TY - UNPB

T1 - Unbalanced Regressions and the Predictive Equation

AU - Osterrieder, Daniela

AU - Ventosa-Santaulària, Daniel

AU - Vera-Valdés, J. Eduardo

PY - 2015/2/4

Y1 - 2015/2/4

N2 - Predictive return regressions with persistent regressors are typically plagued by (asymptotically) biased/inconsistent estimates of the slope, non-standard or potentially even spurious statistical inference, and regression unbalancedness. We alleviate the problem of unbalancedness in the theoretical predictive equation by suggesting a data generating process, where returns are generated as linear functions of a lagged latent I(0) risk process. The observed predictor is a function of this latent I(0) process, but it is corrupted by a fractionally integrated noise. Such a process may arise due to aggregation or unexpected level shifts. In this setup, the practitioner estimates a misspecified, unbalanced, and endogenous predictive regression. We show that the OLS estimate of this regression is inconsistent, but standard inference is possible. To obtain a consistent slope estimate, we then suggest an instrumental variable approach and discuss issues of validity and relevance. Applying the procedure to the prediction of daily returns on the S&P 500, our empirical analysis confirms return predictability and a positive risk-return trade-off.

AB - Predictive return regressions with persistent regressors are typically plagued by (asymptotically) biased/inconsistent estimates of the slope, non-standard or potentially even spurious statistical inference, and regression unbalancedness. We alleviate the problem of unbalancedness in the theoretical predictive equation by suggesting a data generating process, where returns are generated as linear functions of a lagged latent I(0) risk process. The observed predictor is a function of this latent I(0) process, but it is corrupted by a fractionally integrated noise. Such a process may arise due to aggregation or unexpected level shifts. In this setup, the practitioner estimates a misspecified, unbalanced, and endogenous predictive regression. We show that the OLS estimate of this regression is inconsistent, but standard inference is possible. To obtain a consistent slope estimate, we then suggest an instrumental variable approach and discuss issues of validity and relevance. Applying the procedure to the prediction of daily returns on the S&P 500, our empirical analysis confirms return predictability and a positive risk-return trade-off.

KW - Predictive regression, persistent predictor, fractional integration, regression unbalancedness, IV estimation

M3 - Working paper

T3 - CREATES Research Paper

BT - Unbalanced Regressions and the Predictive Equation

PB - Institut for Økonomi, Aarhus Universitet

CY - Aarhus

ER -