Boosted inflation – using machine learning to make sense of non-linear determinants of inflation – Bank Underground

Marcus Buckmann, Galina Potjagailo and Philip Schnattinger

Disentangling the sources of high inflation, exceeding inflation targets in the post- pandemic period, has been a priority for monetary policy makers. We use machine learning for this task – a boosted decision tree model that fits non-linear associations between many indicators and inflation. We add economic interpretability by categorising the data into intuitive blocks representing components of the Phillips curve. To further disentangle inflation drivers, we separate the signals that reflect demand and supply by imposing sign-restrictions on the decision trees. Our model tells us that both global supply and domestic demand spurred UK CPI inflation post-pandemic. We detect important non-linearities: in the Phillips curve relationship with labour market tightness and unemployment and via additional effects from short-term inflation expectations.

Machine learning methods offer a non-parametric way to estimate complex non-linearities. Could they also flexibly learn about instabilities in the inflation process, such as those related to a non-linear Phillips curve slope, amplified effects from inflation expectations, global supply-chain pressures, or spillovers across price segments? We argue that the answer is yes – but this requires overcoming the ‘black box’ of machine learning models, since the learnt associations would otherwise be difficult to disentangle and not necessarily backed by economic intuition. To do this, the machine learning literature can draw inspiration from standard time series methods heavily used in policy institutions, such as wage-price equations or vector-autoregressive models that are commonly informed by economically intuitive restrictions for identification of underlying economic drivers, such as the direction or long-term impact with which a shock can affect a set of variables. International evidence based on time series methods has come to mixed conclusions as to the recent mix of demand and supply drivers of inflation; their linear nature of these models might overlook instabilities. 

There are ways machine learning methods can be infused with restrictions that reflect economic assumptions. A neural network with a block-structure has been recently proposed for modelling the US Phillips curve, and employing a version of that model we have shown pronounced spillovers from goods and input prices into UK services inflation. Yet, a block-structure alone might not achieve identification if the link between inflation and activity indicators is determined simultaneously by demand and supply.

Our model

In an upcoming Staff Working Paper, we propose use of a block-wise Boosted Inflation Model (BIM) that disentangles non-linear demand and supply-like determinants of inflation. The ‘boosted trees’ method sequentially trains many decision trees to minimise forecast error. Its predictive accuracy has made this approach one of the most powerful and widely used machine learning tools. We add a block-wise structure that reflects global and domestic demand and supply determinants and an expectations-informed trend. Within each block, the model learns about non-linear associations between a group of indicators and inflation. Across blocks, the associations are conditionally linear. The joint associations between activity indicators and inflation that the model learns are sign-constrained to separate out demand and supply blocks. For example, trees which capture rising inflation and increasing unemployment are only accepted in a supply-side block, while rising inflation and decreasing unemployment can be captured by trees in a demand side block. In the machine learning literature these constraints are called monotonicity constraints, but to our knowledge have so far not been employed to disentangle demand and supply determinants.

In total, we use 53 global and UK-specific monthly indicators and their lagged realisations, to predict one month ahead monthly UK CPI inflation. The tree splits within demand are restricted to reflect a positive association between inflation and a range of economic activity indicators (negative association with labour market slack), whereas trees within supply reflect a negative association of inflation with economic activity and a positive association with indicators of global supply-chain pressures, costs, and energy prices. Further, an inflation trend block reflects a stochastic time trend, informed by measures of one year ahead household inflation expectations and five year ahead financial market inflation expectations, wage growth and services inflation to reflect domestically generated inflation.

Whereas our model also shows a competitive out-of-sample forecast performance at multiple horizons and against various benchmarks, our focus lies in building a machine learning approach to assess inflation determinants and the non-linearities therein for policy analysis. For this, we rely on estimation via repeated 10-fold cross-validation over the full sample period, 1988m2–2024m12.

Determinants of UK inflation

The model gives an intuitive forecast decomposition of UK CPI inflation around the 2% target (Chart 1). Demand contributes cyclically, and the imposed sign constraints help to detect a negative contribution from global and domestic demand during the global financial crisis and a short-lived drag during the Covid pandemic. Supply tends to drag on inflation during periods of falling global energy prices and pushed up after the global financial crisis. Over the recent episode, a combination of demand and supply factors drove up inflation. These contributions peaked in early 2023, whereas recently global demand and supply slightly pulled down on UK inflation.

Chart 1: The model reads the recent rise in UK inflation as a combination of supply and demand determinants, followed by a rise in expectations-determined trend

Notes: Contributions from model blocks to one month ahead model prediction for CPI inflation (black line), around 2% mean. Dashed line: actual CPI inflation. Grey bars: recession episodes.

Sources: Authors’ calculations, Baumeister and Hamilton (2019), Bloomberg Finance L.P., Citi Group, Federal Reserve Bank of New York, Käenzig (2021), OECD, ONS, Tradeweb and World Bank.

The contribution from the expectations-informed trend built up over the inflation peak and unwound only slowly in 2024. Over much of the sample period, this trend was stable and pulling inflation below target because inflation expectations were low and domestic inflationary pressures weak. The recent shift-like rise looks like the one seen during the high inflation episode in the early 1990s. However, this time around the trend contribution has been less strong, and we see little evidence of shifts in long-term expectations, as discussed below. 

The finding that a mix of supply and to a lesser extent demand were the initial drivers of the recent UK inflation surge, followed by a rise in the trend, survives across a range of specifications with alternative block-structures, including assuming block-exogeneity of the global blocks or the trend, respectively.

Various non-linearities have been at play recently

Chart 2 shows the learnt functional forms for key indicators within the blocks, as scatter plots between an indicator’s contribution to predictions (Shapley values) and the indicator’s realisation over time. These allow us to track non-linearities. On the demand side, UK CPI inflation moved into the non-linear region of the Phillips curve, ie the association with the unemployment rate and with labour market tightness (vacancy-to-unemployment ratio), respectively (left panel). This non-linearity accounts for much of the role of demand determinants detected by the model during 2021–22, and the relatively quick unwind of these effects thereafter. This is illustrated in Chart 3 where in alternative specifications we replace the decision-tree based non-linear associations within a given block by linear regressions. The non-linearities in demand help to identify business cycle type fluctuations, such as the falling contribution from demand during the global financial crisis, and they explain much of the recent rise in demand. This is in line with findings for the United States of an L-shaped Phillips curve.

Chart 2: Non-linearities in key indicators learnt by the model

Notes: Contributions (Shapley values) from an indicator t+1 inflation predictions over the sample period, against the realisations of the indicator (at monthly lag three, in the paper we show the effects are robust across lags). Colours indicate months in 2021–24, dark grey: 1989–92, light grey: 1993–2020. Months where indicator has missing values not shown.

Source: See Chart 1.

Within the supply block, the Federal Reserve Bank of New York global supply-chain pressures index had amplified effects over 2021–22 compared to weak contributions prior to the pandemic (Chart 2, middle panel), in line with evidence for the US. Nonetheless, the recent rise in the supply contribution is also captured when linearising this block, so that non-linearities made less of a difference here (Chart 3). Allowing for non-linearities in supply accounts for somewhat more persistent supply fluctuations throughout the sample.

Chart 3: Non-linearities in demand account for much of its recent contribution

Notes: Contributions from model blocks to inflation prediction, across alternative specifications that replace decision-tree based non-linear associations by linear regressions within given blocks (red: global and domestic demand linear; orange: global and domestic supply linear; and blue: trend linear), while keeping other blocks non-linear via decision trees, respectively. Sign restrictions to separate demand from supply are imposed also on the linear regression models.

Source: See Chart 1.

Since 2023, we also see non-linear effects within the trend component, mainly from households’ short-term inflation expectations (Chart 2, right panel). This can reflect that households over-adjust their expectations following price rises of salient goods such as food and that shocks that raise inflation expectations in presence of uncertainty have large effects on inflation. In contrast to the 1990s inflation episode, there is no indication of a regime-like shift in the effects of long-term inflation expectations. In the aftermath of that early episode, the non-linearities learnt by the model help capturing the rapid stabilisation of the trend following the reanchoring of long-term inflation expectations.

Concluding remarks and policy implications

The key strength of the block-wise BIM lies in its ability to infuse machine learning with economic restrictions to inform policymakers on non-linear inflation determinants. While restrictions may impose limits to the flexibility of machine learning, they enhance interpretability if we incorporate reduced-form economic judgement. This gives rise to a wider applicability and relevance of AI-based methods for policy analysis, beyond forecasting alone and to disentangle determinants of inflation.

Applied to UK inflation, the BIM detects non-linear global supply and domestic demand as drivers of the recent episode. The non-linear demand effects suggests that the UK economy moved towards the steep region of the Phillips curve so that the relatively tight labour market spurred inflation by more than a linear model could account for. These non-linearities supported a relatively quick unwound of inflation supply-side effects from global energy and food prices unwound and as the labour market loosened. However, the model also detects non-linear effects from short-term inflation expectations suggesting that second round effects were at play. These effects have mostly unwound by the end of 2024. Nonetheless, as and if further supply-side shocks occur, monitoring the role of non-linearities and any potential repercussions into inflation expectations remains a priority for monetary policy.

Marcus Buckmann works in the Bank’s Advanced Analytics Division, Galina Potjagailo works in the Bank’s Monetary Policy Innovation Lab and Philip Schnattinger works in the Bank’s Structural Economics Division.

If you want to get in touch, please email us at [email protected] or leave a comment below.

Comments will only appear once approved by a moderator, and are only published where a full name is supplied. Bank Underground is a blog for Bank of England staff to share views that challenge – or support – prevailing policy orthodoxies. The views expressed here are those of the authors, and are not necessarily those of the Bank of England, or its policy committees.