Moment Matching in the Present Value identity, and a New Model

The constrained Vector Autoregression and the fairly recent state space approach are commonly used in the asset pricing literature to estimate present value models. They are used to model time series dynamics of discount rates and expected dividend growth, with the objective of understanding predictability and stock market movements. This paper shows that an ARMA(1,1) structure of price-dividend ratio and realized dividend growth nests an AR(1) speci cation for expected returns and expected dividend growth. A simpler model is proposed which involves estimating realized dividend growth and the price-dividend ratio as an ARMA(1,1), and matching the variance and autocorrelation of the estimated models to those of the present value to estimate parameters. Monte Carlo results show that the state space model has larger standard errors. Expected returns is persistent in both models, unlike expected dividend growth in the ARMA(1,1). A modest application of the model to the predictability literature shows stronger evidence towards dividend growth predictability.