Evaluating linear approximations in a two-country model with occasionally binding borrowing constraints

Under a linear approximation, a standard two-country business cycles model with incomplete markets delivers consumption and debt dynamics that are non-stationary (unit root) and a bond price that is independent of the wealth distribution. We argue that these two features are due to the local nature of the approximation and we show that they survive even when second or third order local approximations are used. However, these features disappear when debt limits and the associated precautionary motives are taken into account by a standard, global solution method. We subsequently investigate whether this qualitative difference has significant quantitative implications regarding the linear solution as an approximation to the model's equilibrium dynamics. Policy function differences between the local and global solutions can be large and remain significant even in the case of debt limits as loose as the natural debt limit. These differences can lead to significant discrepancies in implied simulated second moments. In a benchmark calibration, the cross-country correlation of consumption is 0.61 under linearization, but only 0.38 when a policy iteration algorithm is used.