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

Understanding and quantifying the risks to the economic outlook is essential for effective monetary policy. In this post, we describe an “inflation at risk” model, which helps us assess the uncertainty and balance of risks around the UK inflation outlook, and understand how this uncertainty relates to underlying economic conditions. Using this data-driven approach, we find that higher inflation expectations are particularly important in driving upside risks to inflation, while stronger economic capacity 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 Middle and Beyond: A Fan Chart History

The Bank of England pioneered the approach of including information about the uncertainty and risks around its forecast with its inflation’fan chart‘ – first published in February 1996 (Graph 1). It remains a quarterly staple. Monetary Policy Report (MPR) to this day. The ‘fan’ sets out the MPC’s assessment of the inflation outlook 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. Lighter bands reflect less likely, but still possible outcomes. The chart is constructed so that inflation is expected to be somewhere within the full width of the fan 90 out of 100 times.

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

Changes in the size and shape of the fan reflect changes in the MPC’s views on the level of uncertainty and the balance of risks. A symmetrical fanning up and down implies a higher degree of overall uncertainty about the outlook. Alternatively, a unilateral widening in the fan above or below the dark red central stage 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 could result higher than expected.

The MPC uses a variety of statistical tools and criteria to construct its fan chart. There are a number of challenges involved in any forecasting exercise, and these challenges become even starker when it comes to building risk estimates around the central projection. The problem is that standard statistical tools (for example, linear regression) are designed to produce forecasts for what is expected, i.e. mean, path of macroeconomic variables. They generally do not provide a direct estimate of the uncertainty around these paths. While a measure of uncertainty can be constructed by examining the historical forecast errors of these types of models, this does not help to understand which variables drive uncertainty, nor can it capture changes in uncertainty over time driven by economic conditions. changing.

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

A new approach to quantifying risks: inflation at risk

To do so, we borrow an approach from recent work on academic and policy circles intended to monitor risks to financial stability: ‘GDP-at-Risk’. As other central banks who have taken similar approaches, we trust quantile regression, a statistical tool that allows us to estimate the relationship between a range of indicators and the entire distribution of possible inflation outcomes. Through this, we determine which variables are particularly important, not only in explaining changes in the expected path for inflation, but also in shaping the overall level of risk around that path. We also use a local-projection which allows us to estimate the level of risk through different forecast horizons.

We include several macroeconomic indicators that are typically considered important in driving inflation dynamics, specifically: lagged inflation, inflation expectations (for a mix of households and businesses), the estimated output gap, and world export prices. Our choice of variables reflects those that appear in a Open economy Philips curve. The quantile regression model allows us to investigate how changes in each of these variables affect the overall distribution of possible inflation outcomes over a range of forecast horizons. To estimate our model, we draw on data from several advanced economies (US, UK, euro area, and Japan) with a variety of historical inflation experiences.

Results: tails tales

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

Chart 2 shows the estimated coefficients of these two variables at 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 that surround it— respond to changes in each of the variables. If the line for a coefficient is flat and nonzero, it means that changes in the corresponding variable are associated with a change in the entire distribution. Conversely, if the line is not flat, changes in the variable contribute to a change in the balance of risks. For example, the variable may have a greater effect on the left or right tail of the distribution than on the mean. These results refer to the forecast conditional inflation distribution a quarter aheadbut the panorama in other short-term horizons is very similar.

We find that higher inflation expectations today contribute to an increase in the central inflation forecast for the next quarter, but also shift the balance of risks to the upside, increasing the probability that inflation will exceed 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 inflation forecast while shifting the balance of risks to the downside.

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

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

Notes: Estimates of coefficients between quantiles in the horizon of one quarter ahead. The blue line shows point estimates and the shaded area is a 68% confidence interval. The model is estimated using data from the UK, the US, the euro area and Japan from 1995 to 2022.

We can also use the model to produce forecasts of possible inflation outcomes in the UK. Graph 3 shows the estimated distribution of possible inflation outcomes. a quarter ahead for each period between 2019 and 2022 of our model. In particular, the model estimates an increase in the risk of upward inflation during the last period of 2020; therefore, the model detects upside risks early on that later materialized during 2021.

Chart 3: Model Forecasts for UK Inflation on Covid

Notes: One-quarter probability distributions of year-on-year inflation (%); Fitted distributions from the quantile regression output using a nonparametric 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 are more important for upside inflation risks, while slack is more relevant for short-term downside risks. Our model detects upward inflation risks that steadily increase throughout 2020 before finally materializing in 2021. Therefore, this framework is particularly well-suited for calibrating 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 Global Analysis Division of the Bank, Simon Lloyd works at the banks Monetary Policy Outlook Division and Edward Manuel works in the Bank’s Structural Economics Division.

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