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

Abstract

In this paper we develop a general framework to analyze state space models with timevarying 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 timevarying 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 longrun 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.

THE WORLD ECONOMY: Global outlook overview

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