Optimal Indebtendness of a Small Open Economy with Precautionary Behavior

The model is an application of the precautionary consumer saving model to the external debt policy of a small open economy. Let us assume that the welfare criterion of macroeconomic policy is the utility function of a representative infinitely living dynasty. This approach is in line with the intertemporal optimization model of the current account of Obstfeld-Rogoff [1995]. It is known that assuming differences in tastes or growth rates across countries imply unacceptably extreme long-run predictions in this model. We show that a model with uninsurable wage risks and precautionary behaviour leads to stable stationary indebtedness levels within the range of magnitudes observed in reality. Let us assume that the consumption function of the representative dinasty has the form of a CES function. The positive third derivative of this function and uncertainty together give rise to a precautionary behavior. As a result, countries who grow fast relative to their own time preference, will borrow, but their debt will be constrained by the risk that indebtedness implies. By similar reasoning, a patient or slow-growing country will lend but its lending will converge to an amount where the gained security that its reserves offer is equal to its opportunity cost. We parameterized the model assuming a drifting random-walk aggregate income with a standard error of 2%, a habit factor of 80% of the previous years income incorporated into the CES funtion, risk-aversion and time preference parameters taken from the literature, and found that typical indebtedness ratios observed in the world can be replicated as a policy outcome of our model, in contrast to deterministic models where the rate of the optimal indebtedness was in the range of 20-30 times GDP. The calculations are based on adaptation of the Taylor-series approximation of Skinner [1989]. A sensitivity analysis of the stationary solution to various parameters and various scenarios for effects of assumed shocks and consequences of catch-up growth paths for a converging country are calculated. In another section the problem is discussed whether the level of indebtedness can be considered a goal of macroeconomic policy and if it was a goal how could it be achieved. Let us assume agents with idiosynchratic uninsured wage risks. These risks are correlated but there exists an aggregate risk for the country as a whole. Aggregate risk has to be handled by macroeconomic policy. The optimum intertemporal consumption choice of the social planner (macro-policy maker) does not necessarily coincide with the sum of the optimal decisions of individual agents. Fiscal policy is the tool that creates consistency between the two. It is shown that the model with the parametrizations given above and a proportional income tax system implies that government debt nearly fully appears in external debt, i.e. Ricardian compensation is very close to 0. This means, that the fiscal tool is effective in enforcing the social optimum of indebtedness.