Unbalanced Regressions and the Predictive Equation

56 Pages Posted: 4 Feb 2015

Date Written: January 29, 2015

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.

Keywords: Predictive regression, persistent predictor, fractional integration, regression unbalancedness, IV estimation

JEL Classification: G17, C22, C26, C58

Suggested Citation

Osterrieder, Daniela and Ventosa-Santaulària, Daniel and Vera-Valdes, J. Eduardo, Unbalanced Regressions and the Predictive Equation (January 29, 2015). Available at SSRN: https://ssrn.com/abstract=2560023 or http://dx.doi.org/10.2139/ssrn.2560023

Daniela Osterrieder (Contact Author)

Rutgers Business School ( email )

Janice H. Levin Bldg., Room 121
94 Rockafeller Road
Piscataway, NJ 08854-8054
United States

CREATES ( email )

Aarhus University
Fuglesangs Alle 4
DK-8210 Aarhus C
Denmark

Daniel Ventosa-Santaulària

CIDE ( email )

Carr. México-Toluca 3655
col. Lomas de Santa Fe
Mexico, D.F. 01210
Mexico
+52 55 57279800 x2723 (Phone)

HOME PAGE: http://www.ventosa-santaularia.com

J. Eduardo Vera-Valdes

CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

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