# How do firms pass energy and food costs through the supply chain

Hela Mrabet and Jack Page

The rise in commodity prices after Russia’s invasion of Ukraine had a direct and noticeable impact on consumers’ bills for energy and food. But firms also felt the brunt of higher costs. How did firms pass on these cost shocks through the supply chain and all the way onto consumer prices? How much and how quickly can firms pass through such large cost shocks? In this blog post, we combine information from Supply-Use tables with a rich industry-level data set on input and output price indices to shed light on these questions.

How do cost shocks pass through the supply chain?

Imagine an economy with three sectors (and firms): an energy producer, a food manufacturer and a restaurant. Energy is a primary input into production, and the economy is hit by a large energy price shock. The restaurant will see its energy bills rise as a result; and will seek to pass it through to its customers – this is the ‘first-order’ supply-chain effect on inflation (solid arrow in Chart 1). But the restaurant will also see food prices go up as a result of the energy price shock, and will also attempt to pass this increase through to its customers – this is the ‘second- order’ supply-chain effect on inflation (dashed arrows in Chart 1).

So to generalise this idea for an economy with multiple sectors, an input price shock will generate interactions through the supply chain as the shock is passed to upstream sectors, and these interactions will all affect inflation.

Chart 1: The idea

Source: Authors’ calculations.

A representation through Supply-Use tables

One way to formalise this idea is to use Supply-Use tables. These describe how products are used as intermediate inputs to produce further products (either intermediates or final goods and services), and so allow us to estimate a given input cost pass-through from the full supply-chain interaction.

Let’s use energy (E) as a primary input again in an economy with n different products, and let’s assume a shock $\Delta p_{E}$ to the price of energy. For each of the remaining n-1 products in the economy, the first-order supply-chain effect of the cost shock on the price of product j is the share of energy in the output of product j multiplied by the energy price shock. And the second-order effects and beyond are the price changes of all the other inputs used to produce product j multiplied by their share in output. So overall, the full effect captures how the energy shock ripples through to final products, both directly through first-order supply chain effects, and indirectly, through second-order effects and beyond.

The Supply-Use tables give us the increase in the price of 105 non-energy products following an energy price shock – goods and services in the economy are classified into 105 categories according to the Classification of Products by Activity (CPA). These 105 CPA categories do not perfectly match to CPI components (which are classified by purpose instead), so we use the ONS CPA-COICOP convertor.

We apply a similar methodology to obtain indirect food effects through the supply chain. Chart 5 below shows the contribution of indirect food and energy effects to CPI inflation.

How much and how quickly do cost shocks get passed through the supply chain?

At face value, the representation through Supply-Use tables described above assumes full and immediate pass-through of the energy price (or any other input) shock at each stage of supply chain interaction. We think this is a strong assumption, and might not properly reflect firms’ pricing decisions. For example, the Bank of England’s Agents Intelligence pointed to firms facing a margins’ squeeze over the past year immediately after the commodity price shock, and a gradual rebuild this year and next. This suggests the pass-through of the energy price surge is rather lagged, and possibly incomplete.

To address this, we add information on the scale and speed of pass-through from rich data sets on producer price inflation (PPI) and services producer price (SPPI) to capture firms’ pricing decisions. These provide input and output price indices for manufacturing and services sectors going back to 1997. For manufacturing sectors, we estimate industry-specific error-correction models (ECMs) of output prices on input prices. For services, there are sector-specific output prices, but not sector-specific input costs, so we use the aggregate manufacturing input price PPI on the right hand-side of the regressions instead. Equations 1a and 1b below describe the ECMs long-run relationship and short-run dynamics:

Equation 1a – Long-run (LR) regression: $Output Price_{i} = c^{LR} + \gamma {{i}}^{LR}Input Price_{i}$

Equation 1b – Short-run (SR) Dynamics: $Delta Output Price_{i} = c^{SR} + \gamma {_{i}}^{SR}\Delta Input Price_{i} + LongrunDisequilibrium_{i}$

We estimate these regressions for around 70 sectors with quarterly data going back to 1997 (when available). We use the $\gamma_{i}^{LR}$ coefficients in equation 1a to underpin the long-run pass-through of an input cost shock into the output price of each sector i.

And we use the impulse response functions from the short-run dynamics in equation 1b to underpin the timing of this pass-through for each sector i.

Overall, our sector-level regressions suggest the pass-through of an input cost shock is incomplete (Chart 2), with long-run coefficients ranging from 0.4 (for services industries) to 0.8 (for most manufacturing industries).

Chart 2: Long-run pass-through coefficients by sector

Source: Authors’ calculations.

The dynamics also vary significantly across sectors. For each sector, we use the ECM regressions to plot the impulse response functions of the output price to an input price shock. Chart 3 shows the time (in quarters) needed to pass through 80% of the input price shock for each industry. Pass-through is found to be faster for manufacturing sectors, with eight quarters on average until 80% of the shock is passed through versus 15 quarters on average for services industries.

Chart 3: Time to pass through 80% of the input price shock by sector

Source: Authors’ calculations.

Does what go up go down?

Do firms change prices in the same way irrespective of whether input costs go up or down? This question is interesting from a policy perspective: if firms decide to pass through an input cost increase faster than an input cost fall, then there could be more persistence in inflation from the current commodity shock even as commodity prices start to fall.

We use the industry-level ECM regressions to check for asymmetry on the way down. To do so, we introduce dummy variables into the dynamic part of the equation to separate out periods when CPI inflation was above or below the mean, or alternatively rising or falling. We limit the estimation sample to 2019 Q4, such that it is not biased by the current episode of input cost shock.

We find evidence of asymmetry in the cost-push shock for most manufacturing industries, as well as some services industries (eg food and accommodation services in line with the Bank of England’s Agents Intelligence). Overall, input price shocks get passed into output prices with an additional two quarters’ lag when costs are going down versus going up (Chart 4).

Chart 4: Impulse response functions (IRFs) on the way up versus on the way down

Source: Authors’ calculations.

So how much of CPI inflation is driven by energy and food costs passing through the supply chain?

Taking all this together (Chart 5), we estimate that the pass-through of energy and food price shocks through the supply chain boosted CPI inflation by around 1 percentage point at peak (2022 Q4). And could be a source of persistence in inflation going forward, as firms continue to pass through past input shocks to rebuild their margins. Chart 5 also shows what a ‘full and immediate’ pass-through assumption would suggest, with a larger effect on inflation at peak, but also a lot more short-lived.

Chart 5: Contribution of indirect effects through the supply chain to CPI inflation

Source: Authors’ calculations.

Looking at differences across CPI components (Chart 6), the energy contribution to inflation has been largest for food and non-alcoholic beverages (FNAB); it is estimated to have peaked at approximately 3 percentage points in 2022 Q3 and to have moderated relatively quickly afterwards. Our forecast is consistent with significant further moderation in 2023 Q4. Energy has provided a significant boost to some services sector inflation, for example transport and restaurants & hotels (approximately 1 percentage point at peak). For these sectors, the contribution of energy is relatively persistent, reflecting the longer lags through the supply chain suggested by the PPI regressions.

Chart 6: Contribution of indirect energy effects to inflation across COICOP categories, 2022 Q3–2024 Q2

Source: Authors’ calculations.

Conclusion

In this blog post, we present a way of estimating the inflation effects of energy and food cost shocks through the supply chain, which combines information from Supply-Use tables as well as relationships between input and output prices from the PPI data set. Our key assumption is that the pass-through is gradual, incomplete and asymmetric; and our methodology captures the full set of interactions along the supply chain. The results show that energy and food effects through the supply chain have had a sizeable contribution to inflation over the past year, and – given the asymmetric time lag in passing on cost shocks coming down (slower) versus going up (faster) – might be a source of persistence over the next 12 months as firms try to rebuild their margins.

Hela Mrabet works in the Bank’s Monetary Policy Outlook Division and Jack Page works in the Bank’s External MPC Unit.