Among the 101 middle-income countries in 1960, only thirteen of them managed to sufficiently converge to rich countries and become high-income economies by 2008. Why? We develop a three-country growth model with trade to show how middle-income countries can be sandwiched by poorer countries that chase from behind and richer countries that press from front. It is shown that the chasing effect conditionally exists and never works in both intensive and extensive margins simultaneously, whereas the pressing effect is always active in the intensive margin but only conditionally active in the extensive margin. Empirical evidence also supports these findings. We also show how a middle-income country should optimally allocate resources between boosting productivities of incumbent varieties and enhancing the learning of new varieties by taking into account behaviors of its trade partners.