We use deep neural networks to estimate time-varying equity risk premia. The key innovations are the nonlinear and non-parametric generalisation of Fama-Macbeth regressions through partial derivatives of an arbitrary estimator function with respect to its input and the introduction of Jacobian...

We study the problem of detecting structural instability of factor strength in asset pricing models for financial returns. We allow for strong and weaker factors, in which the sum of squared betas grows at a rate equal to and slower than the number of test assets, respectively: this growth rate...