# A Look at How Oregon’s Unemployment Rate Is Calculated

August 1, 2018

This article examines the technical methods used to compute Oregon’s unemployment rate that is reported by the Oregon Employment Department each month. The unemployment rate is produced in cooperation with the U.S. Bureau of Labor Statistics (BLS) in the Local Area Unemployment Statistics (LAUS) program. LAUS is a Federal-State cooperative program. Each state and the District of Columbia use the same methodology to compute the unemployment rate.

A variety of statistical and mathematical techniques are involved in calculating Oregon’s unemployment rate each month – survey sampling, time-series modeling, model-based benchmarking, seasonal adjustment, and data smoothing. The descriptions of the statistical and mathematical techniques in this article that play a role in producing an unemployment rate each month rest upon deeper statistical and research foundations.

**Labor Force Concepts**

The data published by Oregon and the BLS from the LAUS program are the “labor force data.” Labor force data consist of the civilian labor force, total employment, total unemployment, and the unemployment rate. Labor force concepts used in the LAUS program are based on the U.S. Census Bureau’s Current Population Survey (CPS). The following are basic definitions of labor force concepts:

*Civilian Noninstitutional Population (CNP):* all persons 16 years and older living in the 50 states and the District of Columbia, excluding persons on active duty in the U.S. Armed Forces and the institutional population. The institutional population consists of residents of penal or mental institutions and homes for the aged. This base population is used in the following definitions.

*Civilian Labor Force:* all persons in the CNP classified as either employed or unemployed.

*Labor Force Participation Rate:* the share of the CNP that is in the labor force, expressed as a percent.

*Not in the Civilian Labor Force:* all persons in the CNP who are neither classified as employed or unemployed. Examples include students, persons with disabilities who are unable to work, persons caring for their own homes and families, children or elderly, retirees, and those discouraged by job prospects.

*Employed:* all persons who, during the reference week (the Sunday through Saturday calendar week that includes the 12^{th} day of each month), did any work as paid employees, worked in their own business or profession or on their own farm, or worked 15 hours or more as an unpaid worker in an enterprise operated by a member of their family, or were not working but who had jobs from which they were temporarily absent.

*Employment-population ratio:* the share of the CNP that is employed, expressed as a percent.

*Unemployed:* all persons who had no employment during the reference week, but were available for work, and had made specific efforts to find employment at some time during the four-week reference period ending with the reference week.

*Unemployment Rate:* the share of the civilian labor force that is unemployed, expressed as a percent.

There is a common misperception that the unemployment rate is only a count of people who are receiving Unemployment Insurance (UI) Benefits. However, an individual is counted as unemployed if they meet the criteria in the above definition, irrespective of their status regarding the collection of UI benefit payments. The unemployment rate and labor force data are based primarily on information collected from a survey sample of households (Current Population Survey), an entirely different source of information from UI administrative data sources.

**The Current Population Survey**

The CPS is a survey of households conducted by the U.S. Census Bureau each month. CPS interviewers ask respondents in households selected about the activity of all people age 16 and older. Each person’s activity during the reference week (the Sunday through Saturday calendar week that includes the 12th day of each month) determines their labor force status. The CPS counts an individual’s labor force status only once at the person’s place of residence.

Data collected from the CPS are used to produce labor force estimates directly for the United States and indirectly for the individual states and the District of Columbia. Nationally, there are some 60,000 eligible households in the sample. In Oregon, the sample size is around 1,000 assigned households.

**CPS Design and Methodology**

The CPS is designed to collect information about the civilian nonstitutional population in a cost-effective way. Although interviews with every individual in an area would provide the most accurate labor force data, this would be time consuming and expensive. Therefore, the survey is designed to randomly select and interview a smaller group of households within the larger population of households. Sampling theory asserts that if members of the smaller group are chosen in a particular way, then generalizations can be made about the larger population using data collected from the smaller group. The tradeoff of using survey sample data, however, is that the data will contain sampling error – the difference between the survey sample data and the hypothetical data that would be obtained if the entire population were interviewed.

Households in the CPS are initially selected using a probability design. The sample of households is selected annually from a continually updated file containing addresses. Oregon is divided into smaller geographical units, and households are selected within some of these geographical units to participate in CPS. Steps are taken to ensure the survey is reflective of the area’s demographic and socioeconomic characteristics.

Part of the CPS sample changes each month. This is called the “4-8-4” sample rotation design, where a selected household is questioned for four consecutive months, dropped from the sample for eight months, and then returned to the sample and questioned for another four months. As a result, 75 percent of the households remain the same from month to month. Fifty percent of the households remain in the sample from the prior year. Once a household permanently leaves the sample, it is replaced by a nearby household to ensure that the survey remains reflective of the area’s demographic and socioeconomic characteristics.

**CPS Data Reliability**

The CPS design has implications on the reliability of state CPS data. Reliability refers to the level of confidence that the data meet a certain level of accuracy and are sensitive enough to detect real changes of a given magnitude. Because of a small sample size and design, state CPS data have low reliability.

There are important characteristics of CPS survey error related to survey design. The sample overlap (4-8-4 rotation method) causes autocorrelated sampling error. Autocorrelation is a statistical measure that indicates the dependence of a variable at some point in a time series on variables at other time points. The basic idea is that periods of overestimation and underestimation of the true value result from the way

households are rotated in the survey. Since 75 percent of the households remain the same from month to month, a sample that is not representative of the population one month is likely to carry over into the next month.

Other factors that affect state CPS data reliability are changes to CPS design, sample size, and variation in labor force levels. These changes impact the size of CPS survey error. Thus, the magnitude of CPS survey error varies over time.

The first graph contains CPS unemployment rate data by month from January 2006 to the present and illustrates the important characteristics of CPS survey error. Wide month-to-month swings in CPS data make it difficult to discern real labor market changes from survey error, or “noise.” For this reason, CPS data are not published. Econometric time series models are applied to state CPS data to minimize the impact of survey error on published labor force data for Oregon.

**Time Series Modeling**

A time series is a sequence of data for a particular phenomenon recorded over time. An econometric or time series model is a math function used for identifying, describing, and forecasting underlying patterns in a time series. These patterns provide important information regarding present and future time series observations.

Many economic time series data measured in quarterly or monthly units of time can be separated into components that explain trend, seasonal, and irregular patterns. The trend component represents movements in the data series that last more than a year, including the underlying upward or downward tendency of the time series. The trend component is also useful for identifying turning points in the series. The seasonal component represents patterns in the data that make a complete cycle every 12 months. Seasonal fluctuations in the data are caused by events such as weather, holidays, and school schedules. The irregular component is what is left over after accounting for trend and seasonal components.

CPS labor force data contain trend, seasonal, and irregular patterns, which are found in many economic time series, plus unique patterns related to survey error that are specific to the CPS design. In other words, the CPS unemployment rate for any given month is not only a combination of trend, seasonal, and irregular influences, but also contains some influence from the survey error. The models for Oregon’s CPS data describe the data as a combination of trend, seasonal, and irregular patterns, or “signal,” along with a component that accounts for error patterns in CPS data, or “noise.” Thus, the models take the form of “signal-plus-noise.”

**Employment and Unemployment Signal-Plus-Noise Models**

The CPS employment and unemployment levels are modeled separately using the signal-plus-noise form. There are four models used to derive Oregon’s labor force estimates each month – a model for each signal component and a model for each noise component. The employment and unemployment models are developed for Oregon by BLS statisticians using data back to 1976 that are specific to Oregon. The noise models account for the problem of autocorrelated errors and changing reliability in the state CPS data.

The employment and unemployment models of the signal use trend estimates from regressor variables to explain the trend variation in CPS employment and unemployment levels. This relationship between the trend in the model input variables – UI claims and total nonfarm payroll employment – and the CPS trend are represented by a regression component in the model. This regression component represents the part of the CPS trend that can be explained by the trend in the input variable, and this component is added to another that accounts for the unique behavior of the CPS trend. A filtering algorithm, called the “forward filter,” is used to compute the current monthly employment and unemployment estimates for Oregon. The filter combines CPS data with model-produced estimates to mitigate the influence of survey error on labor force levels.

Time series models create better estimates of the true labor market situation than the volatile survey of households can provide. The second graph shows how the model improves the estimate of the CPS unemployment rate found on the first graph. The model estimates do not contain the large, volatile swings that are present in the CPS monthly data, as the modeling and filtering process reduces the influence of survey error on the unemployment rate. The use of time series models provides a cost-effective way to increase the reliability of state CPS data, as these can be used to reduce monthly volatility that would otherwise have to result from a costly CPS sample expansion.

**Model-Based and Smoothed Seasonal Adjustment**

There are two versions of the unemployment rate published for Oregon each month. One is Oregon’s nonseasonally adjusted unemployment rate. The other is the seasonally adjusted unemployment rate. The seasonally adjusted unemployment rate reflects an adjustment for short-term, recurring seasonal events and a further procedure that smoothes irregular fluctuations from the data. The purpose of seasonal adjustment is to remove short run fluctuations from the data so longer run fluctuations related to the business cycle (the trend) can be more easily analyzed.

Economic time series data often exhibit seasonal fluctuations, movements in the data that recur during a specific time period each year. For example, the winter months in Oregon exhibit higher periods of unemployment while the summer months exhibit lower periods of unemployment. These higher and lower periods of unemployment are a product of the weather (or season), and obscure the underlying direction of unemployment.

The time series models behind Oregon’s employment and unemployment data are designed to produce seasonally adjusted data. The models of the signal are written as a combination of trend, seasonal, and irregular components. Subtracting the seasonal component provides Oregon’s seasonally adjusted unemployment rate. The seasonally adjusted unemployment rate cuts through the center of the unadjusted series, thereby revealing the underlying trend in unemployment that is obscured by the recurring seasonal peaks and troughs.

The seasonally adjusted data are smoothed by the Reproducing Kernel Hilbert Space (RKHS) Filter. The econometric models of CPS simultaneously estimate and benchmark (described in the next section) seasonally adjusted data. More stable estimates of seasonality are produced by the model through the application of a series of linear filters from the X-11 seasonal adjustment method to the benchmarked not seasonally adjusted data series. This step ensures there is no residual seasonality in the series, which could potentially be introduced by the benchmark procedure. The RKHS Filter is a set of weights applied to seasonally adjusted data to smooth irregular fluctuations in the series, resulting in data that are less volatile than those produced using only seasonal adjustment filters. Although labeled as “seasonally adjusted,” seasonally adjusted data in the third graph reflect both seasonal adjustment and smoothing; these data are also referred to as “Smoothed Seasonally-Adjusted.”

**Model-Based Benchmarking**

Published labor force data for Oregon reflect model-based estimation and benchmarking. A “benchmark” is a procedure that ensures that individual state estimates will add up to a more reliable national total as part of monthly estimation.

Model-based estimation and benchmarking ensures that not seasonally adjusted employment and unemployment data for the 50 states and the District of Columbia sum to national labor force levels. This is accomplished as part of the estimation process, where estimates produced for each state by the time series models automatically add up to Census Division control totals. All state models within a Census Division are combined and estimated at once, and as part of estimation a “correction term” is produced for each state that ensures all the estimates add up to the totals for the Census Division. The size of the adjustment to each state’s estimate depends on how much the state contributes to the overall difference between the Census Division totals and the sum-of-state totals within the division.

Oregon’s model-produced data values are benchmarked to Pacific Census Division levels. This division includes Oregon, Washington, California, Alaska, and Hawaii.

**How Accurate Are Oregon’s Labor Force Estimates?**

Producing estimates of labor force values (as opposed to interviewing the entire population) helps to control costs, but the tradeoff is that the estimates likely differ from the hypothetical true values that would be obtained if the entire population were interviewed. This difference is known as “sampling error” in the statistical literature. To help users interpret the likely accuracy of any estimate, it’s useful for data to be reported with standard errors. Standard errors are developed for Oregon’s seasonally adjusted and not seasonally adjusted labor force data.

Standard errors indicate the probable accuracy of Oregon’s labor force estimates. They can be used to construct confidence intervals, or error ranges. An error range is a range of numbers above and below the point estimate that likely contains the true value for a given level of confidence. The width of an error range indicates the level of uncertainty associated with an estimate. Wider error ranges contain more possible numbers that the true value is likely to assume. Thus, broad error ranges indicate less certainty about the accuracy of the estimate, while narrow error ranges indicate more accuracy. Oregon’s preliminary June 2018 seasonally adjusted unemployment rate of 4.0 percent had an error range of 3.5 to 4.5 percent at the 90 percent confidence level.

**Revisions to Labor Force Data**

Like most data from agencies that produce statistics, the labor force numbers undergo revisions. The first time that a number is released to the public, it is labeled as a “preliminary” estimate. The number is revised the following month when the next preliminary estimate in the series is published and is labeled as “revised” or “final” at that time. However, these numbers will be revised again near the beginning of the following year during annual processing.

Annual processing occurs shortly after the completion of each calendar year. At this time, more revisions are made to the labor force data. The historical series of modeled estimates is reprocessed using a smoothing algorithm. This smoothing algorithm is different from the smoothed-seasonal adjustment process, based on the RKHS Filter. Basically, running the initial forward filter estimates through the smoothing algorithm, or “backward smoother” as it is often called, produces better estimates since the smoothing algorithm uses more information than the forward filter had available to create the estimate. This algorithm is called the “smoother” since the estimates it creates are smoother in appearance than those created by the “filter.” The smoothed model estimates are benchmarked to reprocessed Census Division model estimates. In addition, updates to the model inputs and revised state CPS data reflecting new population controls are incorporated into the state labor force data at the annual processing time.

**Conclusion**

Labor force estimates are produced using funding and methodology from the BLS. They are referred to as estimates because they are based on a survey sample of the population, and time series modeling and benchmarking – but not a census. The basic idea behind the LAUS estimating procedure is to take a CPS unemployment rate and remove the survey error and recurring seasonal effects. This reveals a clearer picture of the long-run trend in the labor market.