The U.S. 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 regularly occurring within-year patterns over many years. In the case of price indexes, these within-year patterns may result from changing of seasons, production cycles, model changeovers, holidays, and sales. Seasonally adjusted data are usually preferred for short-term price analysis because they allow for comparability across months without the influence of normal seasonal fluctuations. To seasonally adjust data, the CPI and PPI use the U.S. Census Bureau’s X-13ARIMA-SEATS software to implement a filter-based approach that employs moving averages of historical data to estimate the seasonal pattern of a time series.1 After BLS staff members estimate the seasonal pattern, the data are seasonally adjusted by removing the within-year seasonal movements from the time series.
In 2020, multiple PPI and CPI series measured extreme price movements because of the coronavirus disease 2019 (COVID-19) pandemic. For example, in April 2020, the unadjusted PPI and CPI for gasoline decreased 53.0 and 16.5 percent, respectively. Because the PPI and CPI use historical data to estimate seasonal patterns, extreme price movements in 2020 may have adversely affected seasonal adjustment. This article explains how BLS mitigated 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 2020 seasonal revision (which occurred in January 2021) were similar in magnitude to previous revisions. Throughout this article, an annual seasonal revision is referred to by the most recent year of data revised, not by the calendar year in which the revision occurred. For example, the 2020 annual seasonal revision refers to updating seasonally adjusted indexes from 2016 to 2020. The 2020 seasonal revision actually occurred in calendar year 2021.
This article describes in detail seasonal adjustment methods used. It also summarizes the areas within the PPI and CPI most affected by the COVID-19 pandemic. Next, it provides several examples of time series whose seasonal adjustments would have been less accurate relative to prior revisions if no steps were taken to mitigate the effects of the COVID-19 pandemic. Then, the article describes how BLS mitigated the effects of COVID-19 on seasonal adjustment. The final section summarizes the results.
PPI and CPI seasonal methodology
For both the PPI and the CPI, BLS uses direct and indirect seasonal adjustment methods. To do direct seasonal adjustments, BLS applies seasonal factors to unadjusted data to remove within-year seasonal patterns. 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 the PPI, commodity-based indexes and Final Demand–Intermediate Demand (FD–ID) aggregation system indexes are eligible for seasonal adjustment. Most of the PPI commodity data that receive seasonal adjustment are directly adjusted. By contrast, BLS seasonally adjusts all its FD–ID PPIs using an indirect method. FD–ID PPIs are constructed by using a census value of shipments and revenue data along with U.S. Bureau of Economic Analysis input–output data to combine lower level commodity PPIs. Meanwhile, in the CPI, 330 national-level published series are eligible for direct seasonal adjustment and 65 series receive indirect seasonal adjustment. (CPI directly seasonally adjusts 167.) BLS periodically identifies a set of component CPI series for seasonal aggregation that are mutually exclusive and represent the complete weight of all items in the CPI. BLS selects this component series set to maximize the percentage of weight of the all-items index that receives seasonal adjustment. Therefore, BLS uses direct adjustment for its lower level CPIs (at the seasonal component-level and below) and indirect adjustment for all upper level aggregate indexes. Lower level indexes track price changes for specific goods and services over time, whereas upper level indexes track price changes for groupings of lowerlevel commodity indexes. Upper level CPIs are constructed by BLS using consumer expenditure weight data to combine lower level indexes.
Direct adjustment
BLS tests all PPI and CPI series that are eligible for direct adjustment for seasonality, and if seasonality is found, the series are seasonally adjusted. Using X-13ARIMA-SEATS,2 a software program published by the U.S. Census Bureau, BLS tests both seasonality and direct seasonal adjustment. Seasonal adjustments are based on the X-11 variant of the Census II seasonal adjustment method. X-11 is a filter-based approach that employs moving averages to estimate trend and seasonal components in turn. Components are refined through several iterations of weighted moving averages. For both the PPI and CPI, BLS uses a multiplicative time-series decomposition model by default, calculated as
.
In this model, 
, is the value of the observed series at time t, 
represents the trend-cycle component at time t, 
is the seasonal component at time t, and 
is the irregular component at time t. The multiplicative model is appropriate when a series has changing variation with time, as is often seen with PPI and CPI series. To enable the use of symmetric moving-average filters on a series, X-13 ARIMA-SEATS uses an ARIMA (Auto-Regressive Integrated Moving Average) modeling facility to forecast and backcast observations past the endpoints of the data.
F-tests are among the many diagnostics that are available for assessing the quality and stability of seasonal adjustments. F-tests look for the presence of stable and moving seasonality and quality control (QC) statistics from X-11.3 BLS uses 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. In general, for a series to be deemed seasonal, it must meet the following QC thresholds: F(s) ≥ 7, M7 < 1, Q < 1.
Lower level CPIs and commodity PPIs that are found to exhibit a level of seasonality warranting adjustment (on the basis of meeting the QC thresholds) are directly adjusted by applying a seasonal factor to the unadjusted index according to
,
where
is the seasonal index value at time t, 
is the unadjusted index value at time t, and 
is the seasonal factor (the estimate of seasonal component from the previous equation) at time t. Seasonal factors indicate the seasonal pattern of a time series and are derived from historical unadjusted data. Seasonal factors are relatively stable over time. BLS typically uses 8 years of unadjusted monthly data to develop factors and test seasonality for both sets of indexes.
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 before they are tested for seasonality and before seasonal factors are developed. The goals of intervention analysis are to determine whether a seasonal pattern exists and to correctly estimate seasonal factors despite any distortion that might arise in the pattern. BLS applies intervention analysis to selected directly adjusted PPIs and CPIs. To conduct both CPI and PPI intervention analysis, BLS uses X-13ARIMA-SEATS. Using this method (X-13), BLS estimates ARIMA models that include prespecified intervention variables for a time series. These variables are used to identify the statistical significance and relative effects of nonseasonal events on time series. In cases in which 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 PPIs and CPIs are currently eligible for direct seasonal adjustment. Conducting intervention modeling on this entire set of indexes is not feasible because of resource constraints. Consequently, BLS 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 1 percent of a major FD–ID index. The major FDs–IDs indexes include goods for final demand, services for final demand, 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. Each year, BLS examines all intervention candidates for price index series to determine whether intervention modeling will improve seasonal adjustment of the series and performs intervention modeling if it leads to a more accurate seasonal adjustment. In 2020, these criteria were relaxed to address widespread extreme price movements resulting from the COVID-19 pandemic. (See section “Mitigating the effects of the COVID-19 pandemic,” in this article.)
Indirect adjustment
High-level indexes, such as the PPI for final demand and the CPI for all items, are indirectly seasonally adjusted by aggregating lower level series that are components of higher level indexes. Seasonally adjusted components are used when available (that is, when the lower level index received a seasonal adjustment); otherwise, unadjusted indexes are used. BLS indirectly adjusts all its FD–ID indexes, as well as any indexes that are aggregates of intervention indexes. In this manner, interventions estimated for lower level indexes are indirectly included in aggregate indexes. BLS indirectly seasonally adjusts the all-items CPI and 65 other aggregate series.
Yearly revisions and projected factors
Each year, with the release of the January data, the 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 to 2020 data and seasonal data from 2016 to 2020 were updated according to 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 are used to calculate indexes throughout 2021.
Prices most affected by the COVID-19 pandemic
The COVID-19 pandemic affected both producer and consumer prices for a wide variety of products. This section provides an overview of products whose prices were most affected by the pandemic. This summary, however, does not document all product prices that were affected by the COVID-19 pandemic. It only highlights some areas in which prices and, consequently, seasonal adjustment were severely affected. As such, the summary will focus on prices for food, petroleum products, leisure and hospitality services, and automobile sales.
The COVID-19 pandemic substantially affected domestic producer and consumer prices for foods because stay-at-home orders and other pandemic-related policies affected both purchase and production patterns for food. In general, a notable decrease occurred in demand for food from restaurants, hotels, and institutional customers (primarily schools and universities). In addition, several supply disruptions occurred at food processing plants.4
Foods
The PPI for final-demand foods increased 1.5 percent between March and the end of 2020. (See table 1.) This relatively modest yearly increase does not, however, reflect the underlying volatility within the index, because the index swung significantly throughout the year. In May, the PPI for final-demand foods increased 6.4 percent, before declining 4.7 percent and 1.2 percent in June and July. Prices then rebounded in September and rose through November. Consumer food prices were also affected by the COVID-19 pandemic in 2020, because food-at-home prices typically rose and food-away-from-home prices became more volatile. (See table 1.) Prices for food at home during the year increased the most from March through June, rising 0.5, 2.7, 0.8, and 0.5 percent, respectively. Changes in both the PPI for final-demand foods and the CPI for food at home were driven by high volatility in prices for meat, dairy, eggs, and corn.
Table 1. Producer price and consumer price indexes for selected foods, monthly percent changes, not seasonally adjusted, January to December 2020| Category | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
|---|
Producer price index |
|---|
Final demand foods | 0.1 | –1.8 | 0.1 | –0.2 | 6.4 | –4.7 | –1.2 | –0.4 | 1.3 | 1.8 | 0.1 | –1.2 |
|---|
Slaughter livestock | 3.7 | –2.3 | –5.1 | –6.6 | 14.8 | –10.9 | –6.4 | 7.4 | 3.8 | 5.2 | –0.5 | –4.1 |
|---|
Meats | –1.9 | –2.8 | –0.6 | 6.1 | 43.0 | –26.8 | –11.6 | 0.8 | 3.4 | 1.1 | 1.7 | –1.4 |
|---|
Raw milk | –5.3 | –3.5 | –4.8 | –20.0 | –5.6 | 33 | 13.3 | –8.3 | –4.7 | 12.8 | 5.5 | –13.2 |
|---|
Eggs for fresh use | –35.2 | 33.4 | 26.4 | 31.8 | –44.6 | –12.7 | 6.2 | –9.9 | 16.7 | 25.5 | –2.8 | –24.9 |
|---|
Corn | 4.7 | –1.8 | –0.6 | –18.4 | –2.3 | 4.1 | –0.7 | –5.5 | 16.9 | 8.2 | 9.6 | 2.5 |
|---|
Consumer price index |
|---|
Food at home | 0.6 | 0.4 | 0.5 | 2.7 | 0.8 | 0.5 | –1.0 | –0.1 | –0.4 | 0.2 | –0.6 | 0.3 |
|---|
Meats, poultry, fish, and eggs | 0.0 | 0.2 | 0.5 | 4.5 | 3.4 | 2.1 | –3.6 | –1.5 | –0.6 | 0.2 | –0.2 | –0.3 |
|---|
Beef and veal | –0.1 | 0.2 | 0.6 | 4.2 | 10.9 | 5.5 | –8.2 | –4.6 | –1.4 | –0.3 | –0.1 | –0.4 |
|---|
Eggs | –2.2 | 0.3 | 1.7 | 15.0 | –8.0 | –4.9 | –3.9 | –2.3 | 0.8 | 1.4 | 1.4 | 0.7 |
|---|
Dairy and related products | 0.5 | 0.6 | 0.5 | 1.4 | 0.6 | –0.8 | –0.6 | 1.8 | –0.2 | –0.7 | 0.2 | 1.0 |
|---|
Meat prices were affected by low demand from restaurant and institutional customers and by supply shortages. Many meat processing plants were forced to close because of worker illness, and most plants modified production processes to protect workers once the plants reopened.5 Likewise, COVID-19-related lockdowns substantially decreased demand for dairy products from schools and university dining facilities. Notably, these decreases in demand from institutional customers who purchase milk in bulk quantities lowered producer prices. Dairy farmers who normally sell milk to bulk-packaging customers were forced to dump substantial amounts of their product.6 Egg prices were affected by COVID-19-related lockdowns in relation to Easter. Both the CPI and PPI for eggs rose in April 2020 because of increased consumer demand resulting from Easter. Before Easter, there was an excess of eggs, and because of the lack of restaurant and institutional demand, these eggs were sold mainly to grocery stores, which caused prices to decline.7 Finally, corn prices were affected by the pandemic and by a crude petroleum price war between Russia and Saudi Arabia that drove crude petroleum prices and, subsequently, corn prices lower. Corn is used to manufacture ethanol, which is typically added to gasoline. Ethanol and gasoline are, therefore, complementary goods whose prices often move in tandem. Throughout 2020, the activity in the ethanol market dominated price movements for corn. (See table 1 for a summary of PPI and CPI food price changes during 2020.)
Petroleum products
Prices for crude petroleum products were affected by the COVID-19 pandemic. Initially, they plummeted as worldwide demand for petroleum decreased and supplies remained high, and then later, they rebounded. Price changes for crude petroleum were passed through to refined petroleum prices, which also experienced substantial volatility during 2020.8
As the pandemic began, crude oil prices collapsed in tandem with slowing economic activity across the globe. China (the top oil importer)—having passed the United States in 2016—kicked off the collapse as the first country to undergo COVID-19.9 In response to this massive shock, the Organization of the Petroleum Exporting Countries (OPEC) pushed its members and Russia to cut production. Russia, however, resisted the call, aiming to gain market share. OPEC, unable to convince Russia, reversed its decision and revamped production. Given that demand was already low, this move led to a near-record level stockpile of 535.2 million barrels of crude petroleum in the United States on May 1, 2020.10
In response to these events, the PPI for crude petroleum dropped 14.3, 34.0, and 48.8 percent in February, March, and April, respectively. (See table 2.) Consumer and producer prices for refined petroleum products also declined considerably over this period. Beginning in May, crude petroleum prices started rising as OPEC+ members agreed to record production cuts, and Russia also complied.11 The agreement called for a composite cut of 9.7 million barrels per day through the end of June, the largest production cut ever.12 Prices for refined petroleum products also began rising in either May or June. (See table 2 for a summary of petroleum product price changes during 2020.)
Table 2. Producer price and consumer price indexes for selected petroleum products, monthly percent changes, not seasonally adjusted, 2020| Category | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
|---|
PPI crude petroleum | –2.5 | –14.3 | –34.0 | –48.8 | 35.9 | 50.9 | 6.0 | 4.4 | –3.2 | 1.7 | 3.9 | 14.8 |
|---|
PPI gasoline | 2.3 | –6.4 | –20.2 | –53.0 | 45.0 | 34.9 | 9.9 | –0.8 | –1.5 | –0.2 | –3.9 | 10.3 |
|---|
PPI jet fuel | 4.6 | –18.9 | –14.5 | –48.6 | –6.8 | 47.6 | 13.7 | 4.8 | –6.8 | –2.5 | 4.9 | 22.7 |
|---|
PPI No. 2 diesel fuel | –7.2 | –9.9 | –12.2 | –27.2 | –12.4 | 27.2 | 30.0 | 6.6 | –7.1 | 5.5 | 7.4 | 11.7 |
|---|
CPI gasoline, all types | –0.8 | –3.8 | –7.4 | –16.5 | –0.2 | 10.0 | 4.8 | 0.0 | 0.7 | –1.6 | –2.7 | 3.4 |
|---|
CPI other motor fuels | –0.6 | –3.4 | –5.4 | –8.2 | –3.2 | 0.2 | 0.1 | –0.4 | –0.3 | –1.5 | –0.2 | 4.3 |
|---|
Leisure and hospitality services
The pandemic substantially decreased demand for leisure and hospitality services, which led to large price declines. In April 2020, on some days, the daily number of air passengers declined over 96 percent, compared with that of April 2019.13 Likewise, hotel occupancy rates for the month of April fell by almost 64 percentage points from the prior year.14 Table 3 shows large declines during 2020 in the PPI for guestroom rental in February and April and decreases in the CPI for other lodging (including hotels and motels) from March through April. Producer airline passenger services prices fell considerably from January through April 2020, and the CPI for airline fares decreased from March through May 2020.15
Hotel occupancy rates began to recover somewhat but were still over 28 percentage points lower in September 2020 than in September 2019.16 On October 18, 2020, the Transportation Security Administration screened over 1 million air travelers for the first time since the beginning of the pandemic, but that amount was only 40 percent of prior-year levels.17 As can be seen from the PPIs and CPIs in table 3, prices for hotel lodging and airline fares were relatively volatile for the rest of the year.
Table 3. Producer price and consumer price indexes for selected leisure and hospitality services, monthly percent changes, not seasonally adjusted, 2020| Category | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
|---|
PPI guestroom rental | 1.3 | –3.8 | 1.4 | –16.8 | 1.4 | 1.7 | 2.3 | –1.4 | –0.3 | 0.8 | –4.1 | 1.5 |
|---|
PPI airline passenger services | –4.0 | –1.8 | –7.4 | –10.0 | 8.3 | 6.1 | –6.9 | –6.8 | –0.1 | 5.5 | –4.3 | –4.3 |
|---|
CPI other lodging away from home, including
hotels and motels | 4.6 | 6.7 | –3.5 | –7.0 | 1.5 | 2.2 | 1.2 | –1.6 | –2.9 | –8.0 | –2.0 | –2.1 |
|---|
CPI airline fares | 1.1 | 3.9 | –12.5 | –12.4 | –0.8 | 2.2 | –0.6 | –2.6 | –1.0 | 9.4 | 3.4 | –7.8 |
|---|
Automobiles
The COVID-19 pandemic affected the market for automobiles, particularly used automobiles. According to J.D. Power and Associates, production of new cars decreased during the pandemic because of factory shutdowns and supply chain issues,18 which drove up the price of new cars and reduced sales. As a result, trade-ins were fewer and the inventory of used cars was reduced. At the same time, economic hardship increased the demand for used cars relative to new cars. The combination of all these factors led to large price increases for used cars.19
Table 4 presents monthly percent changes in the PPI for automobile retailing and the CPI for used cars and trucks. Of note, the PPI for automobile retailing (which includes both new and used vehicles) measures trade margins, calculated as the sales price less the acquisition price.20 By contrast, the CPI measures the final sales price of the car or truck. The measurement difference between the PPI and CPI stems from the PPI definition of retail trade, which defines retailers as suppliers of the service of reselling and, thereby, excludes the value of the manufactured product itself. Despite these methodological differences, the two indexes showed large increases in 2020. The PPI for automobile retailing jumped 12.5, 19.5, and 11.8 percent in May, June, and July, respectively. The CPI for used cars and trucks rose 3.3 percent in July and 5.8 percent in August.
Table 4. Producer price and consumer price indexes for selected automobile sales, monthly percent changes, not seasonally adjusted, 2020| Category | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
|---|
PPI for automobile retailing | 3.5 | –0.3 | 4.3 | –13.6 | 12.5 | 19.5 | 11.8 | –0.5 | 0.8 | 5.0 | 1.5 | –6.9 |
|---|
CPI for used cars and trucks | –0.8 | 1.0 | 2.4 | –0.9 | –0.7 | –1.1 | 3.3 | 5.8 | 2.1 | 1.0 | –1.3 | –0.9 |
|---|
Potential negative effects of COVID-19 on seasonal adjustment
In many cases, the extreme price movements in 2020 (such as those outlined in the previous section) created substantial challenges for seasonal adjustment, making detection of seasonality more difficult and estimation of the seasonal patterns less accurate. For example, in many cases, COVID-19 impacts moved indexes in different directions or in different months than would have been historically expected, thereby reducing measured seasonality.
This section highlights the difficulties the COVID-19 pandemic has caused for accurately estimating seasonal data. It compares seasonality tests from 2020 with tests from earlier years for high-level CPIs and PPIs to show the general decline in detectable seasonality brought on by the COVID-19 pandemic. It then shows how both the PPI and CPI for airline fares seasonal patterns were disrupted by the COVID-19 pandemic. For airline fares, seasonality tests and seasonal factors estimated with pre-COVID data (2012 through 2019) are compared with those estimated with data from the COVID-19 pandemic period (2013 through 2020). The seasonal factors and seasonality tests conducted during the COVID-19 period include no action by BLS to mitigate the effects of the COVID-19 pandemic. They are presented to illustrate the difficulties BLS faced with seasonal adjustment for the CPI and PPI during 2020. The later section on mitigating the effects of the COVID-19 pandemic provides additional examples of series whose seasonal patterns were disrupted by the COVID-19 pandemic and also describes the efforts BLS took to mitigate the effects of the pandemic on seasonal adjustment.
Reduction in observed seasonality in aggregate indexes
In general, the extreme price movements resulting from the COVID-19 pandemic are expected to inhibit the typical seasonal signal observed in CPI and PPI data. Table 5 presents QC (quality control) statistics from seasonality tests conducted on high-level CPI and PPI series. Tests were conducted with the use of 8 years of data, ending with the years listed in the table. For example, 2019 tests were conducted with data from 2012 to 2019. If COVID-19-related price movements made detection of seasonality more difficult in PPI and CPI data, a decline in the seasonality test statistics would be expected when 2020 data are included. For all indexes in table 5, tests indicate a decrease in seasonality when 2020 data are included. The all-items CPI F(s) falls from over 43 to approximately 17 when 2020 data are included in the tests and the all-items less food and energy CPI F(s) experiences similar results. Likewise, for PPI, F(s) falls across all categories when 2020 data are included in the tests. (Recall, values of F(s) ≥ 7, M7 < 1 and Q < 1 indicate seasonality.)
Table 5. Quality control statistics for high-level producer price index and consumer price index data, 2018–2020 annual seasonal revisions| Index | F(s) | M7 | Q |
|---|
CPI all items |
|---|
2020 | 16.95 | 0.84 | 0.67 |
|---|
2019 | 43.45 | 0.45 | 0.39 |
|---|
2018 | 37.91 | 0.47 | 0.33 |
|---|
CPI all items less food and energy |
|---|
2020 | 11.44 | 0.79 | 0.55 |
|---|
2019 | 66.84 | 0.29 | 0.26 |
|---|
2018 | 68.97 | 0.31 | 0.27 |
|---|
PPI final demand |
|---|
2020 | 9.04 | 0.75 | 0.61 |
|---|
2019 | 21.95 | 0.49 | 0.37 |
|---|
2018 | 15.58 | 0.54 | 0.37 |
|---|
PPI processed goods for intermediate demand |
|---|
2020 | 9.90 | 0.98 | 0.80 |
|---|
2019 | 15.50 | 0.77 | 0.42 |
|---|
2018 | 15.29 | 0.70 | 0.42 |
|---|
PPI unprocessed goods for intermediate demand |
|---|
2020 | 1.20 | 2.47 | 1.35 |
|---|
2019 | 5.25 | 1.19 | 0.67 |
|---|
2018 | 5.00 | 1.32 | 0.71 |
|---|
PPI services for intermediate demand |
|---|
2020 | 2.81 | 1.99 | 1.00 |
|---|
2019 | 6.99 | 1.02 | 0.57 |
|---|
2018 | 7.66 | 1.02 | 0.58 |
|---|
Airlines
High-level testing indicates a decrease in observable seasonality in 2020. For one to understand the underlying causes of this general decline, a detailed example of airline services prices is presented. The example shows how extreme price movements reduced the amount of detectable seasonality for airline services and distorted the normally observed seasonal patterns. The airline example indicates what occurred for many price indexes in 2020.
Chart 1 presents the PPI for airline passenger services and the CPI for airfares from January 2013 through December 2020. Both indexes experienced declines in the beginning of 2020. From December 2019 through April 2020, the PPI for airline passenger services fell approximately 21 percent. The CPI for airfares decreased approximately 24 percent from February 2020 through May 2020. The PPI then jumped almost 15 percent from April to June and then decreased for most of the remaining the year. The CPI increased in June and then again from October to November, but ultimately, the unadjusted index fell approximately 18 percent from December 2019 to December 2020.
To show how these extreme price movements affected seasonality, charts 2 and 3 compare seasonal factors for airline passenger services estimated with data from two pre-COVID-19 periods (2011–18 and 2012–19) with those estimated with data from the COVID-19 period (2013–20). The factors presented are from the final year of the estimation period. As can be seen, the seasonal patterns for both CPI and PPI estimated with pre-COVID-19 data differ from those estimated with data during the COVID-19 period. For PPI, the pre-COVID-19 factors (estimated from the 2019 annual seasonal revision) project prices to rise approximately 2.3 percent from February to April, while the factors estimated during the COVID-19 period anticipate prices will fall 1.1 percent over this same period. (See chart 2.) For CPI, the factors estimated without COVID-19 period data range from 95.3 to 107.0, whereas the factors estimated with the included 2020 data only range from 98.4 to 100.4. (See chart 3.) For both series, the large declines in airline prices in the early part of 2020 clearly affected seasonal factors.
Depicting seasonality tests, table 6 compares QC statistics estimated with data from 2012 to 2019 with those estimated with data from 2013 to 2020. The pre-COVID-19 QC statistics for both PPI and CPI indicate that airline passenger services are seasonal (F(s) ≥ 7, M7 < 1 and Q < 1). The inclusion of 2020 data substantially changes the seasonality test results for airline passenger services. For PPI, F(s) declines approximately 10 points and no longer indicates seasonality. For CPI, the pre-COVID-19 QC statistics indicate far more seasonality in airline fares than the QC statistics that are estimated, including 2020 data, with F(s) falling close to 60 points when 2020 data are included. (See table 6.)
Table 6. Quality control statistics for producer price index and consumer price index airline services, 2019 and 2020 annual seasonal revisions| Index | F(s) | M7 | Q |
|---|
PPI 2020 | 3.91 | 1.30 | 0.99 |
|---|
PPI 2019 | 13.25 | 0.62 | 0.75 |
|---|
CPI 2020 | 9.90 | 0.83 | 0.64 |
|---|
CPI 2019 | 68.42 | 0.37 | 0.43 |
|---|
Mitigating the effects of the COVID-19 pandemic on seasonal adjustment
BLS expanded the scope of intervention analysis on 2020 data used in the computation of seasonal factors. These factors were then used to seasonally adjust 2021 price indexes as forward factors and to recalculate seasonal data from previous years. For a PPI to be an intervention candidate, the index must comprise at least 1.0 percent of a major FD–ID index. And for a CPI to be an intervention candidate, the index must account for at least 0.5 percent of the all-items CPI weight or be a subset of an already qualifying component series. In 2020, both the CPI and PPI relaxed their relative importance rules for intervention candidates and expanded the number of series for which they conducted intervention analysis. The goal of this increased scope for intervention work was to mitigate the effects the COVID-19 pandemic on seasonal adjustment.
BLS began by extensively investigating 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 it for extreme price movements in 2020. They then generated QC statistics with data from 2013 to 2020 and compared them with those generated with data from 2012 to 2019. Next, they generated seasonal factors with data from 2013 to 2020 and compared them with those generated with data from 2012 to 2019. They then ran automatic outlier detection and manually searched for outliers during the COVID-19 period. Finally, they consulted expert industry and commodity analysts.
Generally, the COVID-19 pandemic was deemed to adversely affect seasonal adjustment of a series relative to prior revisions when some combination of the following occurred:
- Extreme price movements occurred in 2020.
- QC statistics changed substantially when COVID-19 period data were included in their estimation.
- Seasonal factors changed substantially when COVID-period data were included in their estimation.
- Auto-outlier and manual searches detected outlier points in 2020.
- Expert industry and commodity analysts indicated that COVID-19 was interfering with the typical seasonal pattern observed in the data.
In cases in which this testing indicated that COVID-19-related price movements would adversely affect seasonal adjustment of a series, the series was included as an intervention series for 2020. For series that were added because of the impact of COVID, only interventions during 2020 were included in their models. Several examples of the procedures that BLS took are presented in the following subsections.
Gasoline
Chart 4 presents the unadjusted PPI and CPI for gasoline from January 2013 through December 2020. Although gasoline prices are generally volatile, COVID-19-related shocks appeared to cause more extreme price movements in 2020. Both the PPI and CPI for gasoline fell sharply from February through April and then rebounded later in the spring.
To show the effect that the COVID-19 pandemic had on measurement of seasonality for gasoline, charts 5 and 6 compare seasonal factors for gasoline estimated with the 2012–19 data with those estimated with data from 2013 to 2020. The factors presented are from the final year of the estimation period. As can be seen, the factors estimated with 2020 data (without COVID-19 action) are substantially different from those estimated without 2020 data.21 For PPI, the factors estimated with 2020 data expect a large seasonal decline from January to February, while the factors estimated without 2020 data expect a small increase over the same period. The 2020 factors also expect a much smaller increase from March to April than the 2019 factors. The CPI seasonal factors show milder differences between 2019 and 2020 than those for PPI. For CPI, the second quarter 2019 factors expect a larger seasonal increase as compared with the 2020 factors. However, the remainder of the factors in 2020 aligns more closely.
Table 7 compares QC statistics estimated with data from 2012 to 2019 with those estimated with data from 2013 to 2020. Because BLS regularly conducts intervention work on PPI and CPI gasoline prices, the 2019 intervention model was used for estimating both sets of QC statistics. Doing so minimizes differences between the two sets of QC statistics, which isolates the effects of COVID-19-related price movements. The QC statistics generated with data through 2019 clearly indicate seasonality in both the PPI and CPI for gasoline. For PPI, after 2020 data are added, F(s) falls well below the threshold that would indicate seasonality. This result implies that the extreme price movements in 2020 likely made detecting seasonality in gasoline prices more difficult. For CPI, a similar although less pronounced trend occurred. The QC statistics for 2020 imply statistically significant seasonality but with a notable deterioration from the previous year’s test statistics. The greater difference between 2019 and 2020 models in PPI than CPI is most likely due to more extreme price movements in the PPI in 2020.
Table 7. Quality control statistics for producer price index and consumer price index gasoline, 2019 and 2020 annual seasonal revisions| Indexes | F(s) | M7 | Q |
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PPI 2019 | 17.84 | 0.58 | 0.64 |
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PPI 2020 (no COVID-19 interventions) | 3.10 | 1.39 | 1.02 |
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PPI 2020 after modeling | 13.87 | 0.60 | 0.64 |
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CPI 2019 | 17.13 | 0.56 | 0.59 |
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CPI 2020 (no COVID-19 interventions) | 8.62 | 0.70 | 0.73 |
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CPI 2020 after modeling | 18.11 | 0.51 | 0.73 |
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Examination of price movements, QC statistics, and seasonal factors indicate that COVID-19-driven price movements could negatively affect seasonal adjustment of the CPI and PPI for gasoline. For these reasons, BLS developed intervention models for gasoline that included variables to offset the effects of COVID-19-related price movements. The intervention model for PPI included ramps from February 2020 through April 2020 and April 2020 through June 2020. For CPI, the intervention model included a level shift in April 2020. Table 8 presents coefficients, standard errors, and t-statistics from these intervention models.22
Table 8. Intervention models conducted on producer price and consumer price indexes for gasoline, for the 2020 annual seasonal revision| Variable | Coefficient | Standard error | t-value |
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PPI for gasoline: intervention model |
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Level shift 2015.09 | –0.19 | 0.08 | –2.41 |
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Ramp 2020.02 to 2020.04 | –0.58 | 0.05 | –11.24 |
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Ramp 2020.04 to 2020.06 | 0.32 | 0.05 | 6.27 |
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CPI for gasoline (all types): intervention model |
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Ramp 2014.11 to 2015.01 | –0.14 | 0.04 | –3.76 |
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Level shift 2020.04 | –0.18 | 0.05 | –3.92 |
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Charts 5 and 6 compare seasonal factors for gasoline products estimated with the 2012–19 data with those estimated with data from 2013–20 (both with the intervention models presented earlier and without the intervention models). As the charts show, without the intervention models, the 2020 factors deviate considerably from the 2019 factors, which is undesirable because factors should be relatively stable across years. For PPI and CPI, the interventions included to offset COVID-19-related price movements clearly result in factors more similar to those estimated in 2019. For both CPI and PPI, all QC statistics indicate seasonality after modeling for COVID-19. These examples underscore the need for intervention modeling to mitigate the effects of the COVID-19 pandemic on seasonal adjustment.
Automobiles
Chart 7 presents the CPI for used cars and trucks and the PPI for automobile retailing from January 2013 through December 2020. Recall, the PPI for automobile retailing measures trade margins, calculated as the sales price less the acquisition price, whereas the CPI measures the final sales price of the car or truck. Despite 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 retailing jumped from April through July 2020 and then again later in 2020.
As with gasoline, seasonal factors estimated with data from 2012 to 2019 are compared with factors estimated with data from 2013 to 2020.23 (See charts 8 and 9, PPI for automobile retailing and CPI for used cars and trucks, respectively.) The seasonal factors estimated including data from 2020 (without COVID-19 action) 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 were included in their estimation, as compared with those estimated with data from 2012 to 2019.
QC statistics estimated with data from 2012 to 2019 are compared with those estimated with data from 2013 to 2020. The QC statistics indicate a clear decline in detectable seasonality for both PPI and CPI from 2019 to 2020. For PPI, F(s) fell almost 8 points after 2020 data were included in the tests and no longer indicated seasonality in 2020. For CPI, a similar trend happened. 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. (See table 9.)
Table 9. Quality control statistics for automobiles conducted on producer price and consumer price indexes, 2019 and 2020 annual seasonal revisions| Index | F(s) | M7 | Q |
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PPI 2019 | 9.66 | 0.93 | 0.65 |
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PPI 2020 (no COVID interventions) | 1.73 | 2.34 | 1.00 |
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PPI 2020 after intervention modeling | 9.97 | 0.94 | 0.68 |
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CPI 2019 | 21.74 | 0.52 | 0.48 |
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CPI 2020 (no COVID interventions) | 4.41 | 1.54 | 0.91 |
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CPI 2020 after intervention modeling | 53.31 | 0.36 | 0.19 |
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Intervention modeling was used to offset the effects of the COVID-19 pandemic on seasonal adjustment of both the PPI for automobile retailing and the CPI for used cars and trucks. For PPI, the intervention model 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. Table 10 illustrates the intervention models employed for the automobile PPI and CPI.
Table 10. Intervention models conducted on producer price and consumer price indexes for automobiles, for the 2020 annual seasonal revision| Variable | Coefficient | Standard error | t-value |
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PPI for automobile retailing: intervention model |
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Ramp 2020.03 to 2020.04 | –0.16 | 0.02 | –9.13 |
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Ramp 2020.04 to 2020.07 | 0.15 | 0.01 | 14.32 |
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Level shift 2020.11 | 0.06 | 0.02 | 3.23 |
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CPI for used cars and trucks: intervention model |
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Ramp 2020.06 to 2020.09 | 0.05 | 0.01 | 7.83 |
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Charts 8 and 9 compare seasonal factors for automobile sales estimated with 2012–19 data with those estimated with data from 2013 to 2020, employing the intervention models presented earlier. 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 need for intervention modeling to mitigate the effects of the COVID-19 pandemic on seasonal adjustment. Table 9 presents QC statistics for automobiles generated with the intervention models included. For both CPI and PPI, the QC statistics indicate seasonality after controlling for the effects of COVID-19.
Scope of intervention modeling expansion and outcome
After considerable analysis for both the CPI and PPI, BLS expanded the scope of intervention work in 2020 to offset the effects of the COVID-19 pandemic on the seasonal factors used for seasonal adjustment in 2021. Economists applied intervention analysis on 68 CPIs in 2020, as compared with 32 in 2019. Of the 68 series that received intervention analysis, 47 were added to mitigate COVID-19 effects on seasonal adjustment. For these 47 newly added series, clear intervention events occurred related to COVID-19 during 2020. The other 21 series would have received intervention analysis even without COVID-19 effects. 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 with 41 in 2019. Of the 76 series, 36 series were added strictly to mitigate COVID-19 effects on seasonal adjustment and, thereby, only contained interventions in 2020. The total number of interventions for PPI increased 64 percent from 2019 to 2020.
Seasonal revisions
To measure whether its efforts to offset the effects of the COVID-19 pandemic on seasonal adjustment were effective, BLS compared revisions in top-level indexes resulting from the 2020 revision with those from previous revisions. In cases in which the revisions from 2020 data were similar to those from the previous three periods, efforts to offset the COVID-19 pandemic on seasonal adjustment could be inferred as effective, because adding the 2020 data to the estimation of factors did not result in large revisions. Table 11 compares average seasonal revisions to index percent changes based on the 2020 seasonal revision with those of the previous three seasonal revisions. The average annual seasonal revisions to both the PPI for final demand and the all-items CPI were similar in 2020 to those in the previous 3 years.
Table 11. Average seasonal revisions compared with monthly index percent changes of final demand and all items, 2017–2020| Year | PPI final demand | CPI all items |
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2017 | 0.075 | 0.055 |
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2018 | 0.046 | 0.058 |
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2019 | 0.058 | 0.046 |
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2020 | 0.042 | 0.059 |
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Conclusion
The COVID-19 pandemic caused extreme movements in many PPIs and CPIs in 2020. Because BLS uses historical data to estimate seasonal factors, the extreme price movements resulting from the COVID-19 pandemic created difficulties in estimating seasonal data. To overcome these difficulties, BLS expanded the scope of intervention modeling for the CPI and the PPI in 2020. The number of series on which PPI conducted intervention analysis rose by more than 85 percent 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.
United States Department of Labor
