This paper analyzes the different dynamic features displayed by alternative RE equilibria in the context of the present value for stock prices with feedback. It is shown that there exists a unique (bubble-free) RE equilibrium implying cointegration between stock prices and dividends and this unique equilibrium is characterized either by the fundamental or, alternatively, by the backward solution depending on the size of the feedback parameter. Based on this result, it is illustrated a mechanism of switching equilibria caused by small changes in the dividend process parameters. Using historical US data and structural estimation, the hypothesis of feedback from stock prices to dividends is tested. We test for the presence of switching equilibria. The empirical results provide evidence of a significant feedback from stock prices to dividends. When analyzing different sub-samples we find evidence supporting the hypothesis of switching equilibria.