Panel regression models for bilateral exchange rates: The numéraire effect

The objective of this paper is to measure and assess the statistical significance of the numéraire effect. This effect arises from the adoption of a common single-currency numéraire for bilateral exchange rates in bilateral-panel regression models. To achieve this objective, exchange rates and explanatory variables are divided into two hierarchical levels of aggregation: a disaggregated level, which consists of multilateral exchange rates and multilateral explanatory variables, and an aggregated level, which consists of bilateral exchange rates and bilateral explanatory variables. The statistical significance of the numéraire effect is examined by testing whether the slope coefficient in a bilateral-panel regression—at the aggregated level—suffers from aggregation bias. If the slope coefficient in a bilateral-panel regression suffers from aggregation bias, it is recommended that the analysis be performed with a multilateral-panel regression—at the disaggregate level—where the slope coefficient is free from aggregation bias. The numéraire effect is measured as the difference between the slope coefficient in a bilateral-panel regression—based on the common single-currency numéraire—and the slope coefficient in a multilateral-panel regression. To illustrate two applications—the uncovered interest rate parity (UIP) condition, and the uncovered equity parity (UEP) condition—we use a monthly dataset covering 45 years (from 1980 to 2024), comprising six bilateral exchange rates expressed in US dollars. The results indicate that a substantial share of the slope coefficients estimated from bilateral panel regressions exhibit significant aggregation bias. These findings provide strong support for the use of multilateral panel regression models.