We provide a model of product-based cultural change where trade integration leads to cultural convergence. A standard trade model of Dixit-Stiglitz monopolistic competition is coupled with a micro-founded model of cultural dynamics. We show that access to varieties that are attached to a global cultural type changes the incentives of parents to socialize their children and transmit their type. The resulting increase in agents of the global cultural type leads to a magnification of the initial shock. A striking feature of the model is that even temporary shocks to openness may have permanent effects through the changing distribution of preferences in the economy.