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A common assumption in international business cycles models is that world financial markets are complete in the sense that individuals in different countries are able to fully insure country-specific income risks using international financial markets. Under this assumption, the models predict that consumption (or consumption growth) is highly correlated across countries, and in some cases the international consumption correlation is equal to 1 regardless of income or output correlations. The intuition is that since consumers are risk averse they will choose to smooth consumption over time by trading in international financial markets. However, in the data cross country consumption correlations are very low and are even lower than corresponding income correlations in many countries. For example, Backus, Kehoe, and Kydland (1992) solve a two-country real business cycles model and argue that the puzzle that empirical consumption correlations are actually lower than output correlations is the most striking discrepancy between theory and data. In the literature, the empirical low international consumption correlations have been interpreted as indicating international financial markets imperfections – for examples, see Kollman (1990), Baxter and Crucini (1995), and Lewis (1996).

Other extensions have been proposed to make the models better fit the data. For example, Devereux, Gregory, and Smith (1992) show that in the perfect risk-sharing model nonseparability between consumption and leisure has the potential to reduce the cross-country consumption correlation. Stockman and Tesar (1995) show that the presence of nontraded goods in the complete market model can also improve the model’s prediction. Fuhrer and Klein (2006) show that habit formation has important implications for international consumption correlations. In particular, they show that with a shock to the interest rate habit formation by itself can generate positive consumption correlations across countries even in the absence of international risk sharing and common income shocks. They then argue that if habit is a good characterization of consumers’ behavior, the absence of international risk sharing is even more striking than standard tests suggest; that is, existing studies may overstate the extent to which common consumption movements across countries reflect international risk sharing because some of them are due to habit.

In this paper, we examine how introducing two types of information imperfection, preference for robustness (RB, a concern for model misspecification) and information-processing constraints (rational inattention, RI) into an otherwise standard small open economy (SOE) model can im-prove the model’s predictions on the international consumption correlations puzzle we discussed above. Hansen and Sargent (1995, 2007) first introduce robustness into economic models. In robust control problems, agents are concerned about the possibility that their model is misspecified in a manner that is difficult to detect statistically; consequently, they choose their decisions as if the subjective distribution over shocks was chosen by a malevolent nature in order to minimize their expected utility (the solution to a robust decision-maker’s problem is the equilibrium of a max-min game between the decision-maker and nature). Robustness models produce precautionary savings but remain within the class of LQ-Gaussian models, which leads to analytical simplicity. After introducing RB into the standard SOE model and solving it explicitly, we find that RB can help improve the model’s consistency with the empirical evidence on international consumption correlations. Specifically, we show that in the presence of capital mobility in international financial markets, RB lowers the international consumption correlations by introducing heterogenous responses of consumption to income shocks across countries facing different macroeconomic uncertainty.

The reason is that in the model in which agents are concerned about model misspecification, given heterogeneity in fundamental macroeconomic uncertainty, the effects of RB on consumption adjustments are different for the countries we study; consequently, it leads to lower consumption correlations across these countries. After calibrating the RB parameter using the detection error probabilities, we find that although the calibrated RB-SOE model can better match the data on international consumption correlations, it cannot explain the observed consumption correlations quantitatively. Luo and Young (2009a) show that RB by itself fails to generate the hump-shaped impulse responses of consumption to income shocks, and introducing another informational friction, rational inattention (RI), can help produce the realistic consumption dynamics. We therefore introduce RI into our RB-SOE model and examine whether the interaction of the two important informational frictions can further improve the model’s performance on international consumption correlations.

Sims (2003) first introduced rational inattention into economics and argued that it is a plausible method for introducing sluggishness, randomness, and delay into economic models. In his formulation agents have finite Shannon channel capacity, limiting their ability to process signals about the true state of the world. As a result, an impulse to the economy induces only gradual responses by individuals, as their limited capacity requires many periods to discover just how much the state has moved. In contrast, the RE hypothesis implicitly assumes that consumers are endowed with infinite information-processing capacity, allowing them to respond immediately and completely to changes in the economy without making systematic errors. However, individuals in reality do not seem to have unlimited mental capacity: they do not respond swiftly or thoroughly to all available information related to their economic decisions. Sims (2003) and Luo (2008) use this model to explore anomalies in the consumption literature, particularly the well-known excess sensitivity and excess smoothness puzzles. Since RI induces additional uncertainty about the state of the economy and the state is a part of the model, it could be regarded as another source of model uncertainty. Agents in the model can reduce this kind of model uncertainty (the uncertainty about the current state) by learning via finite channels. The two hypotheses actually capture two important aspects of informational frictions. Specifically, agents with finite capacity cannot observe the current state but know what the innovation is and how it affects the transition of the state, while agents with a preference for RB do not know the probability model driven by the innovation but can observe the current state perfectly.

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