A biweight approach to estimate currency exchange rate: the Nigerian example

In this article, we propose a biweight approach to a real-life location problem, namely, the estimation of a realistic exchange rate for the Nigerian currency, naira (for easy reference, we denote the exchange rate parameter byθ).

Our proposal is essentially a critic of the methods being used by the Central Bank of Nigeria (CBN) to derive its estimate θ_CBN of θ. The CBN generates the necessary data by periodically organizing a foreign exchange market (FEM) where it sells a certain amount of US dollars to authorized foreign exchange dealers. (The amount of dollars available for sale is usually inadequate to meet aggregate demand, so there is literally a 'scramble' among dealers for a 'slice of the cake'.) During each session of FEM, each dealer quotes: (a) how much naira (variable Y) it will pay for US$1, and (b) the amount of US dollars (variable X) it wants to buy. The CBN estimates, based on observations of Y, have been found to be unstable and part of the problem seems to lie with the fact that a few atypical or outlier values are generated at FEM sessions and CBN estimation methods are not resistant to these extreme values.

This article presents a robust/resistant model which is designed to tackle the problem of outliers head on: we exploit the resistance property of the biweight to help reduce the influence of any outlier on the final biweight estimate θ_bw. Furthermore, we use the biweight weight, in conjunction with X, as an instrument to check against generation of outliers at FEM.