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Ivan Petrella

3 February 2020
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.
JEL Code
C22 : Mathematical and Quantitative Methods→Single Equation Models, Single Variables→Time-Series Models, Dynamic Quantile Regressions, Dynamic Treatment Effect Models &bull Diffusion Processes
C32 : Mathematical and Quantitative Methods→Multiple or Simultaneous Equation Models, Multiple Variables→Time-Series Models, Dynamic Quantile Regressions, Dynamic Treatment Effect Models, Diffusion Processes
C51 : Mathematical and Quantitative Methods→Econometric Modeling→Model Construction and Estimation
C53 : Mathematical and Quantitative Methods→Econometric Modeling→Forecasting and Prediction Methods, Simulation Methods
E31 : Macroeconomics and Monetary Economics→Prices, Business Fluctuations, and Cycles→Price Level, Inflation, Deflation