2.7 71.6 65.7 14.9

EC 6.2 4.6 85.1 46.7 19.4

BP 9.4 6.5 70.1 41.8 32.8

CONSTANT 28.1 -28.1 0.0 1.5 91.0

TREND 9.9 -0.4 47.8 26.9 37.3

Subcounty

[Areas]{.underline} FINAL 10.3 6.5 72.7 45.1 30.8

EC 11.9 8.0 77.3 41.9 33.8

BP 15.2 9.8 69.5 33.2 41.9

CONSTANT 27.0 -16.4 18.1 14.6 74.1

TREND 25.2 11.5 62.7 16.2 63.2

**TABLE 7. Errors by technique for PPH estimates: counties and subcounty
areas, 1990**

Percent of

[Absolute Errors]{.underline}

[Technique]{.underline} [MAPE]{.underline} [MALPE]{.underline}
[%POS]{.underline} [\<5%]{.underline} [10%]{.underline}

[Counties]{.underline} FINAL 2.3 1.1 65.7 92.5 0.0

FORMULA 2.4 0.8 65.7 92.5 0.0

CONSTANT 6.3 6.1 98.5 37.3 6.0

TREND 7.9 -7.7 3.0 20.9 22.4

Subcounty

[Areas]{.underline} FINAL 5.0 0.5 58.8 65.7 10.2

FORMULA 5.1 0.3 58.2 65.0 11.1

CONSTANT 7.5 5.0 81.9 38.5 23.7

TREND 11.9 -9.4 17.7 25.2 46.9

**TABLE 8. Accuracy and bias of population estimates, 1980 and 1990:
counties and subcounty areas**

WTD WTD [PERCENT OF ERRORS]{.underline}

[YEAR]{.underline} [MAPE]{.underline} [MAPE\*]{.underline}
[MALPE]{.underline} [MALPE\*]{.underline} [POSITIVE]{.underline}
[\<5%]{.underline} [10%]{.underline}

[Counties]{.underline} 1980 5.4 3.9 -2.9 -2.7 34.3 53.7 10.4

1990 5.4 3.0 3.3 1.6 74.6 58.2 16.4

Subcounty

[Areas]{.underline} 1980 14.4 5.6 3.5 -2.7 46.7 33.6 42.4

1990 11.9 4.5 6.0 1.6 68.4 36.5 40.5

\*Weighted by population size in estimation year

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