Journal of Economics

, Volume 126, Issue 2, pp 153–177 | Cite as

Endogenous time preference, consumption externalities, and trade: multiple steady states and indeterminacy

  • Akihiko YanaseEmail author
  • Yukio Karasawa-Ohtashiro


This study presents a two-sector dynamic general equilibrium model with capital accumulation and discusses the role of endogenous time preference and consumption externalities in closed and small open economies. While the economy has a unique and saddle-point stable steady state under autarky, under free trade with decreasing marginal impatience (i.e., a household’s discount rate is a decreasing function of its consumption), there might exist multiple steady states and indeterminacy of equilibrium paths. Specifically, if the degree of decreasing marginal impatience is sufficiently large and individuals’ preferences exhibit admiration, the dynamic equilibria with diversified production might become indeterminate. We also analyze the economy’s long-run trade pattern and its relationship with indeterminacy.


Endogenous time preference Consumption externality Dynamic Heckscher–Ohlin model Multiple steady states Indeterminacy 

JEL Classification

D11 D62 E32 F43 



We thank Takumi Naito, Seiichi Katayama, Henry Wan Jr., Been-Lon Chen, Hiroshi Ohta, Laixun Zhao, Junko Doi, Rui Ota, Kazuo Nishimura, Fumio Dei, Ronald Jones, Hajime Kubota, Ichiroh Daitoh, Hiroto Takahashi, Ngo Van Long, Akira Yakita, Jun-ichi Itaya, seminar and conference participants, three anonymous referees and the editor Giacomo Corneo for their helpful comments and suggestions on earlier versions of this paper. We also gratefully acknowledge the Japan Society for the Promotion of Science (JSPS) for its financial support (No. 16H03612, No. 16K03677, No. 17K03731).


  1. Alonso-Carrera J, Caballé J, Raurich X (2008) Can consumption spillovers be a source of equilibrium indeterminacy? J Econ Dyn Control 32:2883–2902CrossRefGoogle Scholar
  2. Alpizar F, Carlsson F, Johansson-Stenman O (2005) How much do we care about absolute versus relative income and consumption? J Econ Behav Organ 56:405–421CrossRefGoogle Scholar
  3. Andersen S, Harrison GW, Lau MI, Rutström EE (2008) Eliciting risk and time preferences. Econometrica 76:583–618CrossRefGoogle Scholar
  4. Baxter M (1992) Fiscal policy, specialization, and trade in the two-sector model: the return of Ricardo? J Polit Econ 100:713–744CrossRefGoogle Scholar
  5. Benhabib J, Farmer REA (1994) Indeterminacy and increasing returns. J Econ Theory 63:19–41CrossRefGoogle Scholar
  6. Bian Y, Meng Q (2004) Preferences, endogenous discount rate, and indeterminacy in a small open economy model. Econ Lett 84:315–342CrossRefGoogle Scholar
  7. Caliendo L (2011) On the dynamics of the Heckscher–Ohlin theory. Mimeo, New YorkGoogle Scholar
  8. Chang FR (2009) Optimal growth and impatience: a phase diagram analysis. Int J Econ Theory 5:245–255CrossRefGoogle Scholar
  9. Chen Z (1992) Long-run equilibrium in a dynamic Heckscher–Ohlin model. Can J Econ 25:923–943CrossRefGoogle Scholar
  10. Chen BL, Hsu M (2007) Admiration is a source of indeterminacy. Econ Lett 95:96–103CrossRefGoogle Scholar
  11. Chen BL, Nishimura K, Shimomura K (2008) Time preference and two-country trade. Int J Econ Theory 4:29–52CrossRefGoogle Scholar
  12. Chen BL, Hsu M, Mino K (2012) Can consumption habit spillovers be a source of equilibrium indeterminacy? J Econ 109:245–269CrossRefGoogle Scholar
  13. Chen BL, Hsu M, Mino K (2015) Welfare implications and equilibrium indeterminacy in a two-sector growth model with consumption externalities. Macroecon Dyn 19:535–577CrossRefGoogle Scholar
  14. Dowrick S, Golley J (2004) Trade openness and growth: who benefits? Oxf Rev Econ Policy 20:38–56CrossRefGoogle Scholar
  15. Dupor B, Liu WF (2003) Jealousy and equilibrium overconsumption. Am Econ Rev 93:423–428CrossRefGoogle Scholar
  16. Epstein LG (1987) A simple dynamic general equilibrium model. J Econ Theory 41:68–95CrossRefGoogle Scholar
  17. Feenstra RC (2015) Advanced international trade: theory and evidence, 2nd edn. Princeton University Press, PrincetonGoogle Scholar
  18. Galí J (1994) Keeping up with the Joneses: consumption externalities, portfolio choice, and asset prices. J Money Credit Bank 26:1–8CrossRefGoogle Scholar
  19. Harrison GW, Lau MI, Williams MB (2002) Estimating individual discount rates in Denmark: a field experiment. Am Econ Rev 92:1606–1617CrossRefGoogle Scholar
  20. Hirose K, Ikeda S (2012) Decreasing marginal impatience in a two-country world economy. J Econ 105:247–262CrossRefGoogle Scholar
  21. Hu Y, Mino K (2013) Trade structure and belief-driven fluctuations in a global economy. J Int Econ 90:414–424CrossRefGoogle Scholar
  22. Karasawa Y (2007) The dynamics of international trade with variable marginal impatience. In: 2007 winter conference proceedings, no. II. The Korea International Economics Association, pp 15–59Google Scholar
  23. Karasawa-Ohtashiro Y, Cai D, Yanase A (2018) Admiration is a source of multiple equilibria and indeterminacy: a comment on Chen and Hsu (2007). Econ Lett.
  24. Lawrance EC (1991) Poverty and the rate of time preference: evidence from panel data. J Polit Econ 99:54–77CrossRefGoogle Scholar
  25. Meng Q (2006) Impatience and equilibrium indeterminacy. J Econ Dyn Control 30:2671–2692CrossRefGoogle Scholar
  26. Meng Q, Velasco A (2004) Market imperfections and the instability of open economies. J Int Econ 64:503–519CrossRefGoogle Scholar
  27. Naito T (2006) Pattern of trade and indeterminacy. J Macroecon 28:409–427CrossRefGoogle Scholar
  28. Nishimura K, Shimomura K (2002a) Trade and indeterminacy in a dynamic general equilibrium model. J Econ Theory 105:244–260CrossRefGoogle Scholar
  29. Nishimura K, Shimomura K (2002b) Indeterminacy in a dynamic small open economy. J Econ Dyn Control 27:271–281CrossRefGoogle Scholar
  30. Obstfeld M (1990) Intertemporal dependence, impatience, and dynamics. J Monet Econ 26:45–75CrossRefGoogle Scholar
  31. Ogawa K (1993) Economic development and time preference schedule: the case of Japan and East Asian NICs. J Dev Econ 42:175–195CrossRefGoogle Scholar
  32. Oniki H, Uzawa H (1965) Patterns of trade and investment in a dynamic model of international trade. Rev Econ Stud 32:15–38CrossRefGoogle Scholar
  33. Palivos T, Wang P, Zhang J (1997) On the existence of balanced growth equilibrium. Int Econ Rev 38:205–224CrossRefGoogle Scholar
  34. Rodríguez F, Rodrik D (2001) Trade policy and economic growth: a skeptic’s guide to the cross-national evidence. In: Bernanke BS, Rogoff K (eds) NBER macroeconomics, vol 15. MIT Press, Cambridge, pp 261–338Google Scholar
  35. Senik C (2005) Income distribution and well-being: what can we learn from subjective data. J Econ Surv 19:43–63CrossRefGoogle Scholar
  36. Stiglitz JE (1970) Factor price equalization in a dynamic economy. J Polit Econ 78:456–488CrossRefGoogle Scholar
  37. Uzawa H (1968) Time preference, the consumption function, and optimum asset holdings. In: Wolfe JN (ed) Value, capital, and growth: essays in honor of Sir John Hicks. Edinburgh University Press, Edinburgh, pp 485–504Google Scholar
  38. Valentinyi A, Herrendorf B (2008) Measuring factor income shares at the sectoral level. Rev Econ Dyn 11:820–835CrossRefGoogle Scholar
  39. Wälde K (1995) Convergence, divergence and changing trade patterns: theoretical inquiries into the role of preferences, factor accumulation, technological change and government intervention. Physica-Verlag, HeidelbergCrossRefGoogle Scholar
  40. Weder M (2001) Indeterminacy in the small open economy Ramsey growth model. J Econ Theory 98:339–356CrossRefGoogle Scholar
  41. Wong K (1995) International trade in goods and factor mobility. MIT Press, CambridgeGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Graduate School of EconomicsNagoya UniversityNagoyaJapan
  2. 2.Department of EconomicsMcGill UniversityMontrealCanada
  3. 3.Faculty of EconomicsNanzan UniversityShowa-kuJapan

Personalised recommendations