هزینه های صبر، پشتکار و رفاه بازار های ناقص در اقتصاد باز

We investigate the welfare implications of alternative financial market structures in a two-country endowment economy model. We obtain an analytic expression for the expected lifetime utility of the representative household when sovereign bonds are the only internationally traded asset, and we compare this welfare level with that obtained under complete asset markets. The welfare cost of incomplete markets is negligible if agents are very patient and shocks are not very persistent, but this cost is dramatically larger if agents are relatively impatient and shocks are highly persistent. For realistic cases in which agents are very patient and shocks are highly persistent, the welfare cost of incomplete markets is highly sensitive to the specific values of these parameters.

In recent years, numerical methods have been used to analyze a wide variety of open-economy dynamic general equilibrium models with incomplete asset markets. In particular, Baxter and Crucini (1995) showed that the degree of persistence and spillovers of the exogenous shocks plays a critical role in determining the extent to which the behavior of the incomplete-markets economy diverges from that of the economy with complete asset markets.1Tesar (1995) obtained quantitative results regarding the welfare costs of financial market incompleteness under various model specifications.2 However, there has been a relative scarcity of analytical results to elucidate these findings and to clarify the implications of the key structural parameters. In this paper, we use analytical methods to determine the welfare implications of a two-country endowment economy in which sovereign bonds are the only internationally traded asset. We also assume that the two countries are completely symmetric, with no outstanding debt at the beginning of the initial period, and that each country is subject to a single endowment shock that decays at an exponential rate. Under these assumptions, we can obtain the exact non-linear rational expectations solution for the dynamic behavior of the economy; that is, the entire path of each country’s consumption can be expressed in terms of the exogenous endowment process. Then we proceed to derive an analytic expression for the expected lifetime utility of the representative agent (using a second-order Taylor approximation around the steady-state growth path of the endowments), and we compare this welfare level with that obtained under complete markets and under autarky.3 We find that the welfare cost of incomplete markets increases linearly with the degree of relative risk aversion and with the variance of the country-specific component of the endowment shocks, whereas this welfare cost depends nonlinearly on the persistence and spillovers of the endowment shocks and on the growth-adjusted discount factor (which is a simple function of the discount factor, the growth rate, and the intertemporal elasticity of substitution). In particular, the welfare cost of incomplete markets is negligible if agents are very patient and shocks are not very persistent, but this cost is dramatically larger if agents are relatively impatient and shocks are highly persistent. Furthermore, our analysis highlights potentially realistic cases in which the welfare of the incomplete-markets economy is quite sensitive to small changes in the structural parameters.4 These results extend the seminal analysis of Cole (1988), who obtained an exact analytic solution for the behavior of a two-period incomplete market model. Our results complement those of Devereux and Saito (1997), who analyzed an open-economy model in which each country’s output is a linear function of its capital stock (which does not depreciate); in that setting, no international risk-sharing occurs when countries are symmetric and sovereign bonds are the only internationally traded asset. Our analysis is also complementary to that of Davis et al. (2000), who utilized a model in which the global endowment is deterministic, implying a constant world risk-free real interest rate. In contrast, our model allows for a stochastic world endowment and an endogenous risk-free real interest rate, and hence is suitable for analyzing the welfare costs of incomplete markets for relatively large economies.5 The remainder of this paper proceeds as follows. Section 2 presents the specification and analytic solution of the economy. Section 3 presents the general welfare results. Section 4 highlights the welfare implications of patience, persistence, and spillovers. Section 5 concludes. Appendix A provides further details regarding the analytical derivations.

Our analysis suggests that the welfare implications of financial market incompleteness may vary substantially across different types of exogenous disturbances. For example, sovereign bonds may be reasonably effective in facilitating international risk-sharing in response to temporary shifts in a country’s monetary or fiscal policy, but are probably not useful in smoothing consumption in response to longer-term geopolitical or institutional changes. Since moral hazard problems and other contractual difficulties severely limit the extent to which private agents can insure themselves against such events, such shocks tend to generate highly persistent differences in living standards across countries.