We develop a present-value model where the fundamental and
non-fundamental components switch between distinct regimes.
The non-fundamental component is specified as a periodically collapsing bubble of Balke and Wohar [Balke, N. S., & Wohar, M. E.
(2009). Market fundamentals versus rational bubbles in stock prices:
A Bayesian perspective. Journal of Applied Econometrics, 24(1),
35–75. https://doi.org/10.1002/jae.1025]. The fundamental component is constructed as in van Binsbergen and Koijen [van Binsbergen, J. H., & Koijen, R. S. J. (2010). Predictive regressions: A
present-value approach. The Journal of Finance, 65(4), 1439–1471.
https://doi.org/10.1111/j.1540-6261.2010.01575.x], by treating the
expectations of market fundamentals as latent variables. Unlike existing methods, e.g. [Zhu, X. (2015). Tug-of-war: Time-varying predictability of stock returns and dividend growth. Review of Finance,
19(6), 2317–2358. https://doi.org/10.1093/rof/rfu047; Choi, K. H.,
Kim, C., & Park, C. (2017). Regime shifts in price-dividend ratios and
expected stock returns: A present-value approach. Journal of Money,
Credit and Banking, 49(2–3), 417–441. https://doi.org/10.1111/jmcb.
12384; Chan, J. C., & Santi, C. (2021). Speculative bubbles in presentvalue models: A Bayesian Markov-switching state space approach.
Journal of Economic Dynamics and Control, 127, 1–26], ours requires
no unnecessary approximations, accommodates flexible forms of
regime-switching, and the resulting present-value formula is internally consistent.