An investigation of asset pricing puzzles with cyclical risk aversion and intertemporal substitution

Representative agent models that embed the Lucas-Breeden (Lucas (1978), Breeden (1979)) paradigm for explaining asset return differentials are generally regarded as inconsistent with the empirical data. Difficulties such as the equity premium puzzle (Mehra and Prescott (1985)), the risk free rate puzzle (Weil (1989)), etc., are well documented and it has been shown that these puzzles are very robust (Kocherlakota (1996), Campbell (1996) and Cochrane (1997) provide good surveys). Recently, however, several authors (Campbell and Cochrane (1999), Gordon and St. Amour (2000, 2001) and Bakshi and Chen (1996) are some examples) have pointed to time-varying risk aversion as a potential source of mis-specification that may account for these puzzles. However, risk aversion and intertemporal substitution are intertwined in these models, just as they are in the additive expected utility model, therefore it is impossible to interpret unambiguously which feature of preferences varies over the cycle. The preferences suggested by Epstein and Zin (1989) can separate the coefficient of relative risk aversion ('CRRA') from the elasticity of intertemporal substitution ('EIS') and allow average consumption growth to have a much smaller effect than consumption volatility on the risk free interest rate. This paper generalizes the model of Epstein and Zin (1989) by allowing the representative agent to display countercyclical risk aversion and assesses if such behavior can add to the explanation of various empirical phenomena that have been investigated in finance and macroeconomics, such as the Mehra and Prescott (1985) equity premium puzzle. I investigate various combinations of state dependent 'CRRA' with state dependent 'EIS'. In the case of constant ' EIS' and time varying 'CRRA', my results look very similar to those generated without state dependence. However, I also investigate the same model but with time varying 'EIS' and constant ' CRRA'. I find that a time varying 'EIS' provides delightful results. I also find that time varying 'EIS' combined with a time varying 'CRRA' leads to even better results. As a further check, I use my calibrated preference parameters to predict the long-term interest rate. The calibrated preference parameters lead to very sensible term structure predictions. I also investigate a similar problem in an open economy. Based on a two-country general equilibrium model, I investigate the asset pricing puzzles from a different angle; i.e. an analysis of the predictability of excess rates of return on discount bonds, equities and foreign money markets using regression analysis. My work in an open economy setting basically supports Bekaert, Hodrick and David (1997) conclusion. I find that when I introduce both time varying ' EIS' and 'CRRA' into my two country model, the improved predictability of excess returns is insignificant. My results uphold a stronger statement: incorporating first order risk aversion with a simple pattern for time varying risk aversion and intertemporal substitution does not help much either. But my findings do not rule out the possibility that there could exist a richer pattern of time varying [rho] and Ã such that the estimated ßs can match the stylized results.