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Michael Kumhof: Research department, IMF and Assistant Professor at Stanford University; Stijn Van Nieuwerburgh: Ph.D.Candidate at Stanford University. The authors would like to thank Guillermo Calvo, Ken Judd, Carmen Reinhart, Ken Rogoff, Tom Sargent, Martin Schneider, Stephen Turnovsky and seminar participants at the IMF, the 2001 LACEA meetings in Uruguay, and Stanford’s Marco lunch group for helpful comments.
Other references include: Sargent and Smith (1988) on the irrelevance of open market operations in foreign currencies; Chamley and Ptolemarchakis (1984), Sargent and Smith (1987), and Wallace (1981) on the irrelevance of domestic open market operations.
This requires that the risk of the domestic currency is too idiosyncratic to be internationally diversifiable, or that market is too small relative to transactions costs. Both are plausible for emerging markets. Of course individual households can hedge domestically if there is heterogeneity among them. But what matters is that households as a whole cannot hedge their aggregate domestic currency exposure vis-a-vis their own government.
Useful surveys of the technical aspects of stochastic optimal control are contained in Chow (1979), Fleming and Rishel (1975), Malliaris and Brock (1982), Karatzas and Shreve (1991), and Duffie (1996). The seminal papers using this technique to analyze macroeconomic portfolio selection are Merton (1969, 1971) and Cox, Ingersoll and Ross (1985). Other contributions include Dumas and Uppal (2000), Grinols and Turnovsky (1994), and Stulz (1983, 1984, 1987, 1988).
Tradables endowments could therefore be dropped from the model without loss of generality. We chose to retain them in order to follow the convention in much of the small open economy literature.
Subsequent discontinuous exchange rate jumps are ruled out by arbitrage.
Note that qt could be negative and represent government claims on the private sector. In that case ht could also be negative.
In all policy experiments we will assume for simplicity that
The current account can also be written in a more familiar form by letting
A determinate portfolio share is needed in Appendix II to solve for the closed form value function.
This condition is not strictly required because the transversality condition can be shown to hold without it for a range of parameter values.
This implies a contingent time path for the nominal bond stock Q. Fixing a Q-path would imply a contingent time path for the nominal interest rate iq.
Expected steady state spending could be renormalized to zero by introducing an autonomous spending component equal to (E(dGt)/dt)ss, where the subscript ss stands for steady state.
Provided of course that, as will be proved below, the value function is strictly concave in wealth.
In our model lower inflation would be preceded by a discrete nominal depreciation on impact. This could be avoided if the initial drop in real money demand was accompanied by a one-off unsterilized intervention at the outset of the new policy.