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Price Dividend Ratio and Long-Run Stock Returns: A Score-Driven State Space Model

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  • Davide Delle Monache
  • Ivan Petrella
  • Fabrizio Venditti

Abstract

Abstract–In this article, we develop a general framework to analyze state space models with time-varying system matrices, where time variation is driven by the score of the conditional likelihood. We derive a new filter that allows for the simultaneous estimation of the state vector and of the time-varying matrices. We use this method to study the time-varying relationship between the price dividend ratio, expected stock returns and expected dividend growth in the United States since 1880. We find a significant increase in the long-run equilibrium value of the price dividend ratio over time, associated with a fall in the long-run expected rate of return on stocks. The latter can be attributed mainly to a decrease in the natural rate of interest, as the long-run risk premium has only slightly fallen.

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  • Davide Delle Monache & Ivan Petrella & Fabrizio Venditti, 2021. "Price Dividend Ratio and Long-Run Stock Returns: A Score-Driven State Space Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(4), pages 1054-1065, October.
    • Handle: RePEc:taf:jnlbes:v:39:y:2021:i:4:p:1054-1065
    DOI: 10.1080/07350015.2020.1763805
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    Cited by:

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    2. Frederik Krabbe, 2024. "Asymptotic Properties of the Maximum Likelihood Estimator for Markov-switching Observation-driven Models," Papers 2412.19555, arXiv.org, revised Jul 2025.
    3. Zheng, Tingguo & Ye, Shiqi & Hong, Yongmiao, 2023. "Fast estimation of a large TVP-VAR model with score-driven volatilities," Journal of Economic Dynamics and Control, Elsevier, vol. 157(C).
    4. Kirilenko, A. & Kraus, W. & Linton, O. B. & Xiao, M., 2025. "ETF (Mis)pricing," Cambridge Working Papers in Economics 2537, Faculty of Economics, University of Cambridge.
    5. Eric A. Beutner & Yicong Lin & Andre Lucas, 2023. "Consistency, distributional convergence, and optimality of score-driven filters," Tinbergen Institute Discussion Papers 23-051/III, Tinbergen Institute.
    6. Kirilenko, A. & Kraus, W. & Linton, O. B. & Xiao, M., 2025. "ETF (Mis)pricing," Janeway Institute Working Papers 2515, Faculty of Economics, University of Cambridge.
    7. Caravello, Tomás E. & Driffill, John & Kenc, Turalay & Sola, Martin, 2024. "On the sources of the aggregate risk premium: Risk aversion, bubbles or regime-switching?," Journal of Economic Dynamics and Control, Elsevier, vol. 166(C).

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    More about this item

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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