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Long‐run predictability tests are even worse than you thought

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  • Erik Hjalmarsson
  • Tamas Kiss

Abstract

We derive asymptotic results for the long‐horizon ordinary least squares (OLS) estimator and corresponding t$$ t $$‐statistic for stationary autoregressive predictors. The t$$ t $$‐statistic—formed using the correct asymptotic variance—together with standard‐normal critical values result in a correctly‐sized test for exogenous predictors. For endogenous predictors, the test is size distorted regardless of the persistence in the predictor and adjusted critical values are necessary. The endogeneity problem stems from the long‐run estimation and is distinct from the ordinary persistence‐dependent “Stambaugh” bias. The bias for fully stationary predictors appears not to have been previously noted and adds further difficulty to inference in long‐run predictive regressions.

Suggested Citation

  • Erik Hjalmarsson & Tamas Kiss, 2022. "Long‐run predictability tests are even worse than you thought," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(7), pages 1334-1355, November.
  • Handle: RePEc:wly:japmet:v:37:y:2022:i:7:p:1334-1355
    DOI: 10.1002/jae.2930
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    1. Chengwang Liao & Ziwei Mei & Zhentao Shi, 2024. "Nickell Meets Stambaugh: A Tale of Two Biases in Panel Predictive Regressions," Papers 2410.09825, arXiv.org.

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