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November 2023

Interpreting volatility in quarterly labor productivity

Labor productivity—defined as output per hour—exhibited a notable degree of volatility during the COVID-19 pandemic recession and its aftermath. This article focuses on this aspect of quarterly labor productivity data, discussing its underlying sources, ways to interpret it, and alternate measures that offer additional perspective on quarter-to-quarter changes.

The COVID-19 pandemic ended the longest economic expansion of the post-World War II era and brought on the shortest recession of this period.1 The dramatic contraction and subsequent recovery in economic activity during the pandemic period facilitated historically large changes in labor productivity.2 In the second quarter of 2020, as many businesses shut down and the economy stalled, labor productivity spiked 17.3 percent. This gain was the second largest quarterly increase in the labor-productivity series, which begins in 1947. In contrast, as the recovery progressed, labor productivity fell 6.0 percent in the first quarter of 2022—the third-largest quarterly decline in the series (see chart 1).

It may seem counterintuitive for the economy to have experienced a sizable productivity gain while it was contracting and then have a historic decline in productivity 2 years later during a recovery. With so many economic observers focused on this recent volatility in the top-line productivity figure, it is worth exploring what may be underlying the large movements in this measure that we have observed during this period and historically.

This article outlines how movements in output and hours worked combine to influence changes in labor productivity, informing a discussion of various sources of volatility in labor productivity during and after recessions. The Great Recession and the COVID-19 pandemic recession are used as reference cases throughout the article because these two recessions offer examples that illustrate how we can interpret and understand quarterly volatility, from both short-term and cyclical perspectives.3

Overview of the labor-productivity measure

Before we examine sources of volatility in labor productivity, it is important to understand how labor productivity is measured, how quarterly changes are calculated, and how labor productivity moves relative to its component measures, which are output and hours worked.

Labor productivity—output per hour worked—is measured as the ratio of an index of real output to an index of hours worked:



Labor productivity is an economic indicator used to track long-term gains in economic efficiency. The measure can also assist in analyzing short-term and cyclical macroeconomic trends by examining how its underlying series move relative to one another.

Long-term increases in labor productivity signal that businesses and workers have become more efficient in the production of goods and services. U.S. labor productivity has increased steadily since 1947 and so the U.S. economy has been able to produce more real output over time without a proportionate increase in hours worked. This increase in production can ultimately have a positive impact on consumption, leisure, and standards of living through the resulting income that flows to profits and capital gains, worker pay, and government revenue.

Calculating quarterly changes in labor productivity

The U.S. Bureau of Labor Statistics (BLS) calculates quarterly changes in labor productivity and presents them as compound annual growth rates.4 Rather than calculating a traditional percent change between 2 quarters, BLS annualizes the change by compounding the quarterly change over 4 quarters.

The formula for calculating a compound annual growth rate with quarterly data is as follows:





where X represents values in a quarterly time series, a is the start period, b is the end period, and n is the number of quarters between the end points a and b, annualized by dividing n by 4 (since there are 4 quarters in a year).

For example, we can calculate the annualized percent change from the first quarter of 2020 to the second quarter of 2020. The labor productivity index values for these 2 quarters are 108.601 and 113.024, respectively. We report that labor productivity increased by 17.3 percent in the second quarter of 2020, at an annual rate:



If we had instead used the traditional percent change formula to calculate the change over the same period, we would have arrived at a different result:



The key difference between equations (3) and (4) is the exponent term  that is in equation (3) but not in equation (4). This exponent term is what compounds the quarterly change to an annualized growth rate that can be interpreted as what the percent change would be if it continued over 4 consecutive quarters.5

BLS uses annualized percent changes as the standard units of measure in productivity analysis because they allow us to compare the growth rates of periods of different length on the same basis. For example, if we wanted to compare a given quarter’s productivity growth rate to the long-term average historical rate since 1947, using annualized percent changes provides us with a comparable basis to do so.

Comparing quarter-to-quarter with four-quarter changes

In addition to publishing percent changes from the previous quarter at an annual rate, BLS also publishes data for growth from the same quarter a year ago. We calculate the year-ago growth rate using the same formula in equation (2). The labor productivity index values for the second quarter of 2019 and the second quarter of 2020 are 107.485 and 113.024, respectively. Growth for the second quarter of 2020 from the same quarter a year ago is calculated as,



A comparison of the result of 17.3 percent from equation (3) with the result of 5.2 percent from equation (5) reveals that the annualized quarter-to-quarter and year-ago measures can look quite different.

With the volatility of quarter-to-quarter changes, especially during the pandemic period, it has become important to emphasize the usefulness of the year-ago productivity measure. Given that the year-ago measure uses the index value from 4 quarters ago and the current index value as the start and end periods in the calculation, the year-ago measure is not subject to fluctuations to the same extent that the quarter-to-quarter measure is. Thus, compared with the quarter-to-quarter measure, the year-ago measure is smoother, as shown in chart 2, which displays the quarter-to-quarter and year-ago changes for labor productivity over the last 10 years. From chart 2, we can see that the year-ago measure is less volatile than the quarter-to-quarter measure throughout the period. During periods of high volatility such as the COVID-19 pandemic, both measures do experience greater fluctuations than normal. However, the year-ago measure continued to be less volatile than the quarter-to-quarter measure throughout this period.

At the same time, the quarter-to-quarter and year-ago measures are both valuable measures of labor productivity growth for different reasons. Although the quarter-to-quarter movements can be more volatile, they do provide perspective on shorter term movements and cyclical transitions. Being less subject to volatility, the year-ago measure may provide a clearer picture of medium-term and long-term trends in labor productivity.

Interpreting quarterly changes in labor productivity

A unique aspect of labor productivity among federal economic statistics is that data are not collected directly on this measure: there is no such thing as a U.S. national productivity “survey.” Unlike, for example, the Current Population Survey, which is used to calculate the unemployment rate, there is no nationwide productivity survey tracking how productive businesses and people are.

Instead, this measure is calculated indirectly, using a ratio of two other economic indicators: real output and hours worked. Each of these two measures possesses a collection of underlying source data of its own, including both survey and administrative data. As a result, with numerous data sources serving as inputs into the labor productivity measure, the combined volatility of these sources can occasionally yield substantial top-line volatility in the labor productivity measure.

Additionally, since labor productivity is the ratio of two component measures, there are multiple ways for the measure to rise or fall. How real output and hours worked move relative to one another results in increases or decreases in labor productivity. The typical example of an increase in labor productivity is when output grows faster than hours worked does, which is the usual case, as most quarters show increases in both of these measures. However, we do occasionally also see increases in labor productivity when both output and hours are decreasing: if a decline in output is smaller than a decline in hours, labor productivity increases by definition (see equation (1)).

Similarly, while a decline in labor productivity can occur when output and hours are both decreasing (i.e., when output is decreasing faster than hours), labor productivity can also decline when both output and hours are increasing but hours are increasing faster. When hours grow faster than output, the production of goods and services may be becoming less efficient because of diminishing marginal returns to labor. Thus, when we evaluate a productivity change—especially short-term changes where productivity tends to be most volatile—it is critical to keep the underlying movements in output and hours in mind.

Using the case of the Great Recession, chart 3 presents an illustrative example of how relative movements in output and hours can yield volatility in labor productivity. The Great Recession began in the first quarter of 2008 and lasted until the second quarter of 2009.6 This period was characterized, for the most part, with declining output and hours worked. Yet, the productivity story varied throughout. Following a decline in productivity in the first quarter of 2008, the measure increased during the next 2 quarters, though for different reasons. In the second quarter of 2008, productivity increased as output increased and hours decreased, and in the third quarter, productivity increased as a decline in output was smaller than a decline in hours.

While output and hours plummeted in the fourth quarter of 2008 and the first quarter of 2009, labor productivity moved in opposite directions between the 2 quarters. In the fourth quarter of 2008, the decline in output (−11.7 percent) was larger than a decline in hours (−10.6 percent), resulting in a drop in productivity (−1.1 percent). In contrast, in the first quarter of 2009, the decrease in hours (−9.8 percent) was larger than the decrease in output (−6.4 percent), yielding an increase in productivity (3.7 percent). This example illustrates how increases in labor productivity do not always indicate that the economy is strong and expanding since increases can also occur during economic contractions.

Thus, we can see that there is not a one-size-fits-all way to interpret short-term or quarter-to-quarter gains or declines in labor productivity and it is important to investigate the underlying movements in output and hours to understand the health of the economy.

Labor productivity and business cycle turning points

Business cycle activity—particularly recessions and unanticipated economic events—can lead to additional volatility in the labor productivity measure. During cyclical turns, output and hours measures can fluctuate greatly and each measure may also respond at different times. Divergences in magnitude or temporality between output and hours can result in productivity changes that fluctuate more widely than normal during such periods.

Two case studies: the Great Recession and the COVID-19 pandemic recession

Here, we examine two case studies that include historic movements in output, hours worked, and labor productivity. Chart 4 illustrates the behavior of output, hours, and labor productivity during and after the Great Recession, and chart 5 is the same illustration for the COVID-19 recession. Both graphs present indexes that start with the last quarter before the recession began—a business cycle peak—and end in the quarter in which both output and hours have fully recovered to their prerecession levels.

The portion of chart 4 within the gray recession bar was discussed in chart 3. The jagged path of output’s slowdown at the onset of the Great Recession—in contrast to the smoother deceleration of hours worked during this period—yielded additional volatility in labor productivity.

As the Great Recession ended, differing recovery timelines between output and hours worked caused the direction of quarterly changes in the labor productivity measure to fluctuate. While output began to stabilize in the second quarter of 2009 and started recovering in the third quarter, hours continued to decline throughout 2009 and did not begin to recover until 2010. This hours recovery lag led to productivity spiking to above-average rates during this year: in the second, third, and fourth quarters of 2009, growth rates in productivity reached 9.1 percent, 6.0 percent, and 5.9 percent, respectively. Output and hours worked also differed in the duration of their recoveries: although it took output 16 quarters to recover to peak levels, hours worked did not recover until 28 quarters after the fourth-quarter 2007 peak.7

Looking at the recoveries of output and hours worked, economic observers may note that output’s path looks jagged, just as it did during the recession, whereas hours show a smoother trajectory. Output tends to be more volatile than hours, and this attribute of output growth can result in additional volatility in the labor productivity measure. For example, while hours begins recovering in the first quarter of 2010 and continues to increase consistently throughout the recovery, output changes sign (goes from rising to falling, or vice versa) four times between the first quarter of 2010 and the fourth quarter of 2014. During this same period, labor productivity changes sign nine times, not only because of this volatility in output, but also because labor productivity growth depends on whether the output or hours measure is growing faster (a condition that changes frequently).

Chart 5, which illustrates the COVID-19 pandemic recession and recovery, tells a different story than chart 4 because of the differing nature of the COVID-19 pandemic recession relative to the Great Recession. The Great Recession was the longest recession in the post-World War II era. In contrast, the COVID-19 pandemic recession was one of the shortest, brought on by the abrupt business shutdowns at the onset of the pandemic. As a result, there was no lag between output and hours in this recession and recovery, with both measures descending and then turning upward simultaneously.8

The onset of the COVID-19 pandemic brought historic movements in labor productivity, output, and hours worked. Although visually the output and hours index series in chart 5 do not appear that far off from one another in the second quarter of 2020 relative to other quarters in the graph, the gap between these two index values yielded a substantial productivity change. Productivity increased 17.3 percent (which is over eight times larger than the historical average rate), which we can understand when looking at the corresponding historic changes in output and hours (−35.0 percent and −44.6 percent, respectively) in that quarter.9 The recovery began in the third quarter of 2020 with additional historic movements in output and hours worked. In the third quarter of 2020, output increased 47.2 percent and hours worked increased 38.2 percent. Both increases are the largest in their respective series. Amidst these historic movements in its component measures, productivity grew both quarters. Then, from the fourth quarter of 2020 onward, we begin to see volatility in labor productivity as output and hours embark on their respective paths to recovery.

As we saw in the Great Recession, the jaggedness of the output series relative to hours worked also led to some notable volatility during the recovery phase following the COVID-19 recession. In the first quarter of 2022, hours continued their steady increase to recover to prepandemic levels, while output experienced a sudden decline, yielding a 6 percent decline in productivity. Although a 6 percent gain in productivity may be slightly unusual, a 6 percent decline is very unusual. Given that output and hours worked are procyclical measures, that is, they both tend to rise during good economic conditions and fall during declining economic conditions, both measures often move in tandem (with output generally moving slightly faster, thereby reflecting productivity gains). Therefore, when output is significantly outpaced by hours it is particularly anomalous. Specifically, while there have been 43 instances of a quarterly productivity gain of 6 percent or greater since 1947, there have been just 3 cases of a productivity decline of 6 percent or more during this time.

To illustrate this more intuitively, the data indicate that people collectively worked about 2 billion more hours in the first quarter of 2022 than they did in the prior quarter, but these workers produced $97 billion less output at the same time—a curious result.10 Many economic observers reasonably wondered: what could account for the fact that we had robust hours growth that quarter while measured output fell at the same time?

Part of that answer comes from a closer examination of the output measure for the nonfarm business sector and of how gross domestic product (GDP) is calculated. The nonfarm business sector accounts for about three-quarters of U.S. GDP.11 We can break down the 1.6 percent decline in GDP in the first quarter of 2022 into its components: personal consumption expenditures, gross private domestic investment, net exports, and government spending.12 Looking at chart 6, we see that net exports of goods and services showed a −3.1 percentage point contribution to the change in GDP in the first quarter of 2022, which is the third-largest negative contribution to GDP from this component in the entire series, which starts in 1947.13 Compared with the other components of GDP, net exports tend to be rather volatile. In this quarter, the unusual magnitude in this component primarily reflected a large increase in imports of 18.4 percent.14 Supplemented by a −0.4 percentage point contribution from government spending, the decline in GDP that quarter (and therefore the decline in nonfarm business output) primarily reflected this decrease in net exports.15

Average paths of output and hours during business cycles

There have been 12 recessions between 1947 and 2023, the period for which BLS productivity data are available. In addition to using labor productivity data to analyze individual business cycles as we have done above, we can also analyze productivity and its underlying series over an average business cycle. Chart 7 provides a generalized illustration of how output, hours, and productivity move throughout an average recession and recovery in the post-World War II period, showing the average paths of these measures for all recessions between 1947 and 2023.16

To create the average output and hours trends, we can reindex both output and hours to the quarter that precedes the onset of the recession so that the index value of each series at its prerecessionary peak is 100. Each subsequent quarter represents the average index values of output and hours across all business cycles. For an average business cycle, the downturn in output lasts 2 quarters and it takes 5 quarters to recover, while the downturn in hours lasts 5 quarters on average and recovers in 13 quarters.17

During the post-World War II period, it has been typical for hours to stagnate for a longer period and take longer to recover compared with output. Notably, there was not a single recession between 1947 and 2023 in which hours recovered faster than output. This lag may be due to businesses’ hesitancy to rehire workers in the immediate aftermath of a recession, which results in hours growth lagging behind output growth.


As shown in our case studies, volatility is apparent in the quarterly labor productivity series, and at least some of the volatility is inherent from the fact that the measure is calculated indirectly from two component measures, real output and hours worked. Each measure is composed of many underlying data sources with their own independent levels of volatility.

At times, productivity can move in directions that appear counterintuitive, such as the large increase in the measure in the second quarter of 2020. We can better comprehend these quarterly movements by examining them within a larger context using year-ago changes and other medium- and long-term changes, as well as by developing a deeper understanding of the characteristics of the underlying changes in output and hours worked.

ACKNOWLEDGMENTS: I am grateful to Shawn Sprague, my colleague in the BLS Office of Productivity and Technology, for his helpful comments in improving the article, his crucial assistance in keeping the data and figures current, and his assistance in completing the editorial process.

Suggested citation:

Gianna Fenaroli, "Interpreting volatility in quarterly labor productivity," Monthly Labor Review, U.S. Bureau of Labor Statistics, November 2023,


1 The expansion prior to the COVID-19 pandemic recession was 128 months in length, and the COVID-19 pandemic recession was 2 months in length. Recession start and end dates are designated by the National Bureau of Economic Research (NBER). The NBER defines a recession as a “significant decline in economic activity spread across the economy, lasting more than a few months, normally visible in real GDP, real income, employment, industrial production, and wholesale-retail sales.” See “Business Cycle Dating Committee announcement, January 7, 2008” (Cambridge, MA: National Bureau of Economic Research, January 7, 2008), For a list of U.S. recessions and relevant dates see “U.S. business cycle expansions and contractions” (Cambridge, MA: National Bureau of Economic Research, last updated March 14, 2023), Its convention for measuring the duration of a recession is classifying the first month of a recession as being the month that follows the peak and the last month of a recession as being the month of the trough.

2 See “Productivity perspective of the 2020 COVID-19 pandemic,” Commissioner’s Corner (U.S. Bureau of Labor Statistics, March 5, 2021),

3 All figures in this article are for the nonfarm business sector and are current as of the Second Quarter 2023 (Revised) Labor Productivity and Costs release, which was published on September 7, 2023. For more information on the U.S. Bureau of Labor Statistics (BLS) Labor Productivity and Costs (LPC) program, see the productivity page of the BLS website and the technical documentation provided there at

4 BLS Labor Productivity and Costs news releases can be found at

5 See “Why does BEA publish percent changes in quarterly series at annual rates?,” in Frequently asked questions (U.S. Bureau of Economic Analysis, January 13, 2006),

6 According to the NBER Business Cycle Dating Committee, the peak occurred in the fourth quarter of 2007, therefore making the first quarter of 2008 the first quarter of the recession, and the trough occurred in the second quarter of 2009. See NBER, “U.S. business cycle expansions and contractions.”

7 Output surpassed its fourth-quarter 2007 (peak) value in the fourth quarter of 2011, and the measure for hours worked surpassed its fourth-quarter 2007 value in the fourth quarter of 2014.

8 Although hours experienced a slight decline of 0.6 percent in the fourth quarter of 2019, the measure saw a much larger decline of 6.3 percent in the first quarter of 2020 alongside a 6.7 percent decline in output as both measures felt the initial impacts of the COVID-19 pandemic.

9 Nonfarm business labor productivity increased at an average annual rate of 2.1 percent from 1947 to 2022.

10 The hours figure was calculated using the levels series for hours worked in the nonfarm business sector calculated by BLS, and the output figure was calculated using National Income and Product Accounts (NIPA) table 1.3.6. NIPA table 1.3.6 is available at “National data, GDP & personal income” (U.S. Department of Commerce, Bureau of Economic Analysis), Click “Gross Domestic Product and Personal Income,” then click “Interactive Data Tables.”

11 In 2022, nonfarm business sector output accounted for 76 percent of output for the total economy as measured by gross domestic product (GDP).

12 The data in this paragraph reflect the August 30, 2023, GDP release by the Bureau of Economic Analysis.

13 Net exports are the difference between the exports of goods and services and the imports of goods and services.

14 The increase in the importation of goods and services did not by itself cause a decline of $97 billion in domestic production, but the decline rather reflected the Bureau of Economic Analysis’ accounting framework for GDP, in which “the imports variable (M) corrects for the value of imports that have already been counted as personal consumption (C), gross private investment (I), or government purchases (G).” See Scott A. Wolla, “How do imports affect GDP?,” Page One Economics (Federal Reserve Bank of St. Louis), September 2018,

15 Much of the negative contribution from government spending is not reflected in the output measure for nonfarm business as most of the government sector (general government) is excluded from the nonfarm business sector.

16 For the purposes of this analysis, the Q2 1980–Q3 1980 and Q4 1981–Q4 1982 recessions were combined into one recession because the recovery from the Q2 1980–Q3 1980 recession was not yet complete before the onset of the Q4 1981–Q4 1982 recession. Specifically, output had recovered but hours had not.

17 Although there is a slight increase in average hours worked from 2 quarters out from the peak to 3 quarters out, we then see a continued decline in the average hours worked figures until 5 quarters out.

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About the Author

Gianna Fenaroli

Gianna Fenaroli, formerly an economist with the U.S. Bureau of Labor Statistics, Washington, DC, is a Ph.D. student at Duke University in Durham, NC.

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