# A Neural Phillips Curve and a Deep Output Gap

arXiv: https://arxiv.org/abs/2202.04146 · HTML: https://mlsanity.com/paper/2202.04146/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 143 references that are in the map.
- First posted on arXiv 8 Feb 2022.

## Builds on (most cited first, 19 of 19)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [Financial Time Series Forecasting with Deep Learning : A Systematic Literature Review: 2005-2019](https://mlsanity.com/paper/1911.13288/) (2019)
- [Double Trouble in Double Descent : Bias and Variance(s) in the Lazy Regime](https://mlsanity.com/paper/2003.01054/) (2020)
- [Early stopping and non-parametric regression: An optimal data-dependent stopping rule](https://mlsanity.com/paper/1306.3574/) (2013)
- [Deep Factors for Forecasting](https://mlsanity.com/paper/1905.12417/) (2019)
- [Can weight sharing outperform random architecture search? An investigation with TuNAS](https://mlsanity.com/paper/2008.06120/) (2020)
- [How is Machine Learning Useful for Macroeconomic Forecasting?](https://mlsanity.com/paper/2008.12477/) (2020)
- [The Macroeconomy as a Random Forest](https://mlsanity.com/paper/2006.12724/) (2020)
- [Macroeconomic Data Transformations Matter](https://mlsanity.com/paper/2008.01714/) (2020)
- [Deep Dynamic Factor Models](https://mlsanity.com/paper/2007.11887/) (2020)
- [Can Machine Learning Catch the COVID-19 Recession?](https://mlsanity.com/paper/2103.01201/) (2021)
- [Simultaneous Mean-Variance Regression](https://mlsanity.com/paper/1804.01631/) (2018)

## Built on by (most cited first, 5 of 5)

- [Maximally Machine-Learnable Portfolios](https://mlsanity.com/paper/2306.05568/) (2023)
- [From Reactive to Proactive Volatility Modeling with Hemisphere Neural Networks](https://mlsanity.com/paper/2311.16333/) (2023)
- [Maximally Forward-Looking Core Inflation](https://mlsanity.com/paper/2404.05209/) (2024)
- [Ordinary Least Squares as an Attention Mechanism](https://mlsanity.com/paper/2504.09663/) (2025)
- [Quantifying the Risk-Return Tradeoff in Forecasting](https://mlsanity.com/paper/2605.09712/) (2026)

## Abstract (arXiv)

Many problems plague empirical Phillips curves (PCs). Among them is the hurdle that the two key components, inflation expectations and the output gap, are both unobserved. Traditional remedies include proxying for the absentees or extracting them via assumptions-heavy filtering procedures. I propose an alternative route: a Hemisphere Neural Network (HNN) whose architecture yields a final layer where components can be interpreted as latent states within a Neural PC. There are benefits. First, HNN conducts the supervised estimation of nonlinearities that arise when translating a high-dimensional set of observed regressors into latent states. Second, forecasts are economically interpretable. Among other findings, the contribution of real activity to inflation appears understated in traditional PCs. In contrast, HNN captures the 2021 upswing in inflation and attributes it to a large positive output gap starting from late 2020. The unique path of HNN's gap comes from dispensing with unemployment and GDP in favor of an amalgam of nonlinearly processed alternative tightness indicators.