Unknown measures: assessing uncertainty around UK inflation using a new Inflation-at-Risk model

Nikoleta Anesti, Marco Garofalo, Simon Lloyd, Edward Manuel and Julian Reynolds

Understanding and quantifying risks to the economic outlook is essential for effective monetary policymaking. In this post, we describe an ‘Inflation-at-Risk’ model, which helps us assess the uncertainty and balance of risks around the outlook for UK inflation, and understand how this uncertainty relates to underlying economic conditions. Using this data-driven approach, we find that higher inflation expectations are particularly important for driving upside risks to inflation, while a widening in economic slack is important for downside risks. Our model highlights that rising tail-risks can become visible before a turning point, making the approach a useful addition to economists’ forecasting toolkit.

To the mean and beyond: a fan chart story

The Bank of England pioneered the approach of including information on uncertainty and risks around their forecast with their inflation ‘fan chart’ – first published in February 1996 (Chart 1). It remains a staple of the quarterly Monetary Policy Report (MPR) to this day. The ‘fan’ sets out the MPC’s assessment of the outlook for inflation and the risks around it over the forecast horizon. The inner dark red band reflects the ‘central projection’ – the MPC’s view of the most likely outcome for inflation. The lighter bands reflect less likely – but still possible – outcomes. The chart is constructed such that inflation is expected to lie somewhere within the entire width of the fan on 90 out of 100 occasions.

Chart 1: The first inflation ‘fan chart’ (February 1996)

Changes in the size and shape of the fan reflect changes in the MPC’s views on the level of uncertainty and balance of risks. A symmetric widening of the fan to the upside and downside implies a greater degree of overall uncertainty around the outlook. Alternatively, a one-sided widening in the fan above or below the dark red central scenario implies changes in the balance of risks. For example, a widening in the fan above the dark red band implies an increase in the level of risk specifically that inflation might turn out higher than expected.           

The MPC uses a range of statistical tools and judgement to construct its fan chart. There are a number of challenges involved in any forecasting exercise, and such challenges become even starker when trying to construct estimates for risks around the central projection. The issue is that standard statistical tools (eg linear regression) are designed to produce forecasts for the expected, ie mean, path of macroeconomic variables. They typically do not provide a direct estimate of the uncertainty around these paths. While a measure of uncertainty can be constructed by examining historical forecast errors from these types of model, this does not help in understanding which variables drive the uncertainty, nor can it capture changes in uncertainty over time driven by changing economic conditions.

We want to go beyond this approach and explicitly estimate the level and drivers of risk around inflation over time.

A new approach to quantify risks: Inflation-at-Risk

In order to do so, we borrow an approach from recent work in academic and policy circles aimed at monitoring risks to financial stability: ‘GDP-at-Risk’. Like other central banks that have adopted similar approaches, we rely on quantile regression, a statistical tool that allows us to estimate the relationship between a range of indicators and the whole distribution of possible inflation outcomes. Through this, we determine which variables are particularly important, not just for explaining changes in the expected path for inflation, but also in shaping the overall level of risk around that path. We also employ a local-projection framework, which allows us to estimate the level of risk across different forecasting horizons.

We include various macroeconomic indicators that are typically considered important for driving inflation dynamics, specifically: lagged inflation, inflation expectations (for a combination of households and corporates), the estimated output gap, and world export prices. Our choice of variables mirrors those that feature in an Open-Economy Philips Curve. The quantile regression model allows us to investigate how changes in each of these variables affect the whole distribution of possible inflation outcomes across a range of forecast horizons. To estimate our model we rely on data from a number of advanced economies (US, UK, euro area and Japan) with a variety of historical inflation experiences.

Results: tales of tails

Among our main results, we find that inflation expectations and the output gap are particularly important for shaping risks around the central projection in the near term.

Chart 2 shows the estimated coefficients from those two variables across five different quantiles (ie different parts of the inflation distribution) reported on the x-axis. They show how the outlook for future inflation one quarter ahead – and the risks around it – respond to changes in each of the variables. If the line for a coefficient is broadly flat and non-zero, it means that changes in the corresponding variable are associated with a shift in the whole distribution. In contrast, if the line is not flat, then changes in the variable contribute to a change in the balance of risks. For example, the variable may have a larger effect on the left or right tail of the distribution than at the mean. These results refer to the predicted conditional inflation distribution one quarter ahead, but the picture over other short-run horizons is very similar.

We find that higher inflation expectations today contribute to an increase in the central forecast for inflation next quarter, but they also shift the balance of risks to the upside, increasing the likelihood of inflation coming out above the central projection. On the other hand, a more negative output gap (ie a greater degree of economic ‘slack’) contributes to a reduction in the central projection for inflation while simultaneously shifting the balance of risks to the downside.

In contrast to these two variables, we find lagged inflation and world export prices have significant effects over the entire the predicted inflation distribution. Higher past inflation or inflationary pressures from the rest of the world contribute to an increase in the central projection for inflation without affecting the overall balance of risks the forecast.

Chart 2: Inflation expectations, the output gap and the balance of risk

Notes: Coefficient estimates across quantiles at the one quarter ahead horizon. Blue line shows point estimates and shaded area is 68% confidence interval. Model is estimated using data from UK, US, euro area and Japan from 1995–2022.

We can also use the model to produce forecasts for possible UK inflation outcomes. Chart 3 shows the estimated distribution of possible inflation outcomes one quarter ahead for each period over 2019–22 from our model. Notably the model estimates a rise in upside inflation risk over the later period of 2020 – the model thus detects upside risks early on that then materialised over 2021.

Chart 3: Model forecasts for UK inflation over Covid

Notes: One quarter ahead probability distributions for year-on-year inflation (%); distributions fitted from quantile-regression output using non-parametric approach.


Our analysis highlights how quantile regression can be used to assess the level and drivers of risks around the inflation outlook. We show that higher inflation expectations matter more for upside risks to inflation, while slack is more relevant for downside risks in the near term. Our model picks up upside inflation risks rising steadily over the course of 2020 before eventually materialising in 2021. Thus, this framework is particularly well suited for calibration of fan charts produced by central banks and policy institutions.

Nikoleta Anesti works in the Bank’s Current Economic Conditions Division, Marco Garofalo and Julian Reynolds work in the Bank’s Global Analysis Division, Simon Lloyd works in the Banks Monetary Policy Outlook Division and Edward Manuel works in the Bank’s Structural Economics Division.

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