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.

中文翻译：

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平衡生长与外部习惯形成的观察等效性

本文研究了具有凹效用函数的外部习惯形成模型中的两种情况。当效用函数为弱凹时，在刀刃存在条件下存在唯一的历史依赖平衡增长路径（BGP）。当效用函数是严格凹的时，在更通用的条件下存在唯一的 BGP。我发现这两种情况下的 BGP 在观察上是等效的。刀口条件限制了第一种情况的适用性。一般存在条件和观测等效结果缓解了这个问题。我展示了我们的模型可以帮助理解基本面差异很大的国家的各种增长模式。