Jean-Marc Tallon, Fabrice Collard, Sujoy Mukerji, Kevin Sheppard, Toulouse School of Economics (TSE), École des hautes études en sciences sociales (EHESS)-Institut National de la Recherche Agronomique (INRA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées, School of Economics and Finance, Queen Mary, University of London, School of Economics and Finance (QMUL), Queen Mary University of London (QMUL)-Queen Mary University of London (QMUL), Department of Economics and Oxford-Man Institute of Quantitative Finance, University of Oxford [Oxford], Paris School of Economics (PSE), École des Ponts ParisTech (ENPC)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris 1 Panthéon-Sorbonne (UP1)-Centre National de la Recherche Scientifique (CNRS)-École des hautes études en sciences sociales (EHESS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Paris Jourdan Sciences Economiques (PJSE), Université Paris 1 Panthéon-Sorbonne (UP1)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École des hautes études en sciences sociales (EHESS)-École des Ponts ParisTech (ENPC)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Department of Economics and University College, Université Panthéon-Sorbonne (UP1)-École normale supérieure - Paris (ENS Paris)-Institut National de la Recherche Agronomique (INRA)-École des hautes études en sciences sociales (EHESS)-École des Ponts ParisTech (ENPC)-Centre National de la Recherche Scientifique (CNRS), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National de la Recherche Agronomique (INRA)-École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS), and École des Ponts ParisTech (ENPC)-École des hautes études en sciences sociales (EHESS)-École normale supérieure - Paris (ENS Paris)-Université Panthéon-Sorbonne (UP1)-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Recherche Agronomique (INRA)
This paper assesses the quantitative impact of ambiguity on the historically observed equity premium. We consider a Lucas-tree pure–exchange economy with a single agent where we introduce two key non- standard assumptions. First, the agent’s beliefs about the dividend/consumption process is ambiguous, i.e., she is uncertain about the exact probability distribution governing the realization of future dividends and consumption. Second, the agent’s preferences are sensitive to this ambiguity, a property formalized using the smooth ambiguity model. The consumption and dividend process is assumed to evolve according to a hidden state model, popularized by Bansal and Yaron (2004), where a persistent latent state variable describes temporary shocks to the mean of consumption growth prospects. We further extend the model to allow for uncertainty about the magnitude of the persistence of the latent state. The agent’s beliefs are am- biguous due to the uncertainty about the conditional mean of the probability distribution on consumption and dividends in the next period. We show that in this model ambiguity is endogenously dynamic, for example, increasing during recessions. This results in an endogenously volatile and (counter-)cyclical equity premium. We calibrate the level of ambiguity aversion to match only the first moment of the risk-free rate in data, and ambiguity to match the uncertainty conditional on the historical growth path, and evaluate the model using moderate levels of risk aversion. We find that this simple modification of a Lucas-tree model accounts for a large part of the historical equity premium, both in terms of its level and variation over time.