The paper tests expectations theories for stock prices and interest rates by estimating a vector autoregressive moving average model. The existence of moving average components does not force the econometrician to take a position about the type of non-stationarity (trend-stationarity or difference stationarity in the terminology of Nelson and Plosser (1982)) driving the series, and allows the model both to capture mean reversion in fundamentals and to test whether this is correctly incorporated in asset prices. From a VARMA (1,1) it is found that the restrictions imposed by present value models are strongly rejected for stock prices is strongly rejected for stocks, but hold quite well for bonds. A VARMA (1,2) for stock prices is strongly rejected. On the basis of an estimated impulse response function it is shown that stock prices underreact to innovations to dividends but correctly incorporate news about real interest rates, whereas long-term interest rates react in the right way to news about changes in nominal short-term interest rates. The fact that rejections are stronger in econometric models which allow dividends to be trend-stationary (rather than simply difference-stationary as in previous empirical work) suggests that one possible reason for excess volatility of stock prices lies in markets misinterpreting the type of non-stationarity (TS versus DS) driving dividends.
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