The U.S. Bureau of Labor Statistics (BLS) Local Area Unemployment Statistics (LAUS) program produces monthly employment and unemployment estimates for approximately 7,500 subnational areas.¹ The Current Population Survey (CPS), sponsored jointly by the U.S. Census Bureau and BLS, is the official survey instrument for measuring the labor force in the United States. However, the CPS sample is not sufficiently large in most states and substate areas to provide reliable monthly labor force estimates for these states and substate areas. Therefore, BLS employs LAUS time-series models for states, the District of Columbia, and select substate areas to estimate the true values of household employment and unemployment from the CPS series. It is necessary to model these CPS estimates to reduce the impact of sampling error and the associated volatility in the CPS employment and unemployment series. The LAUS time-series models are designed for small samples by pooling sample observations over time; this pooling effectively increases the sample size and reduces the variance of the model estimates relative to the CPS. For each geographic area where model estimates are produced, BLS maintains separate models for both employment and unemployment. Estimates of a geographic area’s unemployment rate and labor force are calculated directly from the model estimates of employment and unemployment. Monthly Census Bureau estimates of the civilian noninstitutional population age 16 and older (CNP16) are used to develop employment–population ratios and labor force participation rates.

The CNP16 is the base population group, or universe, used for CPS statistics published by BLS and represents the population likely to be engaged in the labor force. The civilian noninstitutional population excludes the following: active-duty members of the U.S. Armed Forces; people confined to institutions or facilities, such as prisons, jails, other correctional institutions, and detention centers; and people living in residential care facilities, such as skilled nursing homes. Included in the civilian noninstitutional population are citizens of foreign countries who reside in the United States but do not live on the premises of an embassy. The LAUS program receives monthly CNP16 estimates for each state and modeled substate area from the Census Bureau along with the associated current-year monthly CPS employment status estimates.

Each year, the Census Bureau’s Population Estimates Program utilizes current data on births, deaths, and migration to calculate the change in population since the date of the most recent decennial census. This calculation of the change in population allows the Census Bureau to produce time-series estimates of population, demographic components of change, and housing units. The annual time series of estimates begins with the date of the most recent decennial census enumeration and extends through the most recent calendar year, which is called the vintage year. The reference date is July 1 for each year following the most recent decennial census with April as the base month. The latest vintage of data available supersedes all previous estimates for those dates because each vintage of estimates includes all years since the most recent decennial census. These estimates are referred to as postcensal estimates.

Intercensal estimates are produced each decade by adjusting the existing time series of postcensal estimates for a decade to smooth the transition from one decennial census count to the next. Intercensal estimates differ from the postcensal estimates because intercensal estimates rely on a formula that redistributes the difference between the April 1 postcensal estimate and the April 1 census count for the end of the decade across the estimates for that decade. This difference between the postcensal estimate and the census count is called the error of closure.² Once produced, the intercensal estimates become the preferred series of data for the decade.

At the beginning of each year, the Census Bureau provides BLS with a special tabulation of CNP16 postcensal estimates from the new vintage of population data. The new population data are used to ratio adjust the CPS employment status estimates used in LAUS time-series model estimation. These adjustments reflect the change in CNP16 for a state or modeled area relative to the prior vintage of population controls. Recontrolled CPS estimates are the foundation of the annual reestimation process for the LAUS time-series model.

Over the past several decades, the annual LAUS revision process for CNP16 data introduced discrete jumps, or breaks, in the data when moving from one decennial census base to the next. As we previously described, the CNP16 data for states and modeled substate areas are used both as denominators for the labor force participation rates and employment–population ratios and in the annual ratio adjustment of CPS employment status estimates. Breaks in the CNP16 series introduce structural breaks in the states' labor force time series and raise concerns when making comparisons across time.

In this article, we introduce the approach used by BLS to correct these breaks by implementing established demographic methods to create intercensal CNP16 series. Intercensal estimates represent consistent population time series that are linked from one census to the next, enabling comparisons between population levels over time. These estimates differ from the postcensal estimates, which represent projections starting from a census base that then add demographic components of change (births, deaths, and net domestic and international migration).³ Breaks in the CNP16 series occur on a decennial basis when the CNP16 estimates move from one census base to the next. To remove the errors of closure between the CNP16 postcensal estimates each decade, we employ the standard methodology used by the Census Bureau to produce official intercensal population estimates. Following the Das Gupta method, we assume that the error of closure accumulates as a function of time since the previous census, and we allocate these accumulated errors of closure over the decade by using an exponential factor.⁴ This approach yields a smooth time series linked between two census endpoints. For earlier years where no archive of postcensal CNP16 data exists, we apply a simple forecasting model to synthesize postcensal estimates extrapolated from trends in the CNP16 of each state. Using either official or synthesized postcensal estimates, we compute errors of closure for each state and decade and apply the Das Gupta method to produce smoothed synthetic intercensal time series for each state and modeled substate area from January 1980 through December 2024.

To highlight the advantages of this intercensal transformation over the postcensal CNP16 data, we first show comparisons between the original postcensal data and the revised synthetic CNP16 series to demonstrate both the extent of decennial breaks across states and time and how the intercensal method produces smooth time-series data for each state. We further show how the revised CNP16 data affect labor force rates and ratios, namely the labor force participation rate and employment–population ratio, after introducing the revised population controls. The transformed intercensal CNP16 series provide data users with consistent and linked CNP16 series that eliminate structural breaks induced by changes in the population base. Eliminating the breaks around decennial years enables robust comparisons of labor force rates and ratios over time.

Background

While BLS annually obtains monthly postcensal CNP16 estimates for each subsequent population vintage from the Census Bureau, there is no available tabulation for intercensal CNP16 data following the release of each decennial census. This lack of intercensal CNP16 data leaves breaks in the official BLS CNP16 times series. These data breaks result from decennial closing errors between the April 1 postcensal estimates and the April 1 census counts and appear in many of the state and modeled substate area CNP16 series in decennial census years.

As an earlier attempt to address this issue, BLS implemented a linear-wedge approach over the CNP16 data for the 1990s to minimize closing error breaks in the early 2000s.⁵ BLS took a similar approach following the 2020 decennial census. The Vintage 2021 CNP16 estimates reflected a blended-base approach that controlled the data for totals from the 2020 Census while maintaining a basis in the 2010 Census.⁶ The March–April 2020 timing of the break between the Vintage 2020 CNP16 postcensal data and the Vintage 2021 blended-base CNP16 data coincided with the month that recorded the largest CPS employment status level shifts resulting from the 2020 recession. BLS applied a linear wedge to these breaks between vintages back to April 2010 data, but BLS only replaced the CNP16 data from 2017 forward as part of a standard 5-year replacement period during annual reestimation activities. For states and modeled areas with greater CNP16 breaks between vintages, the replacement of published estimates from 2017 forward resulted in the introduction of breaks in level measures for the data from December 2016 and January 2017.

Leading into an update of estimation inputs throughout the LAUS program in 2025, staff demographers developed intercensal CNP16 data from January 1980 through April 2020 by using the standard demographic methods employed by the Census Bureau’s Population Estimates Program. BLS applied these historical intercensal CNP16 data to the full series of CPS employment status inputs for the LAUS time-series models. The effect of recontrolling the state CPS data to the BLS-produced intercensal CNP16 series was to remove series breaks from some of the historical CPS employment status input series and improve the time-series quality of the published state CNP16 data.

The intercensal CNP16 controls described in this article were applied to monthly CPS employment and unemployment model input data from January 1980 through April 2020. This application of intercensal controls resulted in the elimination of several level-shift outlier specifications in the LAUS time-series models that corresponded to decennial breaks in the CPS employment status inputs.

Data

Each subsequent vintage of monthly CNP16 data is developed by the Population Estimates Program at the Census Bureau and provided to the LAUS program annually. For decades, the Population Estimates Program has used the components-of-change method, namely the cohort-component method, to produce population estimates for national, state, county, and subcounty areas dating back to the 1970s.⁷ The cohort-component method takes a base population, often the census enumeration with adjustments for overcounts and undercounts, and projects it forward by using the demographic components of change.⁸ The demographic components of change are the natural increase of the population (i.e., births minus deaths) and net in-migration, consisting of both domestic and international migration. The basis of the cohort-component method is the balancing equation, which relates the population in a base period to the next period by adding or subtracting the components of change. Over time, the Census Bureau has adjusted their estimation methodology to incorporate methodological innovations and improvements to the data inputs. At the time of the writing of this article, the methodology of the Population Estimates Program is Vintage 2024 and uses the cohort-component method.⁹

To measure each component of change, the Population Estimates Program relies on a variety of administrative data covering vital statistics, immigration, and the group quarters population.¹⁰ Data on births and deaths come from vital records produced by the National Center for Health Statistics and with state partners through the Population Estimates Program’s Federal-State Cooperative for Population Estimates. Migration data come from a variety of administrative sources within the federal government, including immigration data from the Department of Homeland Security and the Office of Refugee Resettlement. Additional data on federal-civilian movement and net recruiting for the Armed Forces are from the Office of Personnel Management and the Department of Defense, respectively. Data on the institutionalized group quarters population combine the population level and demographic characteristics from the most recent enumeration and annual change from the Group Quarters Report, which is submitted by the state partners of the Population Estimates Program through the Federal-State Cooperative for Population Estimates.¹¹ Because changes in the group quarters population more often reflect changes in policy than demographic processes, such as construction of a new correctional facility, the group quarters population and its characteristics are typically held constant throughout the decade unless additional information is received.¹² Finally, data for the Armed Forces population come from the Department of Defense’s Defense Manpower Data Center and are linked to servicemembers’ counties of residence.

Population Estimates Program data are released each year as Vintages, which reflect the latest year of data. For example, the Vintage 2024 data reflect postcensal estimates that begin in April 2020 and end in July 2024. Each new data vintage incorporates updates to the data inputs and changes to county and subcounty geographic boundaries. To produce short-term statewide CNP16 forecasts for LAUS, the Population Estimates Program carries forward the previous year’s annual components of change and linearly interpolates them to each month to produce estimates for the current year through December. The final monthly CNP16 estimates are then controlled to the estimates for the nation.

On a decennial basis, the Population Estimates Program produces two sets of estimates: evaluation estimates and intercensal estimates. The evaluation estimates are postcensal projections from one census date (April 1) to the next and do not incorporate any information from the subsequent enumeration. These data are then used to produce the intercensal estimates, which link the postcensal projections to the known counts from the next enumeration as a time series. In the following discussion, we introduce the standard method used to produce the intercensal estimates.

Methodology

Our objective is to develop smoothed monthly population estimates for each state and substate area that eliminate census breaks from January 1976 through April 2020. This involves intercensal adjustments that reconcile the error of closure between one vintage of population estimates and the next. Demographers use a variety of methods to produce intercensal population estimates that model the relationship between the intercensal estimates and postcensal projections as a function of time. Traditionally, the Population Estimates Program models the error of closure as a function of time elapsed from one census to the next, assuming that errors accumulate geometrically over time.¹³ The current method arose from an internal Census Bureau memo circulated by Prithwis Das Gupta in the 1980s, from which the Das Gupta six-factor method was chosen to produce official estimates.¹⁴ This method was chosen by the LAUS program to produce the intercensal CNP16 series for each state and substate area.¹⁵

We outline the Das Gupta method in equation (1). We let P_t denote the intercensal estimate at time t and let Q_t denote the corresponding postcensal estimate. The Das Gupta method distributes the error of closure as follows:

In equation (1), P_T/Q_T is the relative error of closure in the census period T. The exponent t/T

represents the time in days elapsed since the previous census date (t) relative to the total number of days in the decade (T). The exponent describes the allocation of the error of closure to each population estimate over the decade. For example, the decay factor used for the May 2010 intercensal population estimate is 30/3,653 because May 1, 2010 is 30 days into the 3,653-day decade between the April 1, 2010 and April 1, 2020 enumerations.

While the objective is to produce intercensal estimates for each state and substate area over their full history (from January 1976 to the present), postcensal data prior to 2010 were unavailable. Therefore, it is necessary to develop synthetic postcensal projections for the 1980s and 1990s to produce smoothed intercensal data. This intercensal method is denoted by the Synthetic Method. When official postcensal estimates were available, the standard Das Gupta formula was applied by using the official data and is referred to as the Vintaging Method.

Synthetic Method

The Synthetic Method relies on a synthetic postcensal estimate as an input to the Das Gupta formula. This method uses a simple linear projection to forecast the postcensal estimate . The linear projection provides the most reasonable results to match state-by-state population trends.¹⁶ Using monthly data over the decade, we implement a one-step prediction in our linear model to approximate each state’s postcensal estimate for January 1980, January 1990, and April 2000.

For example, to provide the monthly intercensal estimates from January 1980 to January 1990, we estimate a prediction with our linear model for January 1990 by extrapolating the trend from the state’s time-series history. This prediction becomes the denominator in the error of closure formula shown in (1), with the official published LAUS CNP16 estimate as the numerator. Our application of the Das Gupta formula produces a smooth intercensal population time series for each state and substate area from January 1976 to April 2000.

Vintaging Method

When official postcensal estimates were available, the standard Das Gupta formula applies. This method, the Vintaging Method, corresponds to the standard Census Bureau intercensal methodology.¹⁷ From April 2000 to April 2010, the intercensal series relies on an official postcensal estimate for April 2010. However, the intercensal estimates from April 2010 to April 2020 instead use a blended-base postcensal estimate for April 2020. Because of operational issues with the 2020 enumeration, the Census Bureau relies on a blended-base estimate that incorporates data from a variety of sources.¹⁸ Applying intercensal adjustment by using known postcensal data is straightforward and yields smooth intercensal data from April 2000 to April 2020.

Examining the error of closure

In this section, we document the presence of breaks across state CNP16 time series back to the 1980s that are attributable to errors of closure. Using demographic methods to eliminate the errors of closure, we demonstrate the improvements to the statewide CNP16 series and the resulting improvements to labor force participation rates and employment–population ratios produced by the LAUS program.

Historical evidence for breaks

We first document the existence of time-series breaks across the historical state CNP16 series, and we compute the error of closure for each state over time beginning with the 1990 enumeration. Table 1 shows the error of closure between the enumeration and postcensal estimates for each state and adjustment period, expressed both as levels and percentages.

The corresponding percentages from table 1 appear graphically in chart 1. The adjustment periods range from January 1990 (covering data from the 1980s), April 2000 (covering data from the 1990s), and so on. To adjust each state’s population series in the corresponding decade, we add one to the percentages to yield the exact ratios for the Das Gupta formula in equation (1). We produce postcensal estimates from January 1990 and April 2000 by using the Synthetic Method to project the monthly CNP data. But for the postcensal estimates for April 2010 and April 2020, we use the official postcensal estimates provided by the Population Estimates Program. In chart 1, positive values represent a postcensal underestimate of a state’s population relative to the enumeration, and negative values show a postcensal overestimate.

There was wide within-decade variation in the errors of closure by state in 1990. Despite the enumeration’s reference date of April 1, 1990, our inspection of the data revealed wedging back to January 1990. We therefore treat January 1990 as the end month to adjust CNP16 in the 1980s. Applying the Synthetic Method to obtain a projected postcensal estimate for January 1990 that used trends from the data in the 1980s, we find a wide range of errors of closure across states. Chart 1 shows that the largest overestimates in January 1990 were in Wyoming (-4.07 percent) and South Dakota (-3.75 percent), and the largest underestimates were in Nevada (7.27 percent) and the District of Columbia (7.18 percent).

Shown by state in chart 2 are the errors of closure for April 2000, which were used to adjust data from the 1990s. Also, these were the smallest errors of closure when compared with other decades. The main explanation for such small differences is the result of previous LAUS adjustments for the 1990s, applied during the 2000s. Specifically, the LAUS program applied a linear-wedge adjustment to the 1990s CNP data to reduce decennial breaks in 2000. The 2000 error of closure estimate extrapolates the trend from the previously smoothed series, and the resulting errors of closure for April 2000 were all less than 1 percent.

Chart 3 shows the error of closure by state in April 2010. We apply the standard Vintaging Method to produce intercensal estimates by using the official Vintage 2010 postcensal CNP data available for April 2010. The Vintage 2010 estimates introduce several methodological improvements to the component-change method compared with the 1990s, including improved measurement of migration and incorporation of the American Community Survey into the estimation process. Chart 3 shows the percentage error of closure for each state, with most states showing underestimates relative to the 2010 count.

The final decade we adjust is the 2010s, from April 2010 to April 2020. The April 2020 errors of closure are shown by state in chart 4. Although we adjust the 2010s data by using the Vintaging Method, a key difference for the decade involves the subsequent population base we link to. Specifically, we link the 2010s data to the April 2020 blended-base estimate from Vintage 2024, which is done because of the absence of an official April 2020 count from the enumeration. The blended base resolves data collection issues experienced during the 2020 enumeration because of the COVID-19 pandemic. The blended base augments total population counts from the 2020 enumeration with age and sex details from the 2020 Demographic Analysis and race and ethnicity details from the Vintage 2020 Evaluation Estimates. Both the 2020 Demographic Analysis and the Vintage 2020 Evaluation Estimates are projections from the 2010 enumeration base. Although the blended-base linkage differs from prior intercensal adjustments, we nevertheless found relatively small errors of closure of less than 1 percent for each state.

Applying intercensal adjustments

Chart 5 shows the time series of original and revised CNP16 estimates for Illinois from 1980 to 2000; this presentation of the estimates for Illinois is a motivating example of the intercensal method. Visually, there is a clear break in the Illinois CNP16 series around the 1990 enumeration. Using the Synthetic Method to project Illinois’ postcensal estimate for 1990, we obtain an error of closure of –2.6 percent as of January 1990. This implies that the postcensal projection from the 1980 census overestimates the CNP16 for Illinois by 228,000 people. Taking the ratio of the census value to the synthetic postcensal estimate, we obtain an adjustment factor of 8,626,000/8,854,000 = 0.97. Using this ratio for the error of closure, we apply equation (1) to the postcensal series from January 1980 to December 1989 to obtain the final intercensal CNP estimates.

Chart 6 highlights another example of a time-series break observed in Wyoming around the 1990 enumeration. Similar to Illinois, we found that our projected Wyoming postcensal estimate for January 1990 indicated an overestimate between the 1980-based postcensal projections and the 1990 enumeration. The overestimate was around 14,000 people, or around 4 percent, compared with the official January 1990 count. We also note the stairstep pattern in the earlier CNP16 estimates for Wyoming. Similar patterns appeared in other states with lower populations. The District of Columbia, Delaware, Louisiana, Montana, Rhode Island, North and South Dakota, Vermont, and West Virginia are additional examples with choppy population estimates in earlier decades. Currently, LAUS researchers are reviewing these historical CNP16 series to identify the source of the observed pattern.

Quantifying differences with revised CNP16

In a second evaluation, we examine the differences between the original and revised CNP16 series by using widely accepted statistical measures for demographic estimates.¹⁹ While these statistical measures are commonly used by demographers to evaluate the accuracy of population estimates, we use them here as relative comparisons to show the differences between the original and revised CNP16 series. That is, we conceptualize each measure in terms of differences as opposed to errors.

Table 2 presents each statistical measure by state and census division. The first measure, the mean absolute error, reflects the average total error between the original and revised estimates. The mean absolute percent error and the symmetric mean absolute percent error measure the accuracy of the intercensal method when compared with the original postcensal CNP16 estimates. Finally, the mean algebraic percent error is a measure of bias and its direction.

Total differences, shown in the mean absolute error column of table 2, are directly proportional to a state’s population. At the high end, the difference between the original and revised CNP16 series was in the California estimates and averaged around 130,000 people. Comparatively, Montana had the smallest average difference of only about 1,093 people.

Using the symmetric mean absolute percent error, a measure of relative comparisons, we find that relative differences were weakly correlated with population size and were less than 2 percent across all states on average. The District of Columbia and Nevada showed the largest relative absolute differences of around 1.2 percent each. With the exceptions of Arizona, the District of Columbia, and Nevada, states had an average relative difference of less than 0.5 percent across all years. Overall, revised CNP16 data were often very close to the original values apart from the decennial breaks.

Revision effects on rates and ratios

The second impact of the population recontrols involves changes to labor force rates and ratios, specifically the labor force participation rate (LFPR) and the employment–population (E–P) ratio. The LFPR and the E–P ratio represent the civilian labor force and employment as a share of the CNP16. Because the CNP16 is the denominator for each measure, we expect the intercensal CNP16 controls to directly impact each measure around census years. To make valid comparisons between the original and the revised series, we focus on the seasonally adjusted LFPR and the seasonally adjusted E–P ratio to isolate differences attributable to the new CNP16 data that is not confounded by seasonal variation.

In chart 7, we show the original and revised seasonally adjusted LFPR and E–P ratio for Hawaii centered around the 2010 enumeration. Absent the intercensal CNP16 population controls, we note sizable breaks in both the LFPR and the E–P ratio around the 2010 enumeration of 2.8 and 3.1 percentage points, respectively. Under the old population controls, one might erroneously conclude an economic change in Hawaii’s labor force in April 2010 without implementing a specific outlier treatment for the month. After adjusting the underlying CNP16 series for the decennial break, we find a smooth transition between estimations from the 2000s and 2010s in the revised seasonally adjusted LFPR and the revised seasonally adjusted E–P ratio around the 2010 enumeration.

Decennial breaks in the LFPR and E–P ratio were not isolated to states with lower populations. For example, chart 8 shows large decennial breaks in the LFPR and E–P ratio for Illinois centered around the 1990 enumeration, with around 1.5 percentage points for each measure. The average monthly change in the surrounding years 1989 and 1990 was only around 10 basis points each month. In contrast, the decennial break was 150 basis points.

Discussion

In this article, we introduced the LAUS program’s method to produce intercensal CNP16 estimates for LAUS estimation. Implemented as of the 2024 annual reestimation cycle in March 2025, the intercensal CNP16 estimates replace historical population data and eliminate decennial breaks present in population and labor force measures. Our method applies standard demographic techniques to produce intercensal CNP16 series by distributing the difference between projected CNP16 from one census and the official count in the next census. State-by-state comparisons with previously released LAUS data show substantial improvements to both the CNP16 and labor force rates and ratios. Eliminating the decennial breaks captures smoother transitions around census years, which allows data users to make correct historical inferences about changes in state population and labor markets. Further, LAUS researchers aim to study the behavior of the historical CNP16 series predating April 2000 and to compare this series to auxiliary estimates by using the cohort-component method.