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Lubik, Thomas A.. "Non-stationarity and instability in small open-economy models even when they are "closed"." Economic Quarterly. Federal Reserve Bank of Richmond. 2007. HighBeam Research. 16 Oct. 2018 <https://www.highbeam.com>.
Lubik, Thomas A.. "Non-stationarity and instability in small open-economy models even when they are "closed"." Economic Quarterly. 2007. HighBeam Research. (October 16, 2018). https://www.highbeam.com/doc/1G1-176588103.html
Lubik, Thomas A.. "Non-stationarity and instability in small open-economy models even when they are "closed"." Economic Quarterly. Federal Reserve Bank of Richmond. 2007. Retrieved October 16, 2018 from HighBeam Research: https://www.highbeam.com/doc/1G1-176588103.html
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Open economies are characterized by the ability to trade goods both intra- and intertemporally, that is, their residents can move goods and assets across borders and over time. These transactions are reflected in the current account, which measures the value of a country's export and imports, and its mirror image, the capital account, which captures the accompanying exchange of assets. The current account serves as a shock absorber, which agents use to optimally smooth their consumption. The means for doing so are borrowing and lending in international financial markets. It almost goes without saying that international macroeconomists have had a long-standing interest in analyzing the behavior of the current account.
The standard intertemporal model of the current account conceives a small open economy as populated by a representative agent who is subject to fluctuations in his income. By having access to international financial markets, the agent can lend surplus funds or make up shortfalls for what is necessary to maintain a stable consumption path in the face of uncertainty. The international macroeconomics literature distinguishes between an international asset market that is incomplete and one that is complete. The latter describes a modeling framework in which agents have access to a complete set of state-contingent securities (and, therefore, can share risk perfectly); when markets are incomplete, on the other hand, agents can only trade in a restricted set of assets, for instance, a bond that pays fixed interest.
The small open-economy model with incomplete international asset markets is the main workhorse in international macroeconomics. However, the baseline model has various implications that may put into question its usefulness in studying international macroeconomic issues. When agents decide on their intertemporal consumption path they trade off the utility-weighted return on future consumption, measured by the riskless rate of interest, against the return on present consumption, captured by the time discount factor. The basic set-up implies that expected consumption growth is stable only if the two returns exactly offset each other, that is, if the product of the discount factor and the interest rate equal one. The entire optimization problem is ill-defined for arbitrary interest rates and discount factors as consumption would either permanently decrease or increase. (1)
Given this restriction on two principally exogenous parameters, the model then implies that consumption exhibits random-walk behavior since the effects of shocks to income are buffered by the current account to keep consumption smooth. The random-walk in consumption, which is reminiscent of Hall's (1978) permanent income model with linear-quadratic preferences, is problematic because it implies that all other endogenous variables inherit this non-stationarity so that the economy drifts over time arbitrarily far away from its initial condition. To summarize, the standard small open-economy model with incomplete international asset markets suffers from what may be labelled the unit-root problem. This raises several issues, not the least of which is the overall validity of the solution in the first place, and its usefulness in conducting business cycle analysis.
In order to avoid this unit-root problem, several solutions have been suggested in the literature. Schmitt-Grohe and Uribe (2003) present an overview of various approaches. In this article, I am mainly interested in inducing stationarity by assuming a debt-elastic interest rate. Since this alters the effective interest rate that the economy pays on foreign borrowing, the unit root in the standard linearized system is reduced incrementally below unity. This preserves a high degree of persistence, but avoids the strict unit-root problem. Moreover, a debt-elastic interest rate has an intuitive interpretation as an endogenous risk premium. It implies, however, an additional, essentially ad hoc feedback mechanism between two endogenous variables. Similar to the literature on the determinacy properties of monetary policy rules or models with increasing returns to scale, the equilibrium could be indeterminate or even non-existent.
I show in this article that commonly used specifications of the risk premium do not lead to equilibrium determinacy problems. In all specifications, indeterminacy of the rational expectations equilibrium can be ruled out, although in some cases there can be multiple steady states. It is only under a specific assumption on whether agents internalize the dependence of the interest rate on the net foreign asset position that no equilibrium may exist.
I proceed by deriving, in the next section, an analytical solution for the (linearized) canonical small open-economy model which tries to illuminate the extent of the unit-root problem. Section 2 then studies the determinacy properties of the model when a stationarity-inducing risk-premium is introduced. In Section 3, I investigate the robustness of the results by considering different specifications that have been suggested in the literature. Section 4 presents an alternative solution to the unit-root problem via portfolio adjustment costs, while Section 5 summarizes and concludes.
1. THE CANONICAL SMALL OPEN-ECONOMY MODEL
Consider a small open economy that is populated by a representative agent (2) whose preferences are described by the following utility function:
[E.sub.0] [[infinity].summation over (t=0)] [[beta].sup.t]u([c.sub.t]), (1)
where 0 < [beta] < 1 and [E.sub.t] is the expectations operator conditional on the information set at time t. The period utility function u obeys the usual Inada conditions which guarantee strictly positive consumption sequences {[c.sub.t]}[.sub.t=0.sup.[infinity]]. The economy's budget constraint is
[c.sub.t] + [b.sub.t] [less than or equal to] [y.sub.t] + [R.sub.t-1][b.sub.t-1], (2)
where [y.sub.t] is stochastic endowment income; [R.sub.t] is the gross interest rate at which the agent can borrow and lend [b.sub.t] on the international asset market. The initial condition is [b.sub.-1] [>/<] 0. In the canonical model, the interest rate is taken parametrically.
The agent chooses consumption and net foreign asset sequences {[c.sub.t], [b.sub.t]}[.sub.t=0.sup.[infinity]] to maximize (1) subject to (2). The usual transversality condition applies. First-order necessary conditions are given by
u' ([c.sub.t]) = [beta][R.sub.t][E.sub.t]u' ([c.sub.t+1]), (3)
and the budget constraint (2) at equality. The Euler equation is standard. At the margin, the agent is willing to give up one unit of consumption, valued by its marginal utility, if he is compensated by an additional unit of consumption next period augmented by a certain (properly discounted) interest rate, and evaluated by its uncertain contribution to utility. Access to the international asset market thus allows the economy to smooth consumption in the face of uncertain domestic income. Since the economy can only trade in a single asset such a scenario is often referred to as one of "incomplete markets." This stands in contrast to a model where agents can trade a complete set of state-contingent assets ("complete markets").
In what follows, I assume for ease of exposition that [y. …
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