A Verifiable Estimation and Parametric Inference of the Nonlinear Phillips Curve Using Neural Networks

Methodologies such as situational importance and Shapley Additive explanations (SHAP) are increasingly used to explain machine learning (black-box) models predictions. Based on parametric inference, we develop a methodological framework that uses Shapley values to generalize the data-generating process learned by neural networks. By using Shapley-input relations, we theorize the Shapley-polynomial equation as a parametric function directly interpretable with a comparable predictive ability to the parent model. A Monte-Carlo analysis is implemented and shows how well our methodology can unveil nonlinearities in the data without having an apriori knowledge. Finally, we develop an empirical application where artificial neural network (ANN) and long-short-term memory (LSTM) models are trained on US macroeconomic data (1960Q1 to 2007Q4) to predict inflation levels and make inferences on the data-generating process. We find meaningful polynomial relations between the variables, which hold for our test period from 2008Q1 to 2022Q2. In particular, we find that unemployment is nonlinearly related to future inflation levels. The relation is negative and becomes positive when unemployment reaches a certain level. The tool we offer can give policymakers information on the potential relations between the evolution of future price levels and economic activity