Measurement of real GDP is one of the most important data collection tasks, and remains a difficult one (Song et al. 2013, Coyle 2016). Since the publication of its 2021 ‘Blue Book’, the UK’s Office for National Statistics started to measure real GDP in the national accounts using double deflation.
This methodological update follows the premise that “double deflation is internationally accepted as the best approach to producing volume estimates of industry gross value added”.
Indeed, double-deflation has been the international standard since the System of National Accounts (SNA 1993) was adopted by the international community to facilitate international comparisons of national economic statistics.
In the US, this accounting practice has been used since 1992,
while it has been the standard practice in the euro area since the creation of Eurostat.

Although double deflation is the state-of-the-art method for real value-added measurement, its accuracy relies on assumptions that are not met in practice. As a result, our understanding of relative growth rates across sectors is biased.

## A historical detour

To understand accounting procedures in national accounts, it is useful to come back to the notion of real value-added. According to Sims (1969) and Arrow (1974), real value-added can be defined implicitly from the production function itself. Using Arrow’s words: we can "imagine capital and labor cooperating to produce an intermediate good called real value added (V), which in turn cooperates with materials to produce the final product” (pp. 4-5). Following this view, real value-added in any sector corresponds only to the quantity of a bundle (V) that combines capital and labour. To avoid confusion with what is measured in official data, we can call this object ‘physical value-added’. By construction, changes in the quantity of intermediate inputs impact physical value-added only insofar as they change the quantity of the bundle V through movements in labour, capital, or productivity.

In practice, statistical agencies do not observe physical value-added. Instead, national accountants construct a measure of ‘statistical value added’ using double deflation, a method that consists of taking the difference between gross output and intermediate inputs, both valued using base period prices. By construction, it cannot be measured without prices. Obviously, one cannot simply count the number of goods: for example, one cannot compute real value-added in the automotive sector by taking the difference between the final number of cars produced and the number of its intermediate inputs. Statistical agencies need a common unit of account, which is why base period prices are necessary for the construction of sectoral real value added, as well as aggregate real GDP.

## How about distorted prices?

An important implicit assumption underlying the usage of double deflation is that the base period price used to value intermediate inputs reflects both inputs’ marginal cost and the marginal revenue that can be derived from their usage. If true, then double deflation is indeed an accurate measure of physical value-added.

However, if prices are distorted (for example because firms charge a markup), then embedding this distortion in the construction of real value-added creates a wedge between statistical value-added captured in national accounts and the physical value-added concept inspired by Sims (1969). This is intuitive: if a sector is charging a markup and makes profits, these profits are part of the statistical value added measured using double deflation.

The key element here is that real value-added cannot be constructed without prices, which creates issues when prices are distorted. Importantly, price distortions do not need to vary over time to create a bias in real value-added measurement. Even with constant markups, intermediate inputs generate more revenues than their cost. Therefore, using more inputs mechanically results in more statistical value-added, *even when domestic factors (labour and capital) and technology are unchanged*. This occurs because a sector's net operating surplus is part of the statistical agencies' measure of real value-added. Hence, ceteris paribus, a sector can create statistical value-added by increasing its profits.

## How much does this matter?

This mismatch between physical value-added and statistical value-added measured in the national accounts matters in many contexts. For example, measuring real GDP using double deflation in macroeconomic models has a big impact on its statistical properties. In de Soyres and Gaillard (2021), we argued that using double deflation is key to understanding cross country real GDP co-movement. As a matter of fact, using double deflation in an international business cycle model with markups is a way to reconcile the data and model-based simulations, and it helps solve the ‘trade co-movement puzzle’.

In a new paper (de Soyres et al. 2023) we analyse whether profits have biased reported measures of sectoral GDP and productivity in the US. According to our framework, real GDP featured in the national accounts and physical value-added differ mostly for sectors with two characteristics: markups are large (even if they are constant) and fluctuations in intermediate inputs account for a large part of gross output fluctuations.
Using data from the Bureau of Economic Analysis (BEA) on net operating surplus,
we can build a measure of markups at the sector level which we combine with data on input-output linkages to construct a new version of national account statistics. For each sector, we construct a measure of physical value-added (PVA) and compare it to the statistical measure of real GDP. This exercise brings several insights.

In Figure 1, we compare the evolution of statistical real value-added (i.e. sectoral real GDP) to our measure of PVA once fluctuations in net operating surplus are properly taken into account. We can focus on two sectors that illustrate different biases in national statistics: finance and manufacturing. Both sectors rely heavily on intermediate inputs: between 1997 and 2021, the average share of input cost in total sales amounts to 55% in finance and 70% in manufacturing. While year-to-year growth rates for GDP and PVA are highly correlated, the cumulative bias over time leads to significant differences by the end of our sample. Normalising both measures in 1997, PVA’s cumulative growth in 2021 is more than 21 percentage points higher than real GDP growth in the manufacturing sector. In finance, PVA’s cumulative growth is 19 percentage points *lower* than real GDP growth. In other words, national accounts underestimated cumulative growth of physical value added in manufacturing, while it overestimated it in finance.

**Figure 1** Statistical real value-added and new measure of physical value-added

Next, equipped with our measure of physical value-added, we construct a measure of ‘physical productivity’ as the fluctuations in PVA that are not due to observed movements in labour and capital, which we can then compare to the more standard Solow residual based on real GDP as measured by statistical agencies. Results are presented in Figure 2. By the end of our sample in 2021, cumulative growth of physical productivity is about 13 percentage points smaller than that of the Solow residual in finance, while it is 24 percentage point larger than Solow residual in manufacturing. Once again, national accounts’ data overestimated productivity growth in finance, while it underestimated productivity growth in manufacturing.

**Figure 2 **Solow residual and new measure of physical productivity

For clarity, it is worth emphasising that our analysis aims to quantify how the presence of markups creates a measurement issue in national accounts data. This mismeasurement appears even if markups are constant and uniform across all firms, as long as intermediate input usage is not perfectly correlated with gross output. Hence, our investigation is conceptually distinct from the topic of resource misallocation. Recent papers such as Baqaee and Farhi (2020) highlighted how markup heterogeneity across firms implies that the allocative efficiency of the US economy changed over time, as production factors are reallocated to high-markup firms. While both misallocation and mismeasurement are important issues, they highlight different aspects of how markups impact the economy.

Overall, our findings highlight how economic mismeasurement in widely used data can bias our understanding of economic activity. With recent debates regarding the rise of market power and markup in the US, it is more important than ever to pay close attention to the measurement of economic variables used in policy decisions and academic research.

*Authors’ note: The views expressed are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System.*

## References

Arrow, K (1974), “The Measurement of Real Value Added”, in P A David and M W Reder (eds.), *Nations and Households in Economic Growth: Essays in honor of Moses Abramovitz*, Academic Press, pp. 3–19.

Baqaee, D and E Farhi (2020), “Productivity and Misallocation in General Equilibrium”, *The Quarterly Journal of Economics* 135(1): 105–163.

Coyle, C (2016), “Digitally disrupted GDP”, VoxEU.org, 8 February.

de Soyres, F and A Gaillard (2021), “Value Added and Productivity Linkages Across Countries”, International Finance Discussion Papers 1266.

de Soyres, F, A Gaillard and H Young (2023), “What is Measured in National Accounts?”, Working Paper.

Sims, C (1969), “Theoretical Basis for a Double Deflated Index of Real Value Added”, *The Review of Economics and Statistics* 51: 470–471.

Song, D, F Schorfheide, F Diebold, J Nalewaik and B Aruoba (2013), “A new measure of US GDP”, VoxEU.org, 3 December.

Young, A H (1992), “Alternative Measures of Change in Real Output and Prices”, *Survey of Current Business* 72(4): 32–48.