Genuine Co-Movement, Spurious Trend, and a Ratio That Does Not Help: Variable Construction for Nigerian Macroeconomic Models

Abstract: Macroeconomic models routinely include exchange-rate and trade variables side by side as separate regressors. This paper examines whether they are separate, using 67 quarterly Nigerian observations from 2008Q2 to 2024Q4, and reports two results that point in different directions. First, the co-movement among the exchange rate, exports, imports and total trade is genuine rather than a shared trend. Levels correlations run from 0.95 to 0.99, and they survive first differencing at 0.68 to 0.93, so this is not a spurious-regression artefact. Second, the co-movement between these series and GDP is spurious: the level correlation between the exchange rate and GDP is 0.607 and falls to -0.132 in differences, and trade against GDP falls from 0.599 to -0.106. This matters for a common variable-construction choice. Normalising trade by GDP is often justified as removing shared scale, but here the numerator and denominator have no genuine co- movement, and the available series compounds the problem by dividing nominal trade by real GDP. The resulting ratio reaches 189% of GDP and tests as I(2), which invalidates the ARDL bounds procedure. We recommend testing correlations in differences before treating a ratio as a solution to collinearity, and checking that numerator and denominator share a price basis.

Keywords: Multicollinearity; Spurious Correlation; Trade Openness; Variable Construction; Nigeria.