# **1 Introduction**

A considerable analytical and empirical literature has been concerned with the extent of consumption risk sharing across countries. The relatively high sensitivity of aggregate consumption to domestic income shocks – or, equivalently, the low degree of comovement of aggregate consumption across countries – has been singled out as one of the major puzzles in international macroeconomics (Obstfeld and Rogoff, 2001). In recent years, it has attracted renewed interest due to the growing degree of financial integration of economies across the world. The is if markets are argument straightforward: financial complete – in the sense that the available assets span the set of all idiosyncratic risks – the ratio of the marginal utilities of consumption of any pair of agents (or countries, in this paper’s representative-agent framework) must be constant across dates and states of nature. That is, the economy features perfect consumption risk sharing.<sup>1</sup> In turn, if risk sharing is imperfect and markets are incomplete, financial innovation that expands the set of tradeable assets (or reduces the costs of trading existing assets) should allow enhanced risk diversification, although it might also raise the overall exposure to risk.<sup>2</sup> To the extent that the global increase in international financial openness over the last quarter century (Lane and Milesi-Ferretti, 2007) reflects such kind of innovation, it should be associated with a rise in risk sharing across countries.

A number of papers have performed empirical tests of the null hypothesis of perfect consumption risk sharing. The standard approach is to adopt a parametric assumption for the utility function – typically, imposing constant absolute or relative risk aversion – and use it to check if the theoretical prediction is satisfied in the data. This is often done indirectly, through least squares regressions testing whether idiosyncratic income shocks have a significant effect on individual consumption after controlling for the average consumption of all agents. Obstfeld (1994), Canova and Ravn (1996), and Lewis (1996) are some leading examples of this literature applied to cross-country aggregate data.<sup>3</sup> These conventional tests can be informative about whether perfect risk sharing holds But if the null is – as is almost the case – in empirically. hypothesis rejected invariably

> 1Market completeness represents a sufficient, but not necessary, condition for perfect risk sharing. The same outcome might be achieved by, say, agreement between governments to a suitable system of transfers across countries.

2The reason is that financial integration may also open the door to the propagation of financial turbulence from abroad. For example, Devereux and Yu (2016) find that financial integration reduces the severity of crises as a result of better diversification, but makes them more frequent due to increased opportunities for contagion. As a consequence, the overall degree of risk faced by consumers may rise or fall relative to a situation of financial autarky.

> 3Cochrane (1991) and Townsend (1994) present early implementations of risk-sharing tests based on household level data.

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