CPI-Trim — Bank of Canada Core Inflation

What Is Trimmed-Mean and Median CPI?

Trimmed-mean and median CPI are alternative measures of core inflation designed to identify the underlying trend in consumer prices without relying on a predetermined list of excluded items. Unlike the traditional core CPI, which always removes food and energy regardless of whether those categories are actually behaving erratically in a given month, these statistical measures dynamically filter out extreme price movements from whichever categories happen to be the most volatile at any point in time. The result is a more robust and adaptive signal of underlying inflation.

The trimmed-mean CPI works by ranking all components of the CPI basket by their monthly or annual price change, then removing a fixed percentage of items from both the upper and lower tails of the distribution. A common specification trims the top and bottom 20 per cent of the weighted distribution of price changes, then computes the average of the remaining 60 per cent. This approach discards the most extreme movers in either direction, whether those happen to be energy, food, clothing, or any other category.

The weighted-median CPI takes a related but distinct approach. It identifies the price change at the 50th percentile of the expenditure-weighted distribution of all component price changes. In other words, the median CPI is the inflation rate of the component such that half of the consumer basket (by expenditure weight) experienced lower inflation and half experienced higher inflation. The median is inherently robust to outliers because it is completely insensitive to the magnitude of extreme values at either end of the distribution.

Both measures have gained prominence among central banks over the past two decades. They are viewed as improvements over the traditional exclusion-based core because they do not impose any fixed assumptions about which items are volatile. In a period where food prices happen to be stable but used-car prices are surging, the trimmed-mean and median measures will automatically filter out the used-car spike, something the traditional core CPI would miss entirely.

The intellectual roots of these measures lie in the field of robust statistics, which develops estimators that perform well even when the underlying data contain outliers or depart from standard distributional assumptions. The trimmed mean is a classical robust estimator of location, and its application to inflation measurement represents a natural extension of these ideas to economic data.

How It Is Calculated

For the trimmed-mean CPI, the computation proceeds as follows. Let $\pi_{i,t}$ be the year-over-year or month-over-month price change for component $i$ at time $t$, and let $w_i$ be the expenditure weight of component $i$. The components are sorted by $\pi_{i,t}$ in ascending order. The algorithm then finds the cumulative weight cutoffs: the lowest-weighted $\alpha$ per cent and the highest-weighted $\alpha$ per cent of components are removed.

For a symmetric 20 per cent trim, $\alpha = 20$, and the retained components fall between the 20th and 80th percentiles of the cumulative weight distribution. The trimmed-mean inflation rate is:

where $R$ is the set of retained components after trimming. The denominator renormalizes the weights so that they sum to one over the retained set.

For the weighted-median CPI, the components are again sorted by $\pi_{i,t}$ in ascending order. The median is the price change $\pi_{m,t}$ of the component $m$ at which the cumulative expenditure weight first reaches or exceeds 50 per cent:

In practice, linear interpolation is sometimes used when the cumulative weight crosses the 50 per cent threshold within a single component, yielding a smoother series.

The key advantage of both methods is their data-driven nature. Neither requires the analyst to specify in advance which items to exclude. The trimming or median calculation responds automatically to whichever components are exhibiting unusual price movements in any given period. This makes the measures particularly valuable during episodes of unusual inflation dynamics, such as pandemic-related supply disruptions that affect categories not traditionally considered volatile.

Some central banks publish multiple trim specifications, for example a 20 per cent trim and a 30 per cent trim, to assess the sensitivity of the underlying inflation estimate to the choice of trim width. When different trim widths yield similar estimates, it reinforces confidence in the inflation signal. When they diverge, it suggests that the distribution of price changes is unusually skewed or fat-tailed, warranting closer inspection of the underlying data.

How to Read the Numbers

Trimmed-mean and median CPI are reported as percentage changes, either month-over-month or year-over-year, just like headline and core CPI. The most useful analytical exercise is to compare these measures against both headline and traditional core CPI.

When all three core-type measures, the traditional exclusion-based core, the trimmed mean, and the median, point in the same direction and are clustered around a similar rate, confidence in the underlying inflation signal is high. Divergence among the measures warrants closer examination. For instance, if the trimmed mean and median are running well above traditional core CPI, it may indicate that price pressures are broad-based but happening to be concentrated in categories outside of food and energy, a pattern the traditional core measure would not capture.

The median CPI tends to be the most stable of the three measures because it is influenced by only a single component at the centre of the distribution. It is less sensitive to compositional shifts and provides the smoothest reading of underlying inflation. However, its smoothness can also be a drawback in fast-moving environments, as it may be slow to reflect a genuine shift in the inflation trend.

The trimmed mean offers a middle ground, retaining more information from the tails than the median while still filtering out the most extreme outliers. Its responsiveness to genuine shifts in the inflation trend is generally faster than the median, though it is more sensitive to the choice of trim percentage.

Central banks often present all three measures together in monetary policy reports, emphasizing the range and central tendency rather than relying on any single number. When the range narrows and all measures converge on the inflation target, it provides strong evidence that price stability is being maintained. When the range widens or all measures drift persistently away from the target, it signals that the inflation outlook has become more uncertain or that underlying pressures are building.

Economic Significance

Trimmed-mean and median CPI measures have become essential tools in the central banking toolkit precisely because they address a fundamental weakness of the traditional exclusion-based core. The traditional approach assumes that food and energy are always the primary sources of transitory volatility, but economic reality is more complex. During the COVID-19 pandemic, for example, used-vehicle prices, airfares, and hotel rates experienced extraordinary swings driven by supply constraints and shifting demand patterns. These categories are included in traditional core CPI, and their extreme movements muddied the signal. The trimmed-mean and median measures handled these episodes far more gracefully, automatically filtering out the outliers regardless of which category they belonged to.

Research has consistently shown that trimmed-mean and median CPI are among the best available predictors of future headline inflation. They outperform traditional core CPI in forecasting exercises because they are better at distinguishing between persistent and transitory price movements. This forecasting superiority has been documented across multiple countries and time periods, making these measures increasingly central to monetary policy deliberations.

The adoption of these measures also reflects a broader intellectual shift in central banking toward data-driven, model-free approaches to measuring underlying inflation. Rather than imposing prior beliefs about which sectors are volatile, the trimmed-mean and median approaches let the data speak for itself. This pragmatism resonates with the general trend in applied economics toward robust statistical methods that perform well across a variety of conditions.

For financial market participants, divergences between trimmed-mean or median CPI and traditional core CPI can provide early signals of shifts in the inflation outlook. A persistent rise in the trimmed mean, even when headline and traditional core remain well-behaved, may foreshadow a broader acceleration in prices and signal that central bank policy adjustments are on the horizon.

Despite their advantages, these measures are not without limitations. The choice of trim percentage is somewhat arbitrary, and different trim widths can yield meaningfully different estimates of underlying inflation. The median, while robust, discards a great deal of information about the breadth and distribution of price changes. For these reasons, no single measure is definitive, and the best practice is to examine a range of indicators to form a complete picture of inflationary pressures in the economy.

Related Indicators

• Consumer Price Index (All Items, Year-over-Year)
• Core CPI (Year-over-Year)
• Inflation Expectations
• Policy Interest Rate