The possible trinity: Optimal interest rate, exchange rate, and taxes on capital flows in a DSGE model for a small open economy

A traditional way of thinking about the exchange rate regime and capital account openness has been framed in terms of the 'impossible trinity' or 'trilemma', according to which policymakers can only have two of three possible outcomes: open capital markets, monetary independence and pegged exchange rates. The present paper is a natural extension of Escude (A DSGE Model for a SOE with Systematic Interest and Foreign Exchange Policies in Which Policymakers Exploit the Risk Premium for Stabilization Purposes, 2013), which focuses on interest rate and exchange rate policies, since it introduces the third vertex of the 'trinity' in the form of taxes on private foreign debt. These affect the risk-adjusted uncovered interest parity equation and hence influence the SOE's international financial flows. A useful way to illustrate the range of policy alternatives is to associate them with the faces of an isosceles triangle. Each of three possible government intervention policies taken individually (in the domestic currency bond market, in the foreign currency market, and in the foreign currency bonds market) corresponds to one of the vertices of the triangle, each of the three possible pairs of intervention policies corresponds to one of the three edges of the triangle, and the three simultaneous intervention policies taken jointly correspond to the triangle's interior. This paper shows that this interior, or 'possible trinity' is quite generally not only possible but optimal, since the central bank obtains a lower loss when it implements a policy with all three interventions.