A new quadratic asymmetric error correction model: does size matter?

We introduce a new quadratic asymmetric error correction model that comprehensively accounts for both sign and size asymmetries. We also propose a test protocol that allows to rigorously identify different sources of long-run nonlinearity, namely quadratic nonlinearity, size asymmetry and sign asymmetry. We use a nonparametric residual recursive bootstrap technique to report p-values for the long-run tests. Simulation results confirm the consistency of our proposed estimator in finite samples and show that the bootstrapped tests have reasonably good size and power properties. Although our estimation of the Okun’s Law for the USA confirms previous findings on the direction of the sign asymmetry, its reveals that the magnitude of the impact of economic downturns on unemployment decreases faster than the impact of upturns. Forecasting results show that our new model performs better than NARDL.