A novel methodology in testing the long-run risks model of Bansal and Yaron (2004) is presented based on the observation that, under the null, the potentially latent state variables, "long-run risk" and the conditional variance of its innovation, are known a¢ ne functions of the observable market-wide price-dividend ratio and risk free rate. In linear forecasting regressions of consumption growth and returns by the price-dividend ratio and risk free rate, the model implies much higher forecastability than what is observed in the data over 1931 -2009. The co-integrated variant of the model by Bansal, Gallant, and Tauchen (2007), also implies much higher forecastability of returns than what is observed in the data. Finally, we reject the models' implications in jointly pricing the cross-section of returns and fitting the unconditional time series moments of consumption and dividend growth. The results suggest that either some important state variable is missing or that the models should be generalized in a way that the lagged price-dividend ratio and risk free enter the regressions in a non-linear fashion.
The Bansal and Yaron (2004) model of long run risks (LLR) in aggregate consumption and dividend growth and its extension that captures potential cointegration of the consumption and dividend levels, are tested on a cross-section of asset classes and rejected using annual data over the period 1930-2006 and using both annual and quarterly data over the post-war period. The reversal of earlier empirical conclusions is partly due to the increase in the power of the tests resulting from two observations under the null. First, the latent state variables and, therefore, the pricing kernel are known a¢ ne functions of observables such as the interest rate and the market-wide price-dividend ratio. Second, the parameters of the time-series processes of consumption and dividend growth, the LLR variable, and its conditional variance impose constraints on the parameters of the pricing kernel. The value of the persistence parameter of the LRR variable that best …ts the data implies that its half-life is shorter than that of the business cycle.
Probably not. First, allowing the probabilities of the states of the economy to di¤er from their sample frequencies, the Consumption-CAPM is still rejected in both U.S. and international data. Second, the recorded world disasters are too small to rationalize the puzzle unless one assumes that disasters occur every 6-10 years. Third, if the data were generated by the rare events distribution needed to rationalize the equity premium puzzle, the puzzle itself would be unlikely to arise. Fourth, the rare events hypothesis, by reducing the cross-sectional dispersion of consumption risk, worsens the ability of the Consumption-CAPM to explain the cross-section of returns.
Christian Julliard is a Lecturer in the Department of Economics and senior research associate of the Financial Market Group at the London School of Economics and Political Science. He is also a research affiliate of the Centre for Economic Policy Research (CEPR) and editorial board member of the Review of Economic Studies. He was awarded a Ph.D. by the Department of Economics at Princeton University where he was also affiliated with the Bendheim Center for Finance and the Woodrow Wilson School of Public and International Affairs. Anisha Ghosh is a PhD student in the Department of Economics at London School of Economics and Political Science. She completed her BSc in Economics from Presidency College, Calcutta in 2003 and then the MRes in Economics at London School of Economics and Political Science in 2005. Any opinions expressed here are those of the authors and not necessarily those of the FMG. The research findings reported in this paper are the result of the independent research of the authors and do not necessarily reflect the views of the LSE.
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