The methodology for postcensal estimates varies by level of geography with the widest array of methods used in county estimates. This methodological discussion focusses on the county estimates with occasional extensions to include methods specific to states or places. Postcensal population estimates update the last census population based on changes in the population or in components of population change. Actual information on such components of population change as births and deaths or on changes in symptomatic indicators related to changes in the population since the last census provide benchmarks to anchor the estimates.
The art of postcensal estimation of population comes in choosing appropriate benchmarks (or auxiliary data) to use in estimating the population change since the last census. One type of benchmark data, population flow data, consists of measures of the components of population change (eg. births, deaths, internal and external migration). The other type of benchmark data, population stock data, includes indicators that are correlated with population size and uses changes in those indicators to estimate the total change in population. Methods based on each of these two classes of data are found in several variations in the Census Bureau's postcensal population estimates program.
3.1 Flow methods
Flow methods are also known as component methods. They require some estimation of each of the components of population change since the last census. In the most general form, the component method reduces to a basic accounting equation for population change.
Pi,t = population estimate for area i at time t,
Pi,0 = population in area i at beginning of period,
Bi = births in area i since beginning of period,
Di = deaths in area i since beginning of period,
Ii = international immigrants to i,
Ei = international emigrants from i, and
ui = estimator of rate of net internal migration to i.
Direct measurement is possible for some of the components of population change -- births, deaths, and some components of international migration. Vital statistics registration data do a good job of measuring the effects of natural increase but problems can arise with immigration data. Unmeasured migration across international borders is a major cause of estimation error that requires the use of assumptions about the quantity and characteristics of the population flows missed. The issue of small area estimation as defined by this report arises when there is no direct measure of the component of interest. In equation 1, the rate of internal net migration (ui) is not directly measured but must be estimated from an alternative data source devised for another purpose.
In order to simplify the task of finding a good estimator of net internal migration, we confine the use of equation 1 to the household population under 65. The population 65 and over and the population in group quarters (military barracks, prisons, college dormitories, etc.) have different patterns of migration and are better handled separately later in the process by looking specifically at data systems that explicitly measure changes in the 65 and over population and in the group quarters population.
One method for estimating the net internal migration rate (ui) for the household population under 65 uses administrative data that provide addresses for individuals at two different points in time (usually a year apart). Such data provide approximate data on inmigration, outmigration, and even area-to-area flows. While there are several potential sources of these administrative data -- changes in postal addresses, drivers license records, tax returns, and health insurance information -- the problem is to find a source that provides representative coverage and consistency in reporting and tabulation. The Census Bureau uses an administrative records method that compares tax returns from the Internal Revenue Service (IRS) for changes in filing addresses between two consecutive annual tax filings (U. S. Bureau of the Census, 1988). In the estimates process, tax returns from one year are matched with those from previous years by matching Social Security numbers of the filers. For persons with a new address, the new mailing address is coded to state, place, and county. If the state, place, or county is different from the previous year, the filer and all exemptions are classified as migrants. These data are then used to construct net migration rates for each county and place as an input to the population estimation formula. An estimate of the rate of net migration is calculated by dividing the net flow of exemptions (the tax filer plus his or her dependents) moving into the area by the number of exemptions filed in the area (See equation 2).
summation over j of (Tji-Tij)
(2)ui = ----------------------------
Tij = flow of tax exemptions from area i to j,
Ti. = total number of matched tax exemptions living in area i at the beginning of the period.
This net migration rate is then multiplied by the initial population as shown in equation 1. A critical assumption in this method is that the population not covered by the administrative data set moves similarly to the population covered or that the uncovered population is too small to affect the results markedly. Since this assumption is especially inappropriate for the population over 65 and for certain military and institutionalized populations, those populations are handled separately as explained below. Other potential problems include the difficulty of coding addresses to geography, changes in administrative coverage over time, and the elimination of administrative data sources as governmental programs change.
A second method of estimating the net internal migration rate (ui) uses school enrollment data. Changes in the size of the population enrolled in elementary and secondary school can be used to estimate the net migration of the general population. In one such method, component method II, changes in school enrollment are compared to expected changes due to natural increase alone in order to produce indirect estimates of the net migration rate of the school-aged population (Batutis, 1991). The migration rate for the total population is then estimated by adding the difference between the net migration rate of the total population and the net migration rate of the school-aged population in the most recent census.1 The critical assumption here is that the relationship of net school-aged migration and net total migration remains constant over time.
3.2 Change in Stock Methods
A fundamentally different approach to population estimates emphasizes the total change in population size since the last census rather than demographic components of change. These change in stock methods relate changes in population size to changes in other measured variables that are assumed to be correlated with population change.
The choice of possible variables is wide: number of housing units, automobile registrations, total number of deaths (and or births), tax returns, etc. Note that births and deaths in this method are not viewed as components but as indicators of the size of the population. Similarly, drivers licenses and tax returns are not used as indicators of migration as they were in the flow methods but as proxies for the size of the total population.
The U. S. Census Bureau county estimates program uses a special case of the change in stock method known as the ratio-correlation method (Namboodiri, 1972). In this method, we construct a linear regression equation for each state separately, using indicators appropriate for that state. The independent variables are ratios of the proportion of each indicator that is located in a given county in the state as of the date of the most recent census to the comparable proportion at the time of the prior census. The dependent variable is the ratio of the proportion of a state's population in a given county in the most recent census to the comparable proportion in the prior census. The resulting regression parameters(kappa,alpha,Beta,Gamma) are then used to estimate postcensal county populations in equation 3.
Pi,0 Ai,t/As,t Bi,t/Bs,t Ci,t/Cs,t
(3)Pi,t= Ps,t ------[k+a---------+b----------+y---------]
Ps,0 Ai,0/As,0 Bi,0/Bs,0 Ci,0/Cs,0
Ps,0 = state population in the last census,
Ps,t = independent estimate of current state population,
As,0,Bs,0,Cs,0 = indicator variables for state total at date of last census,
Ai,0,Bi,0,Ci,0 = indicator variables for county i at date of last census,
As,t,Bs,t,Cs,t = indicator variables for state total for estimate date, and
Ai,t,Bi,t,Ci,t = indicator variables for county i for estimate date.
The key assumption in this method is that the relationship among geographic units between change in population and change in the selected indicator variables remains constant over time (Tayman and Schafer, 1985). Complications also arise if indicator variables change over time in selected areas for reasons unrelated to population -- for example, changes in the tax law, changes in general fertility rates, increases in automobile registrations per person, etc.
Another population stock method used to estimate the ratio of the current population to the household change is the housing unit method. In this method, tax rolls, construction permits, certificates of occupancy, or utility data could be used to calculate changes in the number of housing units in an area (Smith and Mandell, 1984). In the Census Bureau's methodology the housing stock from the last census is updated using data on housing construction, demolitions, and conversions (Eq. 4).
(4) Ui,t= (Ui,0+Vi-Wi)
Ui,0 = housing units in area i in the last census,
Ui,t = estimated housing units in area i for estimate date (t),
Vi = housing units constructed in area i since last census, and
Wi = housing units in area i demolished since the last census.
The number of households in area i for date t is estimated by multiplying the estimated number of housing units at time t by an updated estimate of the occupancy rate for area i at time t. By assuming that the local occupancy rate changes as the national rate, we can update the area's rate by multiplying the occupancy rate for area i at the time of the census by the ratio of the national occupancy rate at time t from the Current Population Survey (CPS) to the national occupancy rate at the time of the census.
(5)Hi,t= Ui,t ------ -----------
U.,0 = national housing units in the last census,
U.,t = national housing units for estimate date,
Hi,0 = households in area i in the last census,
Hi,t = households in area i for estimate date,
H.,0 = national households in the last census, and
H.,t = national households for estimate date.
Finally, the population for the area i is calculated by multiplying the area's household estimate by an updated estimate of population per household. Again we assume that the area's population per household from the last census can be updated by multiplying by the ratio of the national population per household from the CPS to the national population per household in the last census.
(6)Pi,t= Hi,t ------ -----------
Pi,t = estimated population in area i,
P.,0 = national population in last census, and
P.,t = national population at the date of the estimate.
All of the methods discussed so far refer to the household population under 65. The two other segments of the population, the population 65 and over and the group quarters population, are measured by their own specific change in stock methodologies. Since these two groups have unique characteristics (especially in terms of their migration patterns), we use administrative records systems that are unique to each of the two groups. The population over 65 is estimated by using changes in the medicare population since the last census as a direct measure of the change in the population 65 and over. No such nationwide systems exists for the group quarters populations (defined for estimates purposes as the population in military barracks, college dormitories, prisons and other institutions). Changes in these population since the last census are obtained from an inventory of major group quarters locations that is maintained and annually updated by a special data collection process in the Population Estimates Branch of the Population Division in cooperation with state agencies affiliated with the Federal-State Cooperative Program for Population Estimates.
3.3 Combined methods
The U. S. Census Bureau's postcensal population estimates program combines methods in two ways. Within each level of geography (states, counties, and places) several of the above methods are combined (Table 4). Since certain methods represent given subpopulations better, a combination of methods may be viewed as more robust -- less likely to change due to extraneous factors that might affect one or the other of the estimates. There is a further mixing of methods since the estimates at each level of geography are controlled to the results of the estimates made at the next higher level of geography.
The methodology for making state estimates during the 1980s averaged the results of the administrative record method with those of the composite method. In the composite method, the population is divided into three age groups, each of which is estimated by a separate method. The population under 15 is estimated using changes in the levels of school enrollment (similar to Component Method II). The population ages 15-64 is estimated by a ratio- correlation method in which the independent variables are tax returns, school enrollment, and housing units. The population over 65 is estimated using a method in which changes in the number of persons on medicare since the last census date are added to the population aged 65 and over at the last census (U. S. Bureau of the Census, 1984). The total state population by age is then controlled to equal the estimated national population age structure.
Annual county population estimates are produced independently for each state to coincide with the state's total population estimated above. A distinct methodology for each state is developed in consultation with that state's member of the Federal-State Cooperative Program for Population Estimates. In most cases, it consists of the average of two or three of the methods described above: the administrative records method, component method II, and the ratio-correlation method. Moreover, within the ratio-correlation method, different states use different independent variables which may include school enrollment, tax returns, medicare enrollment, automobile registrations, births, deaths, dummy variables for county size, or other state-specific data series. Additional adjustments are made for changes in selected military and institutional populations and for changes in the population over 65. Final results are controlled to the state population estimate produced by the Census Bureau using a uniform method across all states (van der Vate, 1988).
Place estimates use a strict administrative record methodology where migration is based solely on the migration rates derived from changes in addresses on tax returns. The only other adjustments for place estimates are for changes in selected military and institutional populations and a final control to county level population estimates (U. S. Bureau of the Census, 1980).