  Many problems plague the estimation of Phillips curves. Among them is the
hurdle that the two key components, inflation expectations and the output gap,
are both unobserved. Traditional remedies include creating reasonable proxies
for the notable absentees or extracting them via some form of assumptions-heavy
filtering procedure. I propose an alternative route: a Hemisphere Neural
Network (HNN) whose peculiar architecture yields a final layer where components
can be interpreted as latent states within a Neural Phillips Curve. 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, computations are fast. Third, forecasts are economically
interpretable. Fourth, inflation volatility can also be predicted by merely
adding a hemisphere to the model. Among other findings, the contribution of
real activity to inflation appears severely underestimated in traditional
econometric specifications. Also, HNN captures out-of-sample the 2021 upswing
in inflation and attributes it first to an abrupt and sizable disanchoring of
the expectations component, followed by a wildly positive gap starting from
late 2020. HNN's gap unique path comes from dispensing with unemployment and
GDP in favor of an amalgam of nonlinearly processed alternative tightness
indicators -- some of which are skyrocketing as of early 2022.
