Objective: This study aimed to determine which model best captures the behaviour of rice imports during the North America Free Trade Agreement (NAFTA) regime (1994–2018). Methodology Mexican demand for rice imports is estimated with Autoregressive Distributed Lag Model (ARDL) and Nonlinear Autoregressive Distributed Lag Model (NARDL), both with and without structural change and outliers. Results It starts with the ARDL and NARDL models, obtaining non-cointegration, as well as diagnosis and specification problems. Subsequently an ARDL model is proposed with structural change and outliers, which represents an improvement but still has specification problems. Finally, the best model is obtained incorporating non-linearity. Limitations/Implications It is a study for a specific grain, so the results obtained are only valid for rice imports. Nevertheless, it must be considered that it is a basic grain. Moreover, a new methodology is used to estimate the import demand function. Findings There is evidence of an asymmetric response of rice imports to fluctuations in economic activity and the exchange rate in the short run, and only in the long run for the latter. An increase in rice imports with NAFTA is also confirmed, as well as two extraordinary variations of rice imports during the study period. Keywords Rice imports; ARDL; NARDL; structural change; outliers