Figures and method
The idea
The dashboard lets you change assumptions about oil prices, wages, exchange rates and other variables, and see how the resulting distribution of euro area inflation responds. The focus is not on a single number but on how the whole conditional distribution of inflation shifts: its centre, its width and the balance of upside and downside risks.
The forecasting model
The method builds on my own work developing a quantile regression forest (QRF) to estimate conditional relationships. It is a forecasting model for headline and core inflation, measured as the year-on-year growth rates of the HICP and of the HICP excluding energy and food. Because it is a tree-based method, the QRF can capture non-linear inflation dynamics, such as pass-through that strengthens when inflation is already high. And because it estimates the full set of quantiles, it delivers density forecasts rather than point forecasts.
The forecasts are direct forecasts 1 to 6 months ahead. On top of the baseline forecasts, a separate conditional QRF, trained on historically realised future paths of the explanatory variables, turns your assumptions into conditional forecast scenarios.
What the figures show
- Out-of-sample density forecasts: the forecast distributions the model would have produced in real time, compared with the inflation outcomes that followed.
- Pending predictive quantiles: the latest forecasts whose outcomes are not yet known.
- TreeSHAP groups: how much each group of variables pushes the forecast above or below the model's baseline, both for the latest forecasts and over the out-of-sample window.
- Scenario simulator: the baseline distribution next to the distribution implied by your assumptions, together with updated feature contributions. Both can be downloaded as a CSV file.
- ECB policy indicator: the policy rates implied by the inflation distributions, as described below.
From inflation scenarios to monetary policy
The dashboard also connects your inflation scenario to monetary policy. As a benchmark, I use a theoretical policy rate given by a Taylor rule based on inflation and an estimated output gap:
\[ i^* = r^* + \pi + 0.5\,(\pi - \pi^*) + 0.5\,y, \qquad \pi^* = 2\%, \]where \(r^*\) is the neutral real interest rate, \(\pi\) is inflation and \(y\) is the output gap.
Instead of feeding a single inflation number into the rule, you can feed in your entire forecast distribution. Each quantile of inflation maps into a policy rate, so the result is a distribution of model-implied ECB rates rather than one number. This distribution is shown side by side with the market-implied ECB path (implied by €STR pricing) and the current ECB deposit facility rate.
The neutral real rate
The ECB publishes its own estimates of the neutral real rate \(r^*\). The most useful source is the box Natural rate estimates for the euro area in the February 2025 ECB Economic Bulletin. The ECB deliberately relies on a suite of models rather than a single preferred estimate. For estimates updated through 2024 Q4, the term-structure and semi-structural models put the real \(r^*\) roughly in the range
\[ \boxed{-0.5\% \;\text{to}\; {+}0.5\%}. \]Including Holston–Laubach–Williams (HLW)-type estimates widens the range to
\[ \boxed{-0.5\% \;\text{to}\; {+}1.0\%}. \]The slider in the dashboard covers this wider range, so you can set the real rate you think is right for the euro area.
The output gap
Regular ECB staff projections do not include a published quarterly output gap series. For the output gap, I therefore use the latest euro area estimate from the European Commission's AMECO database.