Diverse Beliefs

Abstract

This paper presents a general framework for studying diverse beliefs in dynamic economies. Within this general framework, the characterization of a central-planner general equilbrium turns out to be very easy to derive, and leads to a range of interesting applications. We show how for an economy with log investors holding diverse beliefs, rational overconfidence is to be expected; volume-of-trade effects are effectively modelled; the Keynesian 'beauty contest' can be modelled and analysed; and bubbles and crashes arise naturally. We remark that models where agents receive private information can formally be considered as models of diverse beliefs. * Wilberforce Road, Cambridge CB3 0WB, UK (phone = +44 1223 337969 , email = A.A.Brown@statslab.cam.ac.uk) † Wilberforce Road, Cambridge CB3 0WB, UK (phone = +44 1223 766806, email = L.C.G.Rogers@statslab.cam.ac.uk) We thank seminar participants at the Cambridge-Wharton meeting, June 2009, particularly our discussant, Frank Diebold.

A Note on Heterogeneous Beliefs with CRRA Utilities

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This note will extend the research presented in Brown & Rogers (2009) to the case of CRRA agents. We consider the model outlined in that paper in which agents had diverse beliefs about the dividends produced by a risky asset.

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“…Remarks If all the agents have the same discount factor and the agents have logarithmic utility, then Brown & Rogers (2009) showed that the price-dividend ratio was simply ρ −1 1 . In particular, this implied that the volatility of the stock was the same as the volatility of the dividend process.…”

Heterogeneous Beliefs with Partial Observations

“…We will now describe our model in detail. As in Brown & Rogers (2009a), we assume that there is unit supply of a single risky asset. This asset produces a dividend continuously in time.…”

“…They each have CARA utility. We can use the optimisation problem to characterise the equilibrium as in Brown & Rogers (2009a). Using market clearing we may then determine the state price density.…”

“…There is a large literature on heterogeneous beliefs, which has been discussed in detail in Brown & Rogers (2009a). Work includes Kurz (2008b), Kurz (1994), Kurz (1997), Kurz & Motolese (2006), Kurz (2008a), Kurz et al (2005), Fan (2006), Harrison & Kreps (1978), Morris (1996), Wu & Guo (2003), Wu & Guo (2004), Harris & Raviv (1993), Kandel & Pearson (1995), Buraschi & Jiltsov (2006), Jouini & Napp (2007).…”