Deep-π*: A Neural Network Estimate of Trend Inflation (European Central Bank)

Summary

• Deep-π* models trend inflation by mapping 122 macroeconomic indicators through neural networks into trend innovations, eliminating latent random-walk shocks and enabling exact Shapley attribution.p.3
• Across 1970 to 2025 US data, trend estimates peaked at about 13% in 1979–80, averaged about 3% during the Great Moderation, and rose to between 6.7% and 7.5% after the pandemic.p.3
• The forward-looking trend peaked in March 2021, leading the current trend by eight to twelve months and headline CPI inflation by more than a year.p.3
• The labour market drove the rise of the current trend, accounting for 41 to 52% of its increase from January 2019 to its peak.p.4
• Energy and commodity prices contributed at most 0.7 of the 4.9 to 5.6 percentage points by which the trends rose post-pandemic, confirming that trends looked through transitory supply shocks.p.4
• In early 2021, when professional forecasters projected inflation at 2.0% over the next year, the forward-looking trend pointed to close to 4%, before inflation reached 7.3%.p.4

Key insights

1. Deep-π* models trend inflation innovations as deterministic functions of observable macroeconomic fundamentals, enabling explicit economic decomposition via exact group Shapley values.p.2
2. Employment-related variables contributed between 41% and 52% of the rise in the current trend between January 2019 and its peak.p.4
3. Supply shocks in energy and commodities contributed at most 0.7 percentage points to the 4.9 to 5.6 percentage point post-pandemic trend surge.p.4