Distorted Asymmetry Inference in NARDL Models with a Stationary Forcing Variable: Evidence from Global Supply Chain Pressures and U.S. Freight Prices

The nonlinear ARDL (NARDL) model by Shin et al. tests for asymmetric adjustment by decomposing a forcing variable into cumulated positive and negative changes. We study this linear-in-parameters partial-sum design when the forcing variable is stationary, as is commonly assumed for composite pressure indices. The two partial sums then share one stochastic trend, carry opposite deterministic trends, and are cointegrated by construction; the long-run symmetry test concerns the coefficient on cumulative absolute variation. If the dependent variable’s drift is not explained by the other level regressors, the estimated asymmetry converges to the unexplained drift divided by half the mean absolute change in the forcing variable, and the test rejects with a probability approaching one. Without a levels relationship, the Wald statistic has a nonstandard limit. Monte Carlo experiments confirm both results. Where a valid levels relationship exists, a linear trend removes the gross distortion and a restricted bootstrap with the trend restores size. For the Global Supply Chain Pressure Index and U.S. long-distance less-than-truckload freight prices over 1998M1–2026M7, the conventional asymmetry estimate (0.0111) is close to its drift benchmark (0.0121), and symmetry is rejected at every lag order without a trend and at none with one. Sign-split innovation models do not support rockets-and-feathers asymmetry, although their estimates are imprecise.