تعادل سوئیچینگ: مدل ارزش فعلی برای بازبینی قیمت سهام

This paper analyzes the dynamic features displayed by alternative rational expectations equilibria in the context of the present value model for stock prices with feedback. In particular, it shows that there exists a unique equilibrium implying cointegration and that equilibrium is characterized by either the fundamental or, alternatively, the backward solution depending on the size of the feedback parameter. It is shown analytically that the existence of switching equilibria induces large stock market swings. Using US data and structural estimation, the hypotheses of feedback and switching equilibria are tested. The empirical results provide evidence of both switching equilibria and feedback.

The present value (PV) model of stock prices assuming rational expectations (RE) was extensively tested during the 1980s (Campbell and Shiller, 1987; Chow, 1989; West, 1988, among others). Many of these studies find US stock prices to be more volatile than implied by the PV model. These studies share two common assumptions. First, they assume a unique RE equilibrium for stock prices. Second, they consider that the dividend process has remained unchanged over the whole sample period. The relaxation of either of these assumptions provides a potentially good approach to explaining the excess volatility found in the literature.1 Following the first approach, Froot and Obstfeld (1991) propose the first parsimonious PV model of stock prices that has found empirical support. They characterize stock prices using a rational intrinsic bubble which depends exclusively on dividends. Recently, Ackert and Hunter (1999) have shown that Froot and Obstfeld's model is observationally equivalent to a PV model of stock prices that in addition explicitly includes control over dividends by managers. Also following the first approach, Timmermann (1994) shows that the existence of feedback in a PV model generates multiple (bubble-free) RE solutions. Moreover, Timmermann provides evidence that stock prices appear to Granger-cause dividends, which he interprets as evidence of feedback from stock prices to dividends. 2 Furthermore, he suggests that the excess volatility observed in stock prices may be explained by switches among the set of RE equilibria. However, Timmermann neither explains what effects the switching between RE equilibria may induce nor empirically studies the existence of switching equilibria. The second approach is followed by Driffill and Sola (1998) and Evans (1998). Using the PV model of stock prices, the two articles provide evidence that a regime-switching model describing the evolution of dividends accounts for much of the variation of US stock prices. However, neither of them considers the effects of switching equilibria. This paper builds upon these two approaches. We analyze a simpler version of Timmermann's (1994) model in order to fully characterize how changes in the dividend process alter the dynamic features displayed by the alternative (bubble-free) RE equilibria. We first show that the presence of the feedback mechanism produces three alternative RE equilibria. Secondly, it is shown that there exists a unique (bubble-free) RE equilibrium implying cointegration between stock prices and dividends. This equilibrium is characterized by a different equilibrium solution depending on the dividend process parameters. Finally, this paper illustrates that the existence of switching equilibria induces large changes in the variance of the spread (i.e., the stationary linear combination between stock prices and dividends as defined by Campbell and Shiller, 1987) and large changes in the response of stock price variation to the spread. These results imply that large stock market swings are feasible, even with a constant discount factor, when switching equilibria occur. We assume cointegration between stock prices and dividends in the empirical analysis. We believe it is the relevant case based on the empirical evidence reported by Campbell and Shiller (1987). Moreover, the error-correction structure implied by the PV model for stock prices under cointegration suggests that the model can be estimated in two steps. Thus, we first estimate the error-correction representation of the cointegrated system in order to summarize the dynamic features exhibited by stock prices and dividends. Second, we apply the simulated moments estimator (SME) suggested by Lee and Ingram (1991) to estimate the parameters of the stock prices model using annual data for the US. We estimate the model for the full sample and the resulting sub-samples detected by Driffill and Sola (1998) using the same data set. The empirical results show a good fit of the PV model for the sub-samples 1910–1955 and 1955–1975. They also provide evidence supporting the hypothesis of switching equilibria that explains the different stock price–dividend relationship observed in the sub-samples 1910–1955 and 1955–1975. Furthermore, we find evidence of a small but very significant presence of feedback from stock prices to dividends in each sub-sample considered. The rest of the paper is organized as follows. Section 2 introduces the PV model for stock prices and obtains the alternative RE solutions. Section 3 characterizes the dynamic properties displayed by the alternative RE equilibria in the space of the parameters describing the dividend process. Section 4 shows that switches between alternative RE equilibria lead to regime-switching in the ARMA representation of dividend process. Section 5 describes the estimation procedure and the empirical evidence found. Section 6 concludes.

Many studies have found that US stock prices are more volatile than is implied by the PV model. This paper shows theory and evidence that the observed excess volatility can be attributed in principle to switches between alternative (bubble-free) RE equilibrium solutions of the PV model. On the one hand, this paper shows analytically that exogenous small changes in the dividend process parameters may induce switching equilibria and switching equilibria result in both large changes in the variance of the spread and large changes in the response of stock price variation to the spread. On the other hand, we use historical annual US data and an indirect inference method to estimate the PV model for stock prices under the assumption that stock prices and dividends are cointegrated. Full-sample estimation results show significant evidence of feedback, although all cointegrating RE equilibria are rejected by the data. When analyzing different sub-samples, the empirical results provide evidence supporting the hypothesis of switching equilibria and a good fit of the PV model for the sub-samples 1910–1955 and 1955–1975. Moreover, we find evidence of a small but very significant presence of feedback from stock prices to dividends in each sub-sample considered. This feedback is smaller in those periods in which the volatility of stock price innovations relative to the volatility of dividend innovations is higher. The latter empirical result supports the Muth–Lucas hypothesis which, in this context, postulates that the informational content given to stock prices when deciding on dividends is inversely related to the volatility of stock price innovations relative to the volatility of dividend innovations.