Unbalanced Regressions and the Predictive Equation

Daniela Osterrieder, Daniel Ventosa-Santaulària, J. Eduardo Vera-Valdés

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Abstract

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.
Original languageEnglish
Place of publicationAarhus
PublisherInstitut for Økonomi, Aarhus Universitet
Number of pages56
Publication statusPublished - 4 Feb 2015
SeriesCREATES Research Paper
Number2015-09

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