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Is Measurement Error a Likely Explanation for the Lack of Productivity Growth in 2014?
Over the past three years nonfarm business sector labor productivity growth has averaged only around 0.75 percent—well below historical norms. In 2014 it was negative, as can be seen in chart 1.
The previous macroblog post by Atlanta Fed economist John Robertson looked at possible economic explanations for why the labor productivity data, taken at face value, have been relatively weak in recent years. In this post I look at the extent to which “measurement error” can account for the weakness we have seen in the data. By measurement error, I mean incomplete data and/or sampling errors that are reduced when more comprehensive data are available several years later. I do not mean the inherent difficulties in measuring productivity in sectors such as health care or information technology.
As seen in chart 1, negative four-quarter productivity growth rates have been quite infrequent in nonrecessionary periods since 1948. In S. Borağan Aruoba's 2008 Journal of Money, Credit and Banking article “Data Revisions Are Not Well Behaved,” he found that initial estimates of annual productivity growth are negatively correlated with subsequent revisions. That is, low productivity growth rates tend to be revised up while high rates tend to be revised down. This is illustrated in chart 2.
In each of the panels, points in the scatterplot represent an initial estimate of fourth-quarter over fourth-quarter productivity growth together with a revised estimate published either one or three years later. For example, the green points in each plot show estimates of productivity growth over the four quarters ending in the fourth quarter of 2011. In each plot, the x-coordinate shows the March 7, 2012, estimate of this growth rate (0.3 percent). The y-coordinate of the green dot in chart 2a shows the March 7, 2013, estimate of fourth-quarter 2011/fourth-quarter 2010 productivity growth (0.4 percent) while the y-coordinate of the green dot in chart 2b shows the March 5, 2015, estimate (0.0 percent).
In each chart, the red dashed line shows the predicted revised value of productivity growth as a function of the early estimate (using a simple linear regression). Chart 2a shows that, on average, we would expect almost no revision to the most recent estimate of four-quarter productivity growth one year later. Chart 2b, however, shows that low initial estimates of productivity growth tend to be revised up three years later while high estimates tend to be revised down. Based on this regression line, the current estimate of -0.1 percent fourth-quarter 2014/fourth-quarter 2013 productivity growth is expected to be revised up to 0.3 percent by April 2018.
The intuition for this is fairly straightforward. Low productivity growth could come about from either underestimating output growth, overestimating growth in hours worked, or a combination of the two. Which of these is most likely to occur, according to historical revisions? This is shown in chart 3, which plots the predicted revisions to four-quarter nonfarm employment growth and four-quarter nominal gross domestic product (GDP) growth conditional on two assumed values for the initial estimate of four-quarter productivity growth: 0 percent (low) and 4 percent (high).
Nominal GDP is used instead of real GDP as methodological changes to the latter (e.g., the introduction of chain-weighting starting in 1996) make an apples-to-apples comparison of pre- and post-revised values difficult. Using fourth-quarter over fourth-quarter growth rates since 1981, the diamonds on the solid lines in chart 3 show that an initial estimate of 0 percent productivity growth would, on average, be associated with a three-year upward revision of 0.39 percentage point to four-quarter nominal GDP growth and a three-year downward revision of 0.10 percentage point to four-quarter nonfarm payroll employment.
With 4 percent productivity growth, the diamonds on the dashed lines show predicted three-year revisions to nominal GDP growth and employment growth of -0.40 percentage point and 0.14 percentage point, respectively. As the chart shows, these estimates are sensitive to the sample period used to predict the revisions. Using only data since 1989 (not shown), the regression would not predict a downward revision to employment growth conditional on an initial estimate of 0 percent productivity growth. Overall, however, the plot suggests that revisions to output growth are more sensitive to initial estimates of productivity growth than revisions to payroll employment growth are. This is consistent with the sentiments expressed by Federal Reserve Vice Chairman Stanley Fischer and Atlanta Fed President Dennis Lockhart at the March 30–April 1 Financial Markets Conference that employment or unemployment data may be more reliably measured than GDP.
Nevertheless, according to charts 2 and 3, the importance of measurement error in productivity growth is fairly modest. Ex-ante, we should not expect last year's puzzlingly low productivity growth simply to be revised away.
Editor's note: Upon request, the programming code and data for charts used in this macroblog post is available from the author.
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