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Two-step seasonal adjustment

How two-step seasonal adjustment smoothes a series that combines data from different sources.

The economic problem

Combining data with different seasonal patterns

One of the most important measures of economic activity is employment. With its Current Employment Statistics (CES) program, the Bureau of Labor Statistics (BLS) produces monthly estimates of total nonfarm payroll employment.[1] To generate a series that provides timely estimates of current payroll employment as well as the most reliable historical figures, the CES series links two sources of data. The most recent employment estimates, referred to as the nonbenchmarked data, rely on the CES survey.[2] This survey samples about one-third of the nation’s business, and it provides timely information on recent payroll employment. In contrast, historical payroll employment numbers, referred to as benchmarked data, offer revisions to these estimates using more comprehensive data.[3]

Employment data often exhibit seasonal patterns, such as hiring at Christmas. To complicate matters further, the benchmarked and nonbenchmarked portions of the payroll employment series exhibit distinct seasonal patterns. For example, both the benchmarked and nonbenchmarked data show a decline in employment from December to January as businesses lay off temporary holiday workers, but the benchmarked data decline more steeply than the nonbenchmarked data during this period (Chart 1). This difference has important implications for seasonal adjustment.

Chart 1

When one combines these data and performs a standard seasonal adjustment, the seasonally adjusted data suggest that employment increases dramatically from December to January. Chart 2 illustrates this phenomenon. In this graph, the change in employment from December to January in the years covered by the benchmarked data appears smooth. But for the year in which the employment numbers rely on the nonbenchmarked CES survey data, it appears that employment increased steeply between these months.

Chart 2

The technical solution

Seasonally adjust each data source separately

As explained in "Seasonally Adjusting Data," the X12 seasonal adjustment procedure estimates the effects that occur every year in the same magnitude and direction and then removes these recurring seasonal components from the series to reveal the trend and remaining variation. Importantly, the magnitude of the seasonal changes differs across the benchmarked and nonbenchmarked data that make up the BLS payroll employment series. The benchmarked data exhibit a larger decline in employment from December to January than the nonbenchmarked data, so when the X12 procedure is applied to the combined data, it overestimates the negative seasonal factor for the December–January period covered by the nonbenchmarked data. As a result, when the data are adjusted to remove these estimated seasonal components, it appears that employment jumped substantially during this period.

Dallas Fed economists recognized that this December–January jump emerged regularly within the nonbenchmarked part of the data but not in the benchmarked part.[4] The Dallas Fed therefore developed an alternative seasonal adjustment procedure, known as the Berger–Phillips two-step method.

With the Berger–Phillips two-step method, the X12 procedure is applied separately to the benchmarked and nonbenchmarked CES survey data. Then, the two types of data are combined to create the complete employment series.

Real-world example

Two-step seasonal adjustment smoothes payroll employment data

Chart 3 plots the two-step seasonally adjusted Texas employment data from November 2009 to November 2012. This clearly illustrates how the steep increase in employment from December 2011 to January 2012 that arises with the standard method disappears with the two-step adjustment. Two-step seasonal adjustment allows analysts to more accurately assess the change in employment from one month to the next.

Chart 3


Seasonally adjusting data that have been constructed from multiple sources may create problems if the different data sources exhibit distinct seasonal patterns. Most notably, this arises when researchers combine employment data to create a continuous monthly series. By seasonally adjusting the data separately, a more accurate view of the trends in the series emerges.


  1. The BLS also releases employment estimates from a household survey, known as the Current Population Survey (CPS). However, the Dallas Fed’s two-step seasonal adjustment procedure is only used on the CES payroll employment series. For more information about the differences between the CPS and the CES, see
  2. This survey is also referred to as the Establishment Survey or the payroll survey.
  3. For more information on the CES survey and the revisions that generate the benchmarked data, see and See Early Benchmarking article in DataBasics for details on how the Dallas Fed’s early benchmarking procedure differs from the BLS methodology.
  4. See “Solving the Mystery of the Disappearing January Blip in Employment Data,” by Franklin D. Berger and Keith R. Phillips, Federal Reserve Bank of Dallas Economic Review, Second Quarter 1994.