Return predictability constitutes a core research topic in empirical finance, conventionally examined via predictive regressions of asset excess returns on highly persistent financial and macroeconomic predictors. Despite the vast literature on return predictability, existing studies largely overlook the inherent bounded nature of standard predictive variables, whose ranges are constrained either by structural construction or institutional policy rules. Moreover, predictability inference is further distorted by time-varying unconditional variances of model innovations. This paper addresses the inferential challenges of predictive regressions by simultaneously accommodating predictor boundedness and unconditional heteroskedasticity, alongside the well-documented features of high predictor persistence and endogeneity. We establish that the asymptotic distributions of the t and Wald predictability tests rely on regulated variance-transformed Brownian motions, which jointly characterize the impacts of predictor boundary constraints and heteroskedastic innovations. To facilitate feasible empirical implementation, we develop residual-based wild bootstrap procedures that consistently approximate the resulting nonstandard null limiting distributions. Extensive Monte Carlo simulations validate the superior finite-sample performance of the proposed framework. In an application to U.S. equity premiums, our approach identifies significant predictive content embedded in the Dow Jones index’s distance-to-52-week-high price and the joint predictor set consisting dividend-price ratio and the T-bill rate, which is undetected by the IVX test.
We develop a Correlation Restriction (CR) test for instrumental-variable validity when the sign of endogeneity is known. Consistent with Gunsilius (), the test demonstrates that additional structural assumptions allow instrument validity to be assessed even in models with continuous endogenous variables. Extending DiTraglia and Garc & iacute;a-Jimeno (), our approach uses the joint correlation structure of the instrument, regressor, and outcome to construct a confidence interval for the partially identified instrument-error correlation via a modified conditional union-bound procedure. Monte Carlo simulations and empirical applications, including analyses of returns to education, recidivism, and development, demonstrate that the CR test detects departures from rho zu=0 once the admissible endogeneity domain is restricted by both sign and magnitude, and characterizes the range of assumed endogeneity magnitudes for which instrument exogeneity remains compatible with the data.
