A test for rational bubbles in stock prices

This paper presents two necessary conditions for the absence of rational bubbles on the assumption that the discount rate is stationary. One condition is that real stock prices and real dividends are cointegrated with the time-varying cointegrating vector. The other is that the order of integration of real stock prices is equal to that of real dividends. The first condition is different from that proposed on the assumption of a constant discount rate. In contrast, the second condition is the same as that presented on this assumption. Examining the second condition using Japanese data, we find that Japanese stock prices and dividends satisfy the necessary condition.