Regime specific predictability in predictive regressions

Predictive regressions are linear specifications linking a noisy variable such as stock returns to past values of a more persistent regressor such as valuation ratios, interest rates etc with the aim of assessing the presence or absence of predictability. Key complications that arise when conducting such inferences are the potential presence of endogeneity, the poor adequacy of the asymptotic approximations amongst numerous others. In this paper we develop an inference theory for uncovering the presence of predictability in such models when the strength or direction of predictability, if present, may alternate across different economically meaningful episodes. This allows us to uncover economically interesting scenarios whereby the predictive power of some variable may kick in solely during particular regimes or alternate in strength and direction (e.g. recessions versus expansions, periods of high versus low stock market valuation, periods of high versus low term spreads etc). The limiting distributions of our test statistics are free of nuisance parameters and some are readily tabulated in the literature. Finally our empirical application reconsiders the literature on Dividend Yield based stock return predictability and contrary to the existing literature documents a strong presence of predictability that is countercyclical, occurring solely during bad economic times.