Extensions to IVX methods of inference for return predictability

Predictive regression methods are widely used to examine the predictability of (excess) returns on stocks and other equities by lagged macroeconomic and financial variables. Extended IV [IVX] estimation and inference has proved a particularly valuable tool in this endeavour as it allows for possibly strongly persistent and endogenous regressors. This paper makes three distinct contributions to the literature. First we demonstrate that, provided either a suitable bootstrap implementation is employed or heteroskedasticity-consistent standard errors are used, the IVX-based predictability tests of Kostakis et al. (2015) retain asymptotically pivotal inference, regardless of the degree of persistence or endogeneity of the (putative) predictor, under considerably weaker assumptions on the innovations than are required by Kostakis et al. (2015) in their analysis. In particular, we allow for quite general forms of conditional and unconditional heteroskedasticity in the innovations, neither of which are tied to a parametric model. Second, and associatedly, we develop asymptotically valid bootstrap implementations of the IVX tests under these conditions. Monte Carlo simulations show that the bootstrap methods we propose can deliver considerably more accurate finite sample inference than the asymptotic implementation of these tests used in Kostakis et al. (2015) under certain problematic parameter constellations, most notably for their implementation against one-sided alternatives, and where multiple predictors are included. Third, under the same conditions as we consider for the full-sample tests, we show how sub-sample implementations of the IVX approach, coupled with a suitable bootstrap, can be used to develop asymptotically valid one-sided and two-sided tests for the presence of temporary windows of predictability.