A Neural Phillips Curve and a Deep Output Gap

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.