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Internal habits formation and optimality

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  • Bambi, Mauro
  • Gozzi, Fausto

Abstract

In a very influential model with internal habits, Carroll et al., (2017, 2000), establish that an increase in economic growth may cause a positive change in savings. The optimality of this result, and of many other contributions using a similar framework, has been questioned by some authors who have observed that the parametrization used in these models always implies a utility function not jointly concave in consumption and habits. In this paper, we revisit the optimality issue and, using advanced techniques in Dynamic Programming, we answer the following long-standing open questions: (i) Is the solution found in Carroll et al., (2017, 2000) optimal? (ii) Is it also unique or do other optimal solutions exist?

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  • Bambi, Mauro & Gozzi, Fausto, 2020. "Internal habits formation and optimality," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 165-172.
    • Handle: RePEc:eee:mateco:v:91:y:2020:i:c:p:165-172
    DOI: 10.1016/j.jmateco.2020.09.008
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    1. Alonso-Carrera, Jaime & Caballe, Jordi & Raurich, Xavier, 2005. "Growth, habit formation, and catching-up with the Joneses," European Economic Review, Elsevier, vol. 49(6), pages 1665-1691, August.
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    Cited by:

    1. Mauro Bambi & Daria Ghilli & Fausto Gozzi & Marta Leocata, 2021. "Habits and demand changes after COVID-19," Papers 2107.00909, arXiv.org, revised Mar 2022.
    2. Stefano Bosi & Carmen Camacho & David Desmarchelier, 2023. "Human capital and welfare," PSE-Ecole d'économie de Paris (Postprint) halshs-03920429, HAL.
    3. Morhaim, Lisa & Ulus, Ayşegül Yıldız, 2023. "On history-dependent optimization models: A unified framework to analyze models with habits, satiation and optimal growth," Journal of Mathematical Economics, Elsevier, vol. 105(C).
    4. Gómez, Manuel A., 2021. "On the closed-form solution of an endogenous growth model with anticipated consumption," Journal of Mathematical Economics, Elsevier, vol. 95(C).

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    More about this item

    Keywords

    Endogenous growth; Habit formation; Sufficient conditions of optimality; Dynamic programming; Viscosity solution;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

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