Decomposing Inflation

From the late 1960s through the early 1980s, inflation rose by at least two to three times in many countries due to preceding high growth, tight labor markets, and two oil shocks in the 1970s. The ensuing interest rate hikes, deceleration in economic growth, and the substantial decline in workers’ bargaining power made high inflation disappear in a decade. Moreover, since the Great Recession, inflation has tended to stay below the target inflation pursued by the central banks. Less than two years into the COVID-19 pandemic, the unusually high inflation made a comeback, leading to a cost-of-living crisis for millions of people, which in turn led to the fall of a series of incumbent governments.

Economists mainly blame four factors for high inflation during the pandemic: supply-chain bottlenecks, fiscal stimuli, concentration in product markets, and the Russia-Ukraine war. The debate on the role of each factor continues.

In some empirical analyses of the pandemic-era high inflation, economists have used the decomposition method to attribute inflation to different “cost” factors, including wages/salaries, profits, and taxes (Duvan 2024; OECD 2023; ONS 2023).

Recently, I worked on a web application project to make the results of decomposition analysis more accessible to the wider public. The project gathers data for 34 OECD-member countries, performs decomposition, and presents the results for each country on an online dashboard, Decomposing Inflation.

In this blog post, I will lay out the decomposition method, introduce the dashboard, and offer a snapshot analysis for the majority of countries.

Decomposition equation

Gross Domestic Product (GDP) can be measured in three different ways relying on either expenditure, output, or income approach. According to the income approach, GDP is measured as the sum of the following three major income components:

1. compensation of employees (wages and salaries paid to employees and their employers’ social contributions) (simply labor costs),

2. gross operating surplus (business profits) and gross mixed income (profits of the self-employed) (simply profits), and

3. taxes on production and imports minus subsidies (i.e., net taxes).

Let $W$, $S$, and $T$ denote these (nominal) income components, respectively. Let also $Y$ and $Y_r$ denote nominal and real GDP, respectively. The income approach leads to the following identity:

$$Y=W+S+T$$

Dividing both sides by real GDP gives us

$$\frac{Y}{Y_r}=\frac{W}{Y_r}+\frac{S}{Y_r}+\frac{T}{Y_r}$$

or

$$P=w+s+t.$$

$P$ on the left-hand side of the equation is simply the GDP deflator. $w$, the total labor costs divided by real GDP, measures the labor costs per product and is called unit labor costs. Similarly, $s$ and $t$ denote unit profits and unit net taxes, respectively. The change in the GDP deflator can then be written as

$$\mathrm{\Delta }P=\mathrm{\Delta }w+\mathrm{\Delta }s+\mathrm{\Delta }t$$

dividing both sides of which by $P$ yields

$$\frac{\mathrm{\Delta }P}{P}=\frac{\mathrm{\Delta }w}{P}+\frac{\mathrm{\Delta }s}{P}+\frac{\mathrm{\Delta }t}{P}$$

which can be further written as

$$\frac{\mathrm{\Delta }P}{P}=\frac{\mathrm{\Delta }w}{w}\frac{w}{P}+\frac{\mathrm{\Delta }s}{s}\frac{s}{P}+\frac{\mathrm{\Delta }t}{t}\frac{t}{P}$$

or

$$\frac{\mathrm{\Delta }P}{P}=\frac{\mathrm{\Delta }w}{w}\frac{W}{Y}+\frac{\mathrm{\Delta }s}{s}\frac{S}{Y}+\frac{\mathrm{\Delta }t}{t}\frac{T}{Y}.$$

Finally, we can write

$$\mathrm{\%}\mathrm{\Delta }P=\mathrm{\%}\mathrm{\Delta }w\frac{W}{Y}+\mathrm{\%}\mathrm{\Delta }s\frac{S}{Y}+\mathrm{\%}\mathrm{\Delta }t\frac{T}{Y}$$

where $W/Y$, $S/Y$, and $T/Y$ denote labor share, profit share, and tax share of income, respectively.

In words, the percentage change in the GDP deflator, i.e., domestic inflation, is the weighted sum of the percentage changes in unit labor costs, unit profits, and unit net taxes, where the weights are the corresponding shares of income.¹ Each additive term in the equation represents the contribution of a distinct income component per product to domestic inflation, decomposing the latter into three measurable parts. Empirically, all one needs to do is divide each nominal income component by real GDP to find the unit income component, compute the percentage change in it, and then multiply it by the respective income share for each period.

¹ Domestic inflation and more common Consumer Price Index inflation are different in various ways. Domestic inflation measures the percentage change in the price of final goods and services produced domestically.

The dashboard, Decomposing Inflation, presents the results of the decomposition analysis outlined above. You can select a country on the sidebar and view the quarterly contribution of unit labor costs, unit profits, and unit net taxes to domestic inflation for the selected country. You can also focus on the pandemic patterns and view the decadal averages of the contributions of unit components. The underlying data behind visuals can be downloaded on the Tables tab of the dashboard.

The decomposition analysis relies heavily on quarterly national accounts data provided by OECD’s data warehouse OECD Data Explorer. I obtained the quarterly nominal GDP and components series from here, real GDP and deflator series from here, and finally Consumer Price Index series from here.

R scripts that extract the series from OECD data and perform the decomposition analysis are all available on the project repository on Github.

A snapshot analysis

Exploring the dashboard reveals differences across countries in the contributions of unit labor costs, unit profits, and unit taxes to domestic inflation. Here, I will offer a snapshot analysis for the majority of countries included in the dashboard.

The figure below shows the cross-country simple average of country-based four-quarter trailing moving averages of annual contributions and inflation, focusing on the eighteen OECD-member countries.²

² The countries included in the analysis are Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Italy, Luxembourg, Netherlands, Portugal, Spain, Sweden, Switzerland, United Kingdom, and the United States. I don’t show the contribution of unit taxes in the figure because the pandemic-era government aid packages led to much larger changes in this variable, blurring the picture. However, the dashboard provides data for this variable.

The deflator inflation surged in 2021 and 2022, peaked in the first quarter of 2023, and started falling thereafter. In the first year of the pandemic, the contributions of unit labor costs were greater than that of unit profits, with a slight increase in deflator inflation.³ This pattern completely changed in the next two years in that the contributions of unit profits exceeded the contributions of unit labor costs with inflation surging. The roles were swapped again after the second quarter of 2023, with an ensuing sustained fall in the contribution of unit profits and an accompanying fall in inflation.

³ In contrast, CPI inflation fell in 2021.

In the previous section, we saw that the deflator inflation can be decomposed into the contribution of unit incomes.

To better understand these patterns, let us observe that the last equation in the previous section suggests

1. that the percentage contribution of, say, unit labor costs equals the percentage change in labor compensation minus the percentage change in real GDP times labor share of income and

2. that, so long as labor share and profit share are close to each other, which is the case for many countries, what differentiates the contribution of unit labor costs and unit profits is the percentage change in the nominal labor compensation and nominal profits, given that the percentage change in real GDP appears in all contributions.

Therefore, we can focus on nominal labor compensation and profits, and real GDP to explain the patterns outlined above. The following figure shows the annual growth in labor compensation, profits, and real GDP.⁴

⁴ Similarly, the figure is based on the cross-country simple average of country-based four-quarter trailing moving average of annual growth in each variable.

Based on the previous observations, the period from the beginning of the COVID-19 pandemic in 2020 to the present can be divided into three episodes:

1. 2020-2021, where both labor compensation and profits fell, but real GDP fell more, and inflation remained suppressed;

2. 2021-2023, where both labor compensation and profits grew at a higher-than-usual speed, with the latter at a much faster rate and inflation surged; and lastly

3. 2023 to the present, where the growth in labor compensation was sustained, but the growth in profits decelerated fast, and inflation fell.

The remarkable nature of the faster growth in profits in the second episode can be better understood through a comparison with the previous two decades (see the figure above). In the same countries as above, while profits grew on average at 3.53% per year between 2000 and 2019, they grew at 6.68% between the first quarter of 2020 and the second quarter of 2023!⁵ In contrast, the annual average growth in labor compensation was 3.62% and 4.91% in the same periods, respectively.

⁵ 2023 Q2 was the last quarter in which the growth in profits remained above the growth in labor compensation.

References

Duvan, Osman Berke. 2024. “TÜRKİYE’DE ŞİRKET KÂRLARI VE ENFLASYON: ADAM SMİTH HAKLI MI?” Uluslararası İktisadi ve İdari İncelemeler Dergisi, no. 45 (October): 167–82. https://doi.org/10.18092/ulikidince.1512414.

OECD. 2023. “OECD Economic Outlook, Volume 2023 Issue 1: A Long Unwinding Road.” 113. Paris: OECD Publishing. https://doi.org/10.1787/ce188438-en.

ONS. 2023. “The Role of Labour Costs and Profits in UK Inflation.” Office for National Statistics.