IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v106y2023ics0304406823000228.html
   My bibliography  Save this article

On the concavity of consumption function under habit formation

Author

Listed:
  • Liu, Haoyu
  • Li, Lun

Abstract

This paper studies the concavity of the consumption function of a habit-forming consumer with convex absolute risk tolerance. Compared with a model without habit formation, we show the conditions required for concave consumption are weaker if habit parameters are above a certain threshold. Contrary to the results of a standard consumption-saving model with time-separable utility, we show that the consumer’s consumption function can be convex when young and becomes concave when old. These results advance our understanding of the (non-)concavity of consumption function when preferences are not time-separable.

Suggested Citation

  • Liu, Haoyu & Li, Lun, 2023. "On the concavity of consumption function under habit formation," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    • Handle: RePEc:eee:mateco:v:106:y:2023:i:c:s0304406823000228
    DOI: 10.1016/j.jmateco.2023.102829
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406823000228
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2023.102829?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Thomas Dohmen & Armin Falk & Bart H. H. Golsteyn & David Huffman & Uwe Sunde, 2017. "Risk Attitudes Across The Life Course," Economic Journal, Royal Economic Society, vol. 127(605), pages 95-116, October.
    2. Ravn, Morten O. & Schmitt-Grohe, Stephanie & Uribe, Martín & Uuskula, Lenno, 2010. "Deep habits and the dynamic effects of monetary policy shocks," Journal of the Japanese and International Economies, Elsevier, vol. 24(2), pages 236-258, June.
    3. Abel, Andrew B, 1990. "Asset Prices under Habit Formation and Catching Up with the Joneses," American Economic Review, American Economic Association, vol. 80(2), pages 38-42, May.
    4. Toda, Alexis Akira, 2021. "Necessity of hyperbolic absolute risk aversion for the concavity of consumption functions," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    5. Andreas Fagereng & Martin B. Holm & Gisle J. Natvik, 2021. "MPC Heterogeneity and Household Balance Sheets," American Economic Journal: Macroeconomics, American Economic Association, vol. 13(4), pages 1-54, October.
    6. Jonathan A. Parker, 2000. "Spendthrift in America? On Two Decades of Decline in the US Saving Rate," NBER Chapters, in: NBER Macroeconomics Annual 1999, Volume 14, pages 317-387, National Bureau of Economic Research, Inc.
    7. Aylin Seckin, 2000. "Consumption with Liquidity Constraints and Habit Formation," CIRANO Working Papers 2000s-41, CIRANO.
    8. John Campbell & Angus Deaton, 1989. "Why is Consumption So Smooth?," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(3), pages 357-373.
    9. Gary Chamberlain & Charles A. Wilson, 2000. "Optimal Intertemporal Consumption Under Uncertainty," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(3), pages 365-395, July.
    10. Aylin Seckin, 2000. "Consumption-Leisure Choice with Habit Formation," CIRANO Working Papers 2000s-40, CIRANO.
    11. Gong, Liutang & Zhong, Ruquan & Zou, Heng-fu, 2012. "On the concavity of the consumption function with the time varying discount rate," Economics Letters, Elsevier, vol. 117(1), pages 99-101.
    12. Luc Aroondel & Frédérique Savignac & Kévin Tracol, 2014. "Wealth and Consumption: French Households in the Crisis," International Journal of Central Banking, International Journal of Central Banking, vol. 10(3), pages 163-204, September.
    13. Tullio Jappelli & Luigi Pistaferri, 2014. "Fiscal Policy and MPC Heterogeneity," American Economic Journal: Macroeconomics, American Economic Association, vol. 6(4), pages 107-136, October.
    14. Hara, Chiaki & Huang, James & Kuzmics, Christoph, 2007. "Representative consumer's risk aversion and efficient risk-sharing rules," Journal of Economic Theory, Elsevier, vol. 137(1), pages 652-672, November.
    15. Stachurski, John & Toda, Alexis Akira, 2019. "An impossibility theorem for wealth in heterogeneous-agent models with limited heterogeneity," Journal of Economic Theory, Elsevier, vol. 182(C), pages 1-24.
    16. Ferson, Wayne E. & Constantinides, George M., 1991. "Habit persistence and durability in aggregate consumption: Empirical tests," Journal of Financial Economics, Elsevier, vol. 29(2), pages 199-240, October.
    17. Ma, Qingyin & Stachurski, John & Toda, Alexis Akira, 2020. "The income fluctuation problem and the evolution of wealth," Journal of Economic Theory, Elsevier, vol. 187(C).
    18. Carroll, Christopher D & Kimball, Miles S, 1996. "On the Concavity of the Consumption Function," Econometrica, Econometric Society, vol. 64(4), pages 981-992, July.
    19. Bouakez, Hafedh & Cardia, Emanuela & Ruge-Murcia, Francisco J., 2005. "Habit formation and the persistence of monetary shocks," Journal of Monetary Economics, Elsevier, vol. 52(6), pages 1073-1088, September.
    20. Braun, Phillip A. & Constantinides, George M. & Ferson, Wayne E., 1993. "Time nonseparability in aggregate consumption : International evidence," European Economic Review, Elsevier, vol. 37(5), pages 897-920, June.
    21. Lawrence J. Christiano & Martin Eichenbaum & Charles L. Evans, 2005. "Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy," Journal of Political Economy, University of Chicago Press, vol. 113(1), pages 1-45, February.
    22. Hall, Robert E & Mishkin, Frederic S, 1982. "The Sensitivity of Consumption to Transitory Income: Estimates from Panel Data on Households," Econometrica, Econometric Society, vol. 50(2), pages 461-481, March.
    23. Constantinides, George M, 1990. "Habit Formation: A Resolution of the Equity Premium Puzzle," Journal of Political Economy, University of Chicago Press, vol. 98(3), pages 519-543, June.
    24. Naik, Narayan Y & Moore, Michael J, 1996. "Habit Formation and Intertemporal Substitution in Individual Food Consumption," The Review of Economics and Statistics, MIT Press, vol. 78(2), pages 321-328, May.
    25. Gollier, Christian & Zeckhauser, Richard J, 2002. "Horizon Length and Portfolio Risk," Journal of Risk and Uncertainty, Springer, vol. 24(3), pages 195-212, May.
    26. Bover, Olympia, 2006. "Wealth Effects on Consumption: Microeconometric Estimates from a New Survey of Household Finances," CEPR Discussion Papers 5874, C.E.P.R. Discussion Papers.
    27. repec:dgr:kubcen:199554 is not listed on IDEAS
    28. Aylin Seckin, 2000. "Consumption with Habit Formation," CIRANO Working Papers 2000s-39, CIRANO.
    29. Thomas Dohmen & Armin Falk & Bart H. H. Golsteyn & David Huffman & Uwe Sunde, 2017. "Risk Attitudes Across The Life Course," Economic Journal, Royal Economic Society, vol. 127(605), pages 95-116, October.
    30. Holm, Martin Blomhoff, 2018. "Consumption with liquidity constraints: An analytical characterization," Economics Letters, Elsevier, vol. 167(C), pages 40-42.
    31. Martin Lettau & Harald Uhlig, 2000. "Can Habit Formation be Reconciled with Business Cycle Facts?," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(1), pages 79-99, January.
    32. Flavin, Marjorie A, 1981. "The Adjustment of Consumption to Changing Expectations about Future Income," Journal of Political Economy, University of Chicago Press, vol. 89(5), pages 974-1009, October.
    33. Jeffrey C. Fuhrer, 2000. "Habit Formation in Consumption and Its Implications for Monetary-Policy Models," American Economic Review, American Economic Association, vol. 90(3), pages 367-390, June.
    34. Frank Smets & Raf Wouters, 2003. "An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area," Journal of the European Economic Association, MIT Press, vol. 1(5), pages 1123-1175, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lijun Bo & Yijie Huang & Xiang Yu, 2023. "An extended Merton problem with relaxed benchmark tracking," Papers 2304.10802, arXiv.org, revised Jul 2024.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rob Alessie & Federica Teppa, 2010. "Saving and habit formation: evidence from Dutch panel data," Empirical Economics, Springer, vol. 38(2), pages 385-407, April.
    2. Christopher D. Carroll & Edmund Crawley & Jiri Slacalek & Kiichi Tokuoka & Matthew N. White, 2020. "Sticky Expectations and Consumption Dynamics," American Economic Journal: Macroeconomics, American Economic Association, vol. 12(3), pages 40-76, July.
    3. M Boschi & S d'Addona & A Goenka, 2012. "Testing external habits in an asset pricing model," CAMA Working Papers 2012-20, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    4. James M. Nason & Takashi Kano, 2004. "Business Cycle Implications of Habit Formation," Computing in Economics and Finance 2004 175, Society for Computational Economics.
    5. Jacobs Martin, 2016. "Accounting for Changing Tastes: Approaches to Explaining Unstable Individual Preferences," Review of Economics, De Gruyter, vol. 67(2), pages 121-183, August.
    6. Havranek, Tomas & Rusnak, Marek & Sokolova, Anna, 2017. "Habit formation in consumption: A meta-analysis," European Economic Review, Elsevier, vol. 95(C), pages 142-167.
    7. IWAMOTO Koichiro, 2011. "Food Consumption Expenditure and Habit Formation: Evidence from Japanese Household Panel Data," ESRI Discussion paper series 264, Economic and Social Research Institute (ESRI).
    8. Christopher D. Carroll & Jiri Slacalek & Martin Sommer, 2011. "International Evidence on Sticky Consumption Growth," The Review of Economics and Statistics, MIT Press, vol. 93(4), pages 1135-1145, November.
    9. M. Fatih Guvenen, 2003. "A Parsimonious Macroeconomic Model for Asset Pricing: Habit Formation or Cross-sectional Heterogeneity?," RCER Working Papers 499, University of Rochester - Center for Economic Research (RCER).
    10. Gómez Manuel A., 2010. "Endogenous Growth, Habit Formation and Convergence Speed," The B.E. Journal of Macroeconomics, De Gruyter, vol. 10(1), pages 1-32, January.
    11. Auray, Stéphane, 2009. "Consommation, effet de substitution intertemporelle et formation des habitudes," L'Actualité Economique, Société Canadienne de Science Economique, vol. 85(4), pages 437-473, décembre.
    12. Federico Di Pace & Matthias Hertweck, 2019. "Labor Market Frictions, Monetary Policy, and Durable Goods," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 32, pages 274-304, April.
    13. Emilio Fernandez-Corugedo, 2004. "Consumption Theory," Handbooks, Centre for Central Banking Studies, Bank of England, number 23, April.
    14. Raquel Carrasco & José M. Labeaga & J. David López-Salido, 2005. "Consumption and Habits: Evidence from Panel Data," Economic Journal, Royal Economic Society, vol. 115(500), pages 144-165, January.
    15. Choi, Kyoung Jin & Jeon, Junkee & Koo, Hyeng Keun, 2022. "Intertemporal preference with loss aversion: Consumption and risk-attitude," Journal of Economic Theory, Elsevier, vol. 200(C).
    16. Jaccard, Ivan, 2018. "Stochastic discounting and the transmission of money supply shocks," Working Paper Series 2174, European Central Bank.
    17. Orazio P. Attanasio, 1998. "Consumption Demand," NBER Working Papers 6466, National Bureau of Economic Research, Inc.
    18. Johdo, Wataru, 2009. "Habit persistence and stagnation," Economic Modelling, Elsevier, vol. 26(5), pages 1110-1114, September.
    19. Ma, Qingyin & Toda, Alexis Akira, 2022. "Asymptotic linearity of consumption functions and computational efficiency," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    20. Francisco Alvarez-Cuadrado & Jose Maria Casado & Jose Maria Labeaga, 2016. "Envy and Habits: Panel Data Estimates of Interdependent Preferences," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 78(4), pages 443-469, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:106:y:2023:i:c:s0304406823000228. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.