Observational equivalence of balanced growth with external habit formation

This paper investigates two scenarios in the external habit formation model with concave utility functions. When the utility function is weakly concave, there exists a unique history-dependent balanced growth path (BGP) under a knife-edge existence condition. When the utility function is strictly concave, a unique BGP exists under a more generic condition. I find that the BGPs in the two scenarios are observationally equivalent. The knife-edge condition limits the applicability of the first scenario. The generic existence condition and the observational equivalence result mitigate this issue. I show that our model can help understand a variety of growth patterns of countries that differ in their fundamentals substantially.