The present value model of u.s. stock prices revisited

According to the linear PV model, stock prices are fundamentally determined by the discounted value of their future dividends, which derive their value from future expected earnings (e.g., see Campbell et al., 1997; Cochrane, 2001). Since the work of Campbell and Shiller (1987), empirical studies of the validity of linear PV model of stock prices have been extensively conducted in the cointegration framework. The cointegration between stock prices and dividends has implications for return predictability, cash-flow predictability and the debate on rational bubbles. However, the empirical evidence is far from conclusive (e.g., see Campbell and Shiller, 1987, Diba and Grossman (1988), Froot and Obstfeld (1991), Craine (1993), Lamont (1998), and Balke and Wohar (2002)).

 With respect to non-linearities, recent research has found that the relationship between real stock prices and dividends may best be characterized by using a nonlinear PV model; see, e.g., Gallagher and Taylor (2001), Kanas (2003, 2005), Esteve and Prats (2008, 2010), MacMillan (2009), and MacMillan and Wohar (2010). On the other hand, some researchers have argued that the dividend-stock price relationship exhibits fractional cointegration, resulting from the high persistence of temporary deviations from the long run equilibrium between real stock prices and dividends (see, e.g., Caporale and Gil-Alana, 2004, Cuñado et al., 2005, and Koustas and Serletis, 2005). Finally, some empirical studies have used Markov switching models to detect regime shifts in the dividends process (when the cointegrating vector is subject to Markov regime shifts). These models have found the existence of different phases in stock markets, (see, e.g, Bonomo and Garcia , 1994, Schaller and Van Norden, 1997, Driffill and Sola, 1998, Psaradakis, Sola and Spagnolo, 2004, and Sarno and Valente, 2005).

 In this paper we consider the possibility that a linear cointegrated regression model with multiple structural changes would provide a better empirical description of the Present Value model of U.S. stock prices between 1871-2010. Our methodology is based on instability tests recently proposed in Kejriwal and Perron (2008, 2010) as well as the cointegration tests developed in Arai and Kurozumi (2007) and Kejriwal (2008). The results obtained are consistent with the existence of linear cointegration between the log stock prices and the log dividends. However, our empirical results also show that the cointegrating relationship has changed over time. In particular, the Kejriwal-Perron tests for testing multiple structural breaks in cointegrated regression models suggest a model of three or two regimes.