The time-varying GARCH-in-mean model

•Estimation of the stochastic time-varying risk premium parameter within the TVGARCH-in-mean models.•The proposed kernel-based iterative estimator attains good finite sample performance.•The risk premium parameter is found to be time-varying and highly persistent.

I propose an estimation strategy for the stochastic time-varying risk premium parameter in the context of a time-varying GARCH-in-mean (TVGARCH-in-mean) model. A Monte Carlo study shows that the proposed algorithm has good finite sample properties. Using monthly excess returns on the CRSP index, I document that the risk premium parameter is indeed time-varying and shows high degree of persistence.