We study the growth process among a large group of economies where consumption relative to a reference group determines the discount factor of the household agents. We characterize all possible balanced growth paths and their stability properties. The model can explain why two economies having similar production technologies, preferences, and total factor productivity growth rates can differ in labor supply behavior and have diverging growth paths depending on their initial conditions. Numerical analysis of the model suggests that growth path divergence is plausible based on cross‐country differences in savings rates. History dependence on time preference also generates realistic transitional dynamics.