Brandt, Cochrane, and Santa-Clara (2004) pointed out that the implicit stochastic discount factors computed using prices, on the one hand, and consumption growth, on the other hand, have very different implications for their cross country correlation. They leave this as an unresolved puzzle. We explain it by combining Epstein and Zin (1989) preferences with a model of predictable returns and by positing a very correlated long run component. We also assume that the intertemporal elasticity of substitution is larger than one. This setup brings the stochastic discount factors computed using prices and quantities close together, by keeping the volatility of the depreciation rate in the order of 12% and the cross country correlation of consumption growth around 30%.JEL classification: G12; G15; F31.

a b s t r a c t We propose a model of dynamic correlations with a short-and long-run component specification, by extending the idea of component models for volatility. We call this class of models DCC-MIDAS. The key ingredients are the Engle (2002) DCC model, the Engle and Lee (1999) component GARCH model replacing the original DCC dynamics with a component specification and the Engle et al. (2006) GARCH-MIDAS specification that allows us to extract a long-run correlation component via mixed data sampling.We provide a comprehensive econometric analysis of the new class of models, and provide extensive empirical evidence that supports the model's specification.

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Focusing on US and UK, we document that both the Backus and Smith (1993) finding, concerning the low correlation between consumption differentials and exchange rates, and the forward-premium anomaly, concerning the tendency of high interest rate currencies to appreciate, have become more severe through time. After accounting for different capital mobility regimes, we show that these anomalies turn into general equilibrium regularities in a two-country and two-good economy with Epstein and Zin (1989) preferences, frictionless markets, and highly correlated long-run endowment growth prospects.