Campbell and Shiller (1987) examine the validity of present value models in rational expectations theory using cointegration techniques. They address two key issues: nonstationarity in time series and incomplete information on market participants. Using U.S. data, they find encouraging results for the term structure model but puzzling results for stock price models. Present value models are simple dynamic stochastic models where the value of a variable is a linear function of the discounted expected future values of another variable. The paper develops a test for present value relations that is valid when variables are stationary in first differences. They use a large information set, including current and lagged values of both variables, to test the model. They also explore the implications of predictable returns and rational bubbles. The paper applies these methods to bond and stock markets, finding that the spread between long and short rates is stationary, and that the present value model holds in the term structure. However, in the stock market, the evidence for cointegration is weaker. The paper concludes that the present value model is supported in the term structure but not in the stock market, highlighting the importance of testing for stationarity and the role of cointegration in evaluating economic models.Campbell and Shiller (1987) examine the validity of present value models in rational expectations theory using cointegration techniques. They address two key issues: nonstationarity in time series and incomplete information on market participants. Using U.S. data, they find encouraging results for the term structure model but puzzling results for stock price models. Present value models are simple dynamic stochastic models where the value of a variable is a linear function of the discounted expected future values of another variable. The paper develops a test for present value relations that is valid when variables are stationary in first differences. They use a large information set, including current and lagged values of both variables, to test the model. They also explore the implications of predictable returns and rational bubbles. The paper applies these methods to bond and stock markets, finding that the spread between long and short rates is stationary, and that the present value model holds in the term structure. However, in the stock market, the evidence for cointegration is weaker. The paper concludes that the present value model is supported in the term structure but not in the stock market, highlighting the importance of testing for stationarity and the role of cointegration in evaluating economic models.