Habit, Long-Run Risks, Prospect? A Statistical Inquiry
We use recently proposed Bayesian statistical methods to compare the habit persistence asset pricing model of Campbell and Cochrane, the long-run risks model of Bansal and Yaron, and the prospect theory model of Barberis, Huang, and Santos. We improve these Bayesian methods so that they can accommodate highly nonlinear models such as the three aforementioned. Our substantive results can be stated succinctly: If one believes that the extreme consumption fluctuations of 1930–1949 can recur, although they have not in the last sixty years even counting the current recession, then the long-run risks model is preferred. Otherwise, the habit model is preferred. We reach this conclusion by undertaking two types of comparisons, relative and absolute, over two sample periods, 1930–2008 and 1950–2008, using real, annual, U.S. data on stock returns, consumption growth, and the price to dividend ratio. Comparisons are conducted using a trivariate series of all three, a bivariate series comprised of consumption growth and stock returns, and a univariate series of stock returns alone. The prior for each model is that the ergodic mean of the real interest rate be 0.896 within ±1 with probability 0.95 together with a preference for model parameters that are near their published values. The prospect theory model is not considered for the trivariate series because it puts all its mass on a two-dimensional subspace thereby violating the regularity conditions of the methods employed. For the trivariate series, in the relative comparison, the long-run risks model dominates the habit model over the 1930–2008 period, while the habit persistence model dominates the long-run risks model over the 1950–2008 period; in the absolute assessment, both models fail over both sample periods. Empirical results for the bivariate series are explored more completely because it has the most substantive relevance. For the bivariate series, in the relative comparison, the long-run risks model dominates over the 1930–2008 period, while the habit persistence model dominates over the 1950–2008 period; in the absolute assessment, the habit model fails in the 1930–2008 period and the prospect theory model fails in the 1950–2008 period. Out-of-sample, the models show interesting differences in their forecasts over the 2009–2013 horizon. In-sample, all three models track the conditional volatility of stock returns about the same. They differ mainly in how they track the conditional volatility of consumption growth and the conditional correlation between consumption growth and stock returns. For the univariate series and for both sample periods, the models perform about the same in the relative comparison and fit the series reasonably well in the absolute assessment. The main value of the univariate series is that the near equal performance of the three models permits exploration of methodological issues.
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