Abstract
In this paper 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 parameters. 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.
Highlights
A decade after the Great Recession the global economy is mired in an environment of low real interest rates, low growth and high stock valuations
We derive the analytical expressions for a new set of recursions that, running in parallel with the Kalman Filter (KF), update at each point in time both the vector of time-varying parameters (TVP) and the latent states
The likelihood of any Gaussian state space model with TVP is available in closed form and the model can be estimated by maximum likelihood (ML)
Summary
A decade after the Great Recession the global economy is mired in an environment of low real interest rates, low growth and high stock valuations. In this paper we contribute to this debate by developing a general method to analyze state space models where parameters change over time and by applying this method to study the evolving relationship between stock valuations, stock returns and dividend growth. We use the methodology developed in the first part of the paper to revisit the relationship between the price dividend ratio, the return on stocks and dividend growth in present value models. This decline accelerated in the 1960s and in the 1990s, prior to the stock market crashes of the early 1970s and 2000s, and is reflected in an upward trend of long-run price dividend ratio, which so far the literature failed to explain An intuition for this result is sketched by Fama and French (2002) in their seminal paper on the equity risk premium.
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