## Annexes

### Annex A: PPI data sources

#### ONS producer prices statutory surveys

- Monthly Survey for Index Numbers of Producer Prices – collects prices used to compile the PPIs. A sample of manufacturers is selected from ONS’s UK Manufacturers’ Sales by Product (PRODCOM) survey.
- Monthly Survey for Index Numbers of Export Prices – collects prices for products manufactured and exported from the UK, used to compile the EPIs. Includes all UK trading businesses within the manufacturing and mining sectors registered with HM Revenue and Customs (HMRC) for Value Added Tax (VAT) or Pay As You Earn (PAYE).
- Monthly Survey for Index Numbers of Import Prices – collects prices for goods and raw materials imported into the UK, used to compile the IPIs. Includes all UK trading businesses within the manufacturing and mining sectors registered with HMRC for VAT or PAYE.

#### Main data sources used for weighting

- PRODCOM (ONS) – most sales values and volumes for UK manufacturing are sourced from the PRODCOM survey.
- Annual export and import sales value data (HMRC) – used as weights in the EPIs and IPIs. The coverage is split between trade to or from an EU and non-EU country, which correlates with the index structure in the EPI and IPI.
- Annual Business Survey (ABS) (ONS) – a sample survey that collects annual sales data for UK businesses across the whole economy, including businesses within the manufacturing sector, and was also used during the last rebasing exercise. ABS data are used for calculating annual sales values that include duty; annual sales values for the water and forestry support service indices; and annual sales values for products that are not covered by other sources.

#### Survey and administrative data from other government departments and organisations

- Agriculture – Department for Environment, Food and Rural Affairs (Defra)
- Energy (including crude oil) – Department for Energy Security and Net Zero (DESNZ)
- Fish – Marine Management Organisation (MMO)
- Water Supply – Water Services Regulatory Authority (OFWAT)
- Basic Iron and Steel products – International Steel Statistics Bureau
- Timber –Forest Research

#### Published sources of price data

- Commodities such as oil, gold and copper – Financial Times
- Exchange rates – Financial Times
- Wheat and grains, oilseeds and oil, fats and nuts – Bloomberg
- Milling and feed wheat – Agricultural and Horticulture Development Board
- Metal Ores and Kaolin – Industrial Minerals
- Other Metal Products – Metal Bulletin
- Rubber – The Rubber Board
- Cotton – IndexMundi
- Meat Products – Smithfield Market Coffee – International Coffee Organization
- Tea – International Tea Committee

### Annex B: PPI errors

Between November and December 2022, ONS identified a series of errors in the PPIs:

**Diesel fuel was not allocated a correct weight within the output price index**.

This resulted in Petroleum Products being around half the correct weight of 6.5% since the start of the 2022. The correction in Output PPI weights, and the inclusion of diesel prices within the data, meant that from January to October 2022 Petroleum Products had the largest positive contribution to the 12-month rate of output inflation. The error did not affect the overall trend, but it led to the headline 12-month output price rate being revised up by an average of 1.8 percentage points during this period. For October 2022 Petroleum Products contributed 6.1 percentage points to the 12-month rate (revised from 0.0). The issue occurred because of a processing error during manual intervention. The business prices team corrected all affected datasets.

**Human error resulted in not updating the indices in the published table**.

This happened because some material was copied from one Digital Access Platform (DAP) to another as part of the process of correcting the Diesel fuel error. PPI is calculated and compiled using two pipelines; a ‘monthly’ pipeline used to calculate all data for all periods direct from source data, and a ‘publication’ pipeline that stores data so that the business prices team has ongoing repository of published data. Within DAP, one database is used to facilitate the monthly PPI releases and another is used to run any data tests. The business prices team introduced a set of internally consistent spreadsheets to match the data already on the website.

**The two most recent mapper files for 2021 were used instead of the 2022 file**.

The mapper files help link the monthly price data to the annual weights. Because there is no consistent classification for PPI, these mapper files help ensure that the various data are fed into the right indices with the right weights. These errors only affected the PPI input price index. The business prices team rebuilt the mapper files because there was an error in the 2022 mapper file and reviewed all other existing mapper files.

**Some historical data (pre-2021) were incorrectly hidden from the time series viewer on ONS’s website**.

The issue was caused by how the central database handles price indices that are imported from DAP. ONS corrected these data when it started republishing the PPIs in January 2023 and worked with DST to put in place checks for the import process.

### Annex C: Revisions analysis

C.1 The aim of our revisions analysis was to understand to volatility of the indices and the reliability of preliminary figures. In particular, we wanted to understand the direction and size of revisions.

C.2 We took data from the Producer Price Inflation Time Series datasets covering the period from April 2021 to May 2023. These datasets are published alongside the monthly statistical bulletin and provide a time series for the PPIs, EPIs and IPIs. It is important to note that this is an indicative analysis. It is not a complete analysis of revisions to all PPIs, EPIs and IPIs. Instead, it is based on a subset of 129 indices that are published in every dataset – the headline output and input index and 127 lower-level indices.

C.3 The analysis was carried out on percentage growth rates. For each index, we calculated the annual percentage growth rate as the difference in the index value for a given month and the same period 12 months earlier, divided by the index value for the earlier time period.

C.4 For each month, we calculated the revision as the percentage point difference between the first published estimate and the final growth rate published 12 months later, as the revision window for PPIs is 12 months. We did this for each of the annual growth rates for years ending June 2021 to May 2022, the latter of which is the latest available that has been fully revised. For each of the 129 indices, we then calculated the average size of revision as the mean of the revisions for each of the 12 annual growth rates.

C.5 We recognise that the 12-month period we have chosen may not be representative of the direction and size of revisions made over a longer time period. For instance, our analysis includes revisions made following the series of errors identified between November and December 2022 (see Annex B), and these revisions were relatively large.

C.6 We found that the headline indices are frequently revised upwards. For the headline output index, the annual percentage growth rate for any given month is revised upwards, on average, 0.80 percentage points. For the headline input index, the annual percentage growth rate for any given month is revised upwards, on average, 0.86 percentage points. This shows that the preliminary figure underestimates the true size of the price change. Because the average size of these total revisions is less than one percentage point it is unlikely that revisions will cause a change in the direction of price movements (for example, the revised index showing positive growth whereas the initial estimate suggested negative growth). We did not test whether the average size of revisions was significantly different from zero.

C.7 We found the same pattern for the lower-level indices: they are consistently revised upwards, although the average size of revisions tends to be small. This suggests that the indices are systematically underestimating price changes. Figure C.1 shows the average size of revisions for our subset of 129 indices.

**Figure C.1. Average size of revisions between June 2021 and May 2022 for our subset of 129 indices**

#### Figure C.1.

This chart shows the average size of revisions for our subset of 129 indices between June 2021 and May 2022. The average size of revisions for most indices, including the headline output index and headline input index, is above 0, which means that they are revised upwards. This suggests that the indices are systematically underestimating price changes.

### Annex D: Detailed methods information

#### Index Formula

D.1 There is a variety of index formulae available for producing price indices. The IMF’s PPI manual says that the Fisher index is widely considered the “best” index formula. However, it is resource intensive and impractical to use as it requires compiling the Paasche index which uses current sales volumes alongside current prices to compile (see below). According to the OECD’s PPI database (which is no longer updated), only one OECD member country (Iceland) uses the Fisher Index, while the remaining countries, including the UK, use types of Laspeyres indices such as the Lowe index (Table D.1).

D.2 The Fisher index is defined as the geometric average of the Laspeyres and Paasche Index:\(\)

$$ {\rm{I}}_{\rm{F}}^{\rm{t}} = \sqrt {I_L^t {\rm{ \times I}}_{\rm{P}}^{\rm{t}} } $$

Where \(I_F^t\) is the Fisher Index in period t, \(I_L^t\) is the Laspeyres Index in period t, and \(I_P^t\) is the Paasche index in period t.

D.3 The Laspeyres index is a base weighted index that tracks the price of a fixed “basket of goods” over time. The Laspeyres index defines how much a basket of goods in a base period would cost in other periods:

\(\)$$ I_L^t = {{\sum\nolimits_{i = 1}^n {p_i^t q_i^0 } } \over {\sum\nolimits_{i = 1}^n {p_i^0 q_i^0 } }} = \sum\limits_{i = 1}^n {{{p_i^t } \over {p_i^0 }}} s_i^0 $$

Where \(p_i^t\) is the price of item i in period t, \(q_i^0\) is the quantity sold of item i in period 0, and \(s_i^0\) is the index weight of item i in period 0.

D.4 The Paasche index is a current weighted index that tracks the price of a fixed “basket of goods” over time. The Paasche index defines how much a basket of goods in the current period would cost in other periods:

\(\)$$ I_p^t = {{\sum\nolimits_{i = 1}^n {p_i^t q_i^t } } \over {\sum\nolimits_{i = 1}^n {p_i^0 q_i^t } }} = \sum\limits_{i = 1}^n {{{p_i^t } \over {p_i^0 }}s_i^t } $$

Where \(p_i^t\) is the price of item i in period t, \(q_i^t\) is the quantity sold of item i in period t, and \(s_i^t\) is the index weight of item i in period t.

D.5 ONS uses the Laspeyres-Lowe Index which is very similar to the Laspeyres Index and can be described as a modified Laspeyres Index. It is defined as:

\(\)$$ I_{Lowe}^t = {{\sum\nolimits_{i = 1}^n {p_i^t q_i^b } } \over {\sum\nolimits_{i = 1}^n {p_i^0 q_i^b } }} = \sum\limits_{i = 1}^n {{{p_i^t } \over {p_i^0 }}} \,s_i^b $$

Where \(I_{Lowe}^t\) is the Lowe index in period t, \(p_i^t\) is the price of item i in period t, \(q_i^b\) is the quantity sold of item i in period b, and \(s_i^b\) is the index weight of item i in period b.

D.6 The primary difference between the Laspeyres and the Laspeyres-Lowe index is that the base period for the Laspeyres-Lowe index will not necessarily be period 0, i.e. the period that the current period is being compared against. It is very likely that b<0 and will precede period 0. The base weights are price updated to reflect the prices in period 0.

D.7 The Laspeyres-Lowe index is a suitable formula for compiling producer price indices as evidenced by its wide use by the international statistical community. The main limitation of the Laspeyres-Lowe index is that it is vulnerable to substitution bias, which is where consumers shift away from products which increase in price. This means that the revenue weights used to compile the index may not be representative as products are substituted for others and the relative revenues change. The theoretical direction of bias is unclear, but it may affect the reliability of the index. Because ONS updates the weights annually, the effect of substitution bias is minimised.

#### International comparability

D.8 Table D.1 below highlights the variation across G7 countries in the methods used to compile PPIs. Only some countries annually rebase and chain-link their PPIs. As explained in the main report, explicit quality adjustment is the recommended method for adjusting for the changing quality of products. Only the UK and Italy use implicit quality adjustment to estimate quality changes.

**Table D.1 Methods used by G7 Countries to compile PPIs**

Country | Index method | Frequency of rebasing | Explicit quality adjustment | Quality adjustment methods |
---|---|---|---|---|

UK | Chained Laspeyres-Lowe | Annually | No | Chaining |

Canada | Fixed-base Laspeyres | Every five years | Yes | Expert adjustment and other methods |

France | Chained and Fixed base Laspeyres | Annually (headline indices); every five years (lower-level indices) | Yes | Hedonic regression, chaining |

Germany | Modified Laspeyres | Every five years | Yes | Chaining, direct price comparison, matched modelling, option prices, expert assessment, hedonic regression |

Italy | Chained Laspeyres | Annually | No | Chaining |

Japan | Chained Laspeyres | Annually | Yes | Direct comparison, chaining, production cost, hedonic regression, option cost |

USA | Modified Laspeyres | Every five years | Yes | Direct comparison, chaining, hedonic regression |