This paper measures risk using proxies based on a GARCH-M model or an instrumental variables method. Using US data, it finds that the lagged dividend yield id correlated with the conditional variance of returns. Once a GARCH-based proxy for the conditional variance of excess returns is included as a regressor, the lagged dividend yield provides no additional explanatory power for excess returns.
Note though that the lagged nominal interest rate helps predict excess returns even after we include alternative measures of the conditional variance.
The paper also presents Monte Carlo evidence on the relative performance of alternative estimators of the conditional variance, and concludes that the use of lagged squared returns is highly inadvisable, and that the instrumental variables method can be extremely inefficient.
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