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Price dividend ratio and long-run stock returns: a score driven state space model

Author

Listed:
  • Delle Monache, Davide

    (Bank of Italy)

  • Petrella, Ivan

    (Univeristy of Warwick)

  • Venditti, Fabrizio

    (European Central Bank)

Abstract

In this paper we develop a general framework to analyse 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 US 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.

Suggested Citation

  • Delle Monache, Davide & Petrella, Ivan & Venditti, Fabrizio, 2020. "Price dividend ratio and long-run stock returns: a score driven state space model," Temi di discussione (Economic working papers) 1296, Bank of Italy, Economic Research and International Relations Area.
    • Handle: RePEc:bdi:wptemi:td_1296_20
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    Cited by:

    1. 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).
    2. 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.
    3. 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.
    4. Pál, Tibor & Storti, Giuseppe, 2025. "Estimating the R-Star in the US: A Score-Driven State-Space Model with Time-Varying Volatility Persistence," MPRA Paper 125338, University Library of Munich, Germany.
    5. Frederik Krabbe, 2024. "Asymptotic Properties of the Maximum Likelihood Estimator for Markov-switching Observation-driven Models," Papers 2412.19555, arXiv.org, revised Dec 2025.
    6. repec:cam:camjip:2515 is not listed on IDEAS
    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).
    8. Gaudio, Francesco Saverio, 2025. "Stock market participation and macro-financial trends," Journal of Monetary Economics, Elsevier, vol. 156(C).

    More about this item

    Keywords

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    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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