This paper by Campbell and Shiller explores the application of cointegration theory to present value models, addressing issues of nonstationarity and incomplete data. They develop a test for the present value relation that is valid when variables are stationary in first differences. The authors use U.S. data to test the rational expectations theory of the term structure and the present value model of stock prices, finding encouraging results for the former but puzzling results for the latter. They introduce the concept of cointegration, which allows for stationary linear combinations of nonstationary variables, and discuss its implications for testing present value models. The paper includes detailed empirical results for both bond and stock markets, showing that short-term and long-term interest rates are cointegrated, while there is weaker evidence of cointegration between stock prices and dividends. The authors also present volatility tests to assess the importance of predictable excess returns. Overall, the study provides insights into the validity of present value models and the role of rational expectations in economic dynamics.This paper by Campbell and Shiller explores the application of cointegration theory to present value models, addressing issues of nonstationarity and incomplete data. They develop a test for the present value relation that is valid when variables are stationary in first differences. The authors use U.S. data to test the rational expectations theory of the term structure and the present value model of stock prices, finding encouraging results for the former but puzzling results for the latter. They introduce the concept of cointegration, which allows for stationary linear combinations of nonstationary variables, and discuss its implications for testing present value models. The paper includes detailed empirical results for both bond and stock markets, showing that short-term and long-term interest rates are cointegrated, while there is weaker evidence of cointegration between stock prices and dividends. The authors also present volatility tests to assess the importance of predictable excess returns. Overall, the study provides insights into the validity of present value models and the role of rational expectations in economic dynamics.