The COVID-19 pandemic dealt a significantly heavy blow to the already competitive air travel industry. As air travel demand is recovering post-pandemic, both airports and airlines are seeking to establish a steady stream of non-aeronautical/ancillary revenues, especially retail, to aid financial recovery. However, a rigorous analysis of passengers' purchasing behaviour during the whole air travel process has been lacking to date. To investigate this matter, we analyse data from a cross-national survey administered in four multi-airport cities (London in the UK, New York City in the US, Shanghai in China, and Sao Paulo in Brazil) in 2020, asking about the respondent's most recent air trip before the pandemic. A Multiple Discrete-Continuous Extreme Value (MDCEV) model was estimated to jointly analyse the discrete decision (to purchase or not) and continuous aspect (of how much is spent) during three stages of travel: at the departure airport, in flight, and at the transfer airport (if applicable). Six hypotheses, about the stage of travel, product and service type, passenger attributes, context of travel, and presence of companions are postulated and examined empirically. The results demonstrate how such factors shape shopping decisions during different stages of travel. The modelling results point towards the need for better pre-flight product information and more tailored offers. Airport retail requires more flexibility in terms of locations, operating hours and channels (in-store, deliveries) to improve shopping convenience. Use of digital tools and passenger data can aid in realising retail revenue improvement. Proposed future research directions include a focus on the transfer airport (where most spending is observed), post-pandemic behaviour changes, the role of product and service attributes, use of non-survey data and environmental impacts of the evolution in air travel retail.