The Optimal Weighting of Indicators for a Crawling Peg

Abstract

This paper derives optimal weights for current-account and reserve indicators for adjusting the exchange rate (a "crawling peg"). Keven (1975)showed that use of a current account indicator alone would not stabi1iereserves, while a reserve indicator results in unstable fluctuations in the exchange rate. This paper begins by analyzing the problem in the frame work of Phillips (1954), in which the current account indicator is "proportional" and the reserve indicator is "integral." We then analyze the problem in a deterministic optimal control framework, and finally as a problem in stochastic control. In all cases the optimal combination is a weighted average, which we call the Keven-Phillips formula. With a fairly low variance of the current account, its weight falls in the range 0.47-0.65. Rising variance reduces its weight in the optimal formula.