PPI and CPI seasonal adjustment during the COVID-19 pandemic

The Bureau of Labor Statistics (BLS) publishes seasonally adjusted Consumer Price Index (CPI) and Producer Price Index (PPI) time-series data monthly. Seasonal adjustment removes within-year seasonal patterns from index data which have demonstrated observable seasonality over many years. In the case of price indexes, these within-year patterns may result from changing climatic conditions, production cycles, model changeovers, holidays, and sales. Seasonally adjusted data are usually preferred for short-term price analysis as they allow data users to focus on changes that are not typical for the time of year. To seasonally adjust, the PPI and CPI use historical data to estimate the seasonal pattern of a series and then remove the estimated seasonal pattern from the series. 

In 2020, multiple PPI and CPI series measured extreme price movements as a result of the COVID-19 pandemic. For example, the unadjusted PPI and CPI for gasoline decreased 54.7 and 16.5 percent respectively in April 2020. Because the PPI and CPI use historical data to estimate seasonal patterns, extreme price movements in 2020 could have adversely affected seasonal adjustment. This information page explains the steps the BLS took to mitigate the effects of the COVID-19 pandemic on seasonally adjusted price indexes. In particular, it outlines how BLS greatly increased the scope of intervention modeling for both the PPI and CPI in 2021 and how this strategy was effective in mitigating the effects of the COVID-19 pandemic on seasonal adjustment. As a result of this increase in intervention work, revisions to the all items CPI and the PPI for final demand during the 2021 seasonal revision were similar in magnitude to pervious revisions.

PPI and CPI seasonal methodology

Direct and Indirect adjustment: For both the PPI and the CPI, BLS utilizes direct and indirect seasonal adjustment methods. Direct seasonal adjustment is accomplished by applying seasonal factors to unadjusted data to remove within-year seasonal patterns. To directly adjust data, the CPI and PPI use the Census Bureau’s X-13ARIMA-SEATS software to implement a filter-based approach that employs moving averages of historical data to estimate the seasonal factors for the time series. PPI and CPI typically estimate factors using eight years of historical data for these estimates. Prior to conducting direct seasonal adjustment on a series, however, the PPI and CPI test it for seasonality and only adjust the series if it exhibits statistically significant seasonality. The Bureau utilizes three primary measures to determine whether a particular PPI or CPI should be seasonally adjusted: F(s), M7, and Q. F(s) is a measure of stable seasonality, M7 determines the amount of moving seasonality relative to the amount of stable seasonality, and Q is a weighted average of several diagnostic statistics.[i]  For a series to be deemed seasonal it must meet the following QC thresholds: F(s) ≥7, M7<1, Q<1. 

Indirect adjustment is a method of seasonal adjustment used for aggregate series. In this method, two or more directly adjusted component indexes are combined into higher level time series. Seasonal factors are not estimated for or applied to indirectly adjusted series. In general, most PPI commodity data are directly adjusted, while FD-ID PPIs are indirectly adjusted. In the CPI, most national level published series are directly seasonally adjusted, while a smaller number of aggregate series receive indirect seasonal adjustment.

Intervention analysis: Nonseasonal events such as natural disasters, pandemics, or wars can distort the underlying seasonal pattern of an index. Intervention analysis entails estimating and removing the one-off effects of these events from indexes prior to testing them for seasonality and developing seasonal factors. The goals of intervention analysis are to determine whether a seasonal pattern exists and to correctly estimate seasonal factors in spite of any distortion that might arise in the pattern. The Bureau applies intervention analysis to selected directly adjusted PPI and CPI indexes. The Bureau uses X-13ARIMA-SEATS to conduct both CPI and PPI intervention analysis.  Using that method, ARIMA models that include prespecified intervention variables are estimated for a time series. These variables are used to identify the statistical significance and relative effects of nonseasonal events on time series. In cases where a nonseasonal event (such as the COVID-19 pandemic) is found to significantly affect a time series, the effects of the event can be removed from the original time series by using the estimated coefficients from the ARIMA model. Three types of intervention variables are employed: outliers, level shifts, and ramps. (Ramps allow for a linear increase or decrease in the level of a series over a specified time interval.)  After nonseasonal effects are removed from the original time series, standard direct seasonal adjustment methods as described earlier are applied to the indexes to test for seasonality and to develop seasonal factors.

More than 1,500 producer and consumer price indexes are currently eligible for direct seasonal adjustment. Conducting intervention modeling on this entire set of indexes is not feasible because of resource constraints. Consequently, the Bureau performs intervention modeling on only a relatively small set of PPIs and CPIs, referred to as intervention candidates. For a PPI to be an intervention candidate, the index must comprise at least one-percent of a major FD-ID index. The major FD-IDs include final demand goods, final demand services, processed goods for intermediate demand, unprocessed goods for intermediate demand, and services for intermediate demand. Likewise, for a CPI series to be an intervention candidate, the index must account for at least 0.5 percent of the All Items CPI or be a subset of an already qualifying component series. The BLS examines all intervention candidates annually to determine whether intervention modeling will improve seasonal adjustment of the series and performs intervention modeling if it would lead to more accurate seasonal adjustment. 

Historical revision: Each year, with the release of the January data, PPI and CPI seasonal factors are recalculated to reflect price movements that occurred during the just-completed calendar year. Seasonal factors are recalculated 5 years back, and all seasonally adjusted data are updated on the basis of these new factors. For example, in January 2021 factors were recalculated from 2013–2020 data and seasonal data from 2016–2020 were updated in accordance with the new set of factors. After the yearly revision, the PPI and the CPI for the upcoming year are calculated with the previous year’s set of seasonal factors. For instance, the 2020 factors, from the January 2021 revision, are used to calculate indexes throughout 2021.

Potential negative effects of COVID-19 on seasonal adjustment

The PPI and CPI expected that the extreme price movements resulting from the COVID-19 pandemic could inhibit the typical seasonal signal observed in their data. To empirically test this expectation, seasonality tests were conducted on high-level unadjusted PPI and CPI series inclusive and exclusive of COVID period data.  In particular, tests were conducted using 8-years of data ending with the year listed in Table 1. For example, 2019 tests were conducted with data from 2012-2019. If COVID-19 related price movements did inhibit the ability to detect seasonality in PPI and CPI data, we would expect a decline in the seasonality test statistics when 2020 data is included their estimation. Table 1 presents QC statistics from seasonality tests conducted on high-level PPI and CPI series. The All Items CPI F(s) falls from over 43 to approximately 17 when 2020 data is included in the tests. Likewise, F(s) for the PPI for final demand falls substantially when 2020 data are included in the tests. 

Turning to a more specific example, Chart 1 presents the CPI for used cars and trucks and the PPI for automobile retailing from January 2013 through December 2020. The PPI for automobile retailing measures trade margins, calculated as the sales price less the acquisition price, while the CPI for used cars and trucks measures the final sales price of the car or truck.[ii]  In spite of these methodological differences, both indexes appear to have been affected by COVID-19 related shocks. The CPI for used cars and trucks rose rapidly from June through September 2020, and margins for automobile sales jumped from April through July and then again later in 2020.  

To better understand how the COVID-19 Pandemic affected seasonality in these series, seasonal factors estimated with pre-Covid data (from 2012-2019) are compared to factors estimated with data from 2013-2020. (See Charts 2a and 2b.) The seasonal factors estimated including data from 2020 differ substantially from those estimated with pre-COVID-19 data. For PPI, the 2020 factors expect an increase from May to June which is not expected in the 2019 factors. Likewise, for CPI, the trend of the seasonal factors diverged from May to June after adding 2020 data. The seasonal factors had a more positive slope when 2020 data was included in their estimation as compared to those estimated with data from 2012-2019. These changes in seasonal factors are likely problematic, as seasonality by its nature should not shift much over time. 

QC statistics estimated with data from 2012-2019 are also compared to those estimated with data from 2013-2020. The QC stats indicate a clear decline in detectable seasonality for both PPI and CPI from 2019 to 2020. For PPI, F(s) falls almost 8 points when 2020 data is included in the tests and no longer indicates seasonality. For CPI, there is a similar trend. The F(s) for used cars and trucks fell more than 17 points after including 2020 data, suggesting that seasonality was strongly attenuated by the COVID-19 pandemic.

This section illustrates, using both high-level CPI and PPI data and a detailed commodity-level example, how the extreme price movements in 2020 affected the detection and estimation of seasonal patterns in price index data.

Intervention analysis to mitigate the effects of the COVID-19 pandemic on seasonal adjustment

This section shows how intervention analysis can be used to mitigate the effects of these extreme price movements on seasonal adjustment, again using automobiles as an example. Recall, intervention analysis entails estimating and removing the effects of non-seasonal events from indexes prior to testing them for seasonality and developing seasonal factors.

Earlier examination of price movements, QC statistics, and seasonal factors indicate that COVID-19 driven price movements could negatively affect seasonal adjustment of the CPI for used automobiles and the PPI for automobile retailing. For these reasons, BLS developed intervention models for these series that included variables to offset the effects of COVID-19 related price movements. The intervention model for PPI included ramps from March 2020 through April 2020 and from April 2020 through July 2020, as well as an outlier in November 2020. For CPI, the intervention model consisted of a ramp from June 2020 through September 2020. Tables 3a and 3b present coefficients, standard errors, and t-statistics from these intervention models.

Charts 3a and 3b compare seasonal factors for automobile sales estimated with the 2012-2019 data to those estimated with data from 2013-2020 (both utilizing the intervention models presented earlier and without the intervention models). Without the intervention models, the 2020 factors deviate considerably from the 2019 factors, which is undesirable as factors should generally be relatively stable across years. For both PPI and CPI, the interventions included to offset COVID-19 related price movements clearly result in factors more similar to those estimated in 2019, which again highlights the necessity of intervention modeling to mitigate the effects of the COVID-19 pandemic on seasonal adjustment. Table 4 presents QC statistics for automobiles generated using the above intervention models. For both CPI and PPI, the QC statistics indicate seasonality after controlling for the effects of COVID-19.

The following example shows how intervention modeling can be effectively used to mitigate the effects of COVID-19 on seasonal adjustment. 

Increase in scope of intervention modeling expansion and outcome 

After considerable analysis, both the CPI and PPI relaxed their relative importance rules for intervention candidates and expanded the scope of intervention work in 2020 in an effort to offset the effects of the COVID-19 pandemic on the seasonal adjustment. Toward that end, BLS conducted an extensive investigation of PPI and CPI series whose seasonal adjustment may have been affected by the COVID-19 pandemic. In particular, economists evaluated each series that was seasonally adjusted in 2019 by visually examining the series for extreme price movements in 2020, generating quality control statistics with data from 2013-2020 and comparing them with those generated with data from 2012-2019, generating seasonal factors with data from 2013-2020 and comparing them with those generated with data from 2012-2019, running automatic outlier detection during the COVID-19 period, and consulting with expert industry and commodity analysts. In cases where this analysis indicated that COVID-19 related price movements would have an adverse effect on seasonal adjustment, the series was included as an intervention series for 2020. For series that were added due to the impact of COVID, only interventions during 2020 were included in their models. 

Economists applied intervention analysis on 68 CPIs in 2020, as compared to 32 in 2019. Of the 68 series that received intervention analysis, 47 were added in order to mitigate COVID-19 effects on seasonal adjustment. For CPI, the total number of interventions increased about 70 percent from 2019 to 2020. Economists applied intervention analysis on 76 PPI series in 2020, as compared to 41 in 2019. Of the 76 series, 36 series were added strictly to mitigate COVID-19 effects on seasonal adjustment. The total number of interventions for PPI increased 64 percent from 2019 to 2020.

To measure whether the efforts undertaken by the BLS to offset the effects of the COVID-19 pandemic on seasonal adjustment were effective, revisions in top level indexes resulting from the 2020 revision were compared to those from previous revisions. If the revisions to 2020 data are similar to those from the previous three periods, it can be inferred that efforts to offset the COVID-19 pandemic on seasonal adjustment were effective, as adding the 2020 data to the estimation of factors did not result in large revisions. Table 5 compares average revisions to index percent changes based on the 2020 seasonal revision to the previous three seasonal revisions. The average annual seasonal revisions to both the PPI for final demand and all items CPI were similar in 2020 to the previous three years.

Conclusion

The COVID-19 pandemic resulted in extreme movements in many producer and consumer price indexes in 2020. Because BLS uses historical data to estimate seasonal factors, the extreme price movements resulting from the COVID-19 pandemic created difficulties in the estimation of seasonal data. To overcome these difficulties, the BLS expanded the scope of intervention modeling for the CPI and the PPI in 2020. The number of series PPI conducted intervention analysis on rose by more than 85 percent in from 2019 to 2020 (from 41 to 76), and CPI intervention series rose by 113 percent over the same period (from 32 to 68). Likewise, the total number of interventions in the PPI increased by approximately 64 percent from 2019 to 2020 (from 172 to 282) and those in the CPI rose 70 percent (from 64 to 109). As a result of this additional intervention modeling, the seasonal revisions to historical data seen in 2020  for both data products were in line with previous revisions, indicating that BLS successfully mitigated the effects of the COVID-19 pandemic on the CPI and PPI seasonally adjusted data.

Additional Information

Additional information may be obtained from the Consumer Price Index program by email or calling 202-691-6968, or from the Producer Price Index program by email or calling 202-691-7705.

Footnotes:

[i] Julius Shiskin, Allan Young, and John Musgrave, “The X-11 variant of the Census method II seasonal adjustment program”, Bureau of Census Technical Paper No. 15, 1967.