["Oxford Bulletin of Economics and Statistics, EarlyView. ", "\nABSTRACT\nIn this paper we extend the two‐level factor model to account for cointegration between group‐specific factors in large datasets. We propose two nonlinear specifications: (i) a threshold vector error correction model (VECM) that allows for asymmetric adjustment across regimes; and (ii) a band VECM that captures state‐dependent adjustment which becomes active only when deviations from equilibrium exceed an inaction threshold. Monte Carlo simulations show that the proposed estimators perform well in finite samples, accurately recovering the cointegration relationship and the regime‐dependent adjustment mechanism in the designs considered. In an empirical application, we estimate a band factor VECM on a panel of government bond yields from multiple countries, extracting one global factor and two group‐specific factors associated with long‐ and short‐term maturities. The results provide evidence of discontinuous adjustment in the global term structure of interest rates, with stronger error correction during periods of larger deviations from the long‐run equilibrium.\n"]