From Tail to Median: Decoding Inflationary Pressures in Portugal

The last few years have been marked by an inflationary shock of unprecedented dimensions in the history of the European economic and monetary union. In this context, there has been an increased need, and interest, in deepening the understanding of the inflationary phenomenon. In Portugal, inflation reached 8.1% in 2022, its highest level since 1992, subsequently decelerating to 5.3% in 2023 and 2.7% in 2024. The deterioration was particularly evident in food prices, whose price levels in 2024 were about 30% higher than those observed in 2021.

A set of tools has been developed, or updated, to identify the most persistent and generalised component of prices. By filtering out from volatile or idiosyncratic movements, these are expected to provide a more informative signal about medium-term inflation. A recent ECB^[1] analysis details the indicators developed by the institution to infer the underlying inflation dynamics. In short, these are grouped into 3 categories of varying complexity: (i) permanent exclusion measures (e.g. inflation excluding food and energy); (ii) temporary exclusion measures (e.g. trimmed means); (iii) model-based measures (e.g. dynamic factor models)

A recent publication by the American Federal Reserve (Fed) adds a new proposal to the existing range.^[2] This new perspective is based on observations recorded in the low and stable inflation regime that lasted for the 25 years prior to the pandemic. The authors confirm the existence of a robust empirical relationship between the inflation recorded in a given month and a measure of asymmetry of the distribution of price changes in the basket of goods and services underlying the price index. The objective is to answer the question: “Given the asymmetry in the underlying distribution of price changes, is the inflation reading for a particular month too high (or too low) to be consistent with the pre-pandemic relationship?”   

The distribution of price changes allows for a more informed interpretation of the inflationary phenomenon. In approximate terms, the total inflation rate, measured by the Harmonised Index of Consumer Prices (HICP), in a given month corresponds to the (weighted) average of price changes across all categories that constitute the price index. Indeed, from a macroeconomic perspective, it is not indifferent whether a price increase above the Central Bank's stability reference is driven by a limited set of goods and services (e.g. fuel prices), or is the result of a broader movement and, therefore, more likely to persist over time.

A distribution is considered skewed whenever the mean diverges from the median of the observations. The authors use the following identity: Mean = Median + (Mean-Median). A higher overall inflation rate (mean) that is driven by a higher median will be more concerning than one that is driven by greater right-skewness (mean - median > 0). As a measure of asymmetry, the authors use the percentile of the distribution in which the overall inflation lies. For example, in a symmetrical distribution, the mean will fall at the 50th percentile, as well as the median. For a right-skewed distribution, the mean is located above the 50th percentile. On the other hand, in a left-skewed distribution, the mean lies below the 50th percentile.

This Box adapts this methodology to the Portuguese reality. A 4-digit COICOP level of granularity of the HICP^[3] was used, corresponding to 90 individual categories of prices of goods or services, in a monthly time sample between 1996 and 2024. Each of these components was  seasonally adjusted to prevent the measurement of price changes from being justified by regular fluctuations motivated by the time of year in which the observation is made (e.g. price of holiday packages during summer). Graph 1 illustrates the distribution of prices of HICP subcomponents in different months of recent years.

Graph 1 – Distribution of monthly price changes

Sources: Eurostat, authors' calculations.

In Portugal, as in the USA, the monthly inflation rate has a predictable relationship with the asymmetry of the distribution. Graph 2 presents the empirical adherence of a locally estimated scatterplot smoothing (LOESS) polynomial regression estimated between monthly inflation and the chosen asymmetry measure, for the pre-pandemic period 1996 to 2019. Each of the grey circles corresponds to an monthly observation during this period. Similar to the evidence for the USA, it is worth noting that the observations are concentrated around the annualised inflation target of around 2% - which corresponds, approximately, to a monthly inflation of 0.16%. This means that higher levels of inflation were associated with a skew in the distribution – reflecting price changes in a relatively small percentage of components (e.g. increases in food prices) – and not a higher median of the distribution. It is also emphasized that the 95% confidence interval is narrower when the mean is close to the median, but wider when it deviates from the median of the distribution.

Graph 2 –  Non-linear relationship between price changes and the asymmetry of their distribution

Source: Authors' calculations.

With this tool, we can identify whether inflation is evolving in a direction inconsistent with price stability. The close relationship identified in the pre-pandemic period allows us to infer whether inflation has a sufficiently broad base to be considered incompatible with the 2% target, or whether it is motivated by a local phenomenon. Graph 3 illustrates the deviations recorded, from 2022 to 2024, between observed inflation and expected inflation based on the distribution of price changes in the 90 HICP components considered. The data are smoothed in 12-month moving averages to reduce their volatility.

There are 14 months – between April 2022 and May 2023 – in which the deviations can be considered statistically significant. That is, for the same degree of asymmetry in the period preceding the inflationary crisis, during those months the level of inflation recorded significantly exceeded what could be expected, resulting in a movement of the previously estimated non-linear relationship curve. In other words, these levels of inflation had only been observed in the past due to shocks in very specific categories of the basket – such as fuel prices – and not in such a general way. Thus, an inflationary crisis that was initially confined to a limited set of goods and services, progressively became more widespread. This interpretation is consistent with the information in Graph 2, which identifies the observations for the year 2022 as outliers.

Graph 3 – Difference between observed inflation and the estimate consistent with the degree of asymmetry of the distribution

Source: Authors' calculations.

The analysis of the distribution of price changes in the consumption basket confirms the consolidation of the disinflation process. Indeed, between June 2024 and January 2025, the European Central Bank (ECB) reduced the interest rate by about 125 basis points, from 4% to 2.75% in the case of the deposit facility. The confidence in this process is also evident in medium-term forecasts which, in the case of the euro area, anticipate convergence to the 2% target during this year. In the particular case of the Portuguese economy, the methodology described here allowed the identification of both the period of upward and generalised inflationary pressures, as well as the subsequent normalisation, although this process may be considered incomplete with the persistence of differentials slightly above zero visible in Graph 3. The use of information on the distribution of inflation in the consumption basket proves its usefulness and complementarity to other measures, given its ability to distinguish between generalised inflationary pressures and specific movements and, thus, offer an informative signal about periods when inflation deviates from the regime observed in the 20 years of the pre-pandemic period.

References

Banbura, M., Bobeica, E., Bodnár, K., Fagandini, B., Healy, P., and Joan Paredes (2023). ‘Underlying inflation measures: an analytical guide for the euro area’. ECB Economic Bulletin, Issue 5.

Smith, Simon C., and Alexander L. Wolman (2024). "New tools to monitor inflation in real time," FEDS Notes. Washington: Board of Governors of the Federal Reserve System, December 20, 2024, https://doi.org/10.17016/2380-7172.3617.

Date of last update: 21/03/2025