Time-series properties of the dividend–price ratio with social dynamics

Abstract

We model an exchange economy where a finite number of standard identical agents interact locally and analyse the time-series properties of the simulated dividend–price ratio dp _t . Our results document that a sufficient degree of social dynamics induces high persistence in dp _t which leads to the failure to reject the null of a unit root, as well as the failure to reject the null that dividends and prices are not cointegrated. At the same time, we find that returns are not significantly autocorrelated, thus, being consistent with weak-form market efficiency. Finally, we document that although dp _t is highly persistent, econometric tests may still find predictability of future returns by current dividend–price ratios.

Keywords:

• return predictability
• predictive regressions
• social dynamics
• hidden Markov chain
• agent-based models

JEL Classification:

• G17
• G12
• D80
• E37

Notes

¹ Nonstationarity would imply counterfactual explosive dividend and price levels.

² See, e.g. Favero et al. (2010) or Esteve and Prats (2010) for more recent evidence.

³ Persistence in valuation ratios can be traced back to the persistence in the stochastic discount factor.

⁴ See e.g. Cochrane (2001).

⁵ For the definition and discussion, see Campbell and Cochrane (1999, p. 209).

⁶ Thus, the dividend process can be characterized as a Markov switching process (hidden markov chain) with an underlying binomial state variable. Such a specification has been advanced by Hamilton (1989) to characterize the business cycle.

⁷ See e.g. Jackson (2008) for the concepts of networks.

⁸ We define the collective state of the neighbourhood as the equally weighted average of the states of the agents in the neighbourhood, i.e. .

⁹ See Hule and Lawrenz (2011) for a more comprehensive discussion of the model.

¹⁰ See e.g. Cecchetti et al. (1990), Goyal and Welch (2003) and Mehra and Prescott (2003).

¹¹ Cointegration analysis has a long tradition in studying e.g. the purchasing power parity (see, e.g. Taylor, 1988; Masih and Masih, 2004; Haug and Basher, 2011), but has also been applied to price and dividend time series as in Timmermann (1995) and Han (1996).

¹² The left panel reports the p-value for the Johansen trace statistic. We obtain exactly similar results by plotting the p-values for the maximum-eigenvalue statistic.

¹³ See also Masih et al. (2010) for a recent contribution that applies a Bayesian approach and Chen and Zhang (2007), who consider structural breaks in predictive regressions.

¹⁴ For a more comprehensive analysis of the evidence of predictability in an exchange economy with social dynamics, see Hule and Lawrenz (2011).