One channel of welfare‐improving globalization is through the increasing integration of trade. Although this is attributed to decreasing effects of distance across countries, the workhorse models of gravity fail to capture it, the so‐called “missing globalization” or “distance puzzle.” This paper shows that this puzzle may be due to the restricting assumption of constant elasticity of substitution (CES) preferences working behind the gravity models. We test the validity of this assumption for different trade intervals and show that it is violated as a result of the distance elasticity of trade decreasing with the amount of trade. Accordingly, we consider a type of non‐CES utility function, namely constant absolute risk version (CARA), and analytically show that the negative relation between trade and distance elasticity of trade is captured by CARA preferences. We estimate the gravity equation implied by CARA preferences, empirically confirm the endogenous relation between trade and distance elasticity of trade, and show that the distance puzzle is solved under CARA preferences. According to the data set used, CARA preferences are also econometrically selected over CES preferences based on their goodness of fit.