IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v47y2011i4p409-416.html
   My bibliography  Save this article

The Markov consumption problem

Author

Listed:
  • Sattinger, Michael

Abstract

The paper provides a new model of consumption behavior under uncertainty as the solution to a continuous-time dynamic control problem in which an individual moves between employment and unemployment according to a Markov process. Behavior at low asset levels and at break-even points is analyzed. An iterative procedure is developed to derive numerical solutions. The solution takes the form of two curves relating consumption to assets, one for each state of employment.

Suggested Citation

  • Sattinger, Michael, 2011. "The Markov consumption problem," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 409-416.
    • Handle: RePEc:eee:mateco:v:47:y:2011:i:4:p:409-416
    DOI: 10.1016/j.jmateco.2011.04.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406811000474
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2011.04.001?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Hall, Robert E, 1978. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 971-987, December.
    2. Rosenzweig, Mark R & Wolpin, Kenneth I, 1993. "Credit Market Constraints, Consumption Smoothing, and the Accumulation of Durable Production Assets in Low-Income Countries: Investment in Bullocks in India," Journal of Political Economy, University of Chicago Press, vol. 101(2), pages 223-244, April.
    3. Miller, Bruce L, 1974. "Optimal Consumption with a Stochastic Income Stream," Econometrica, Econometric Society, vol. 42(2), pages 253-266, March.
    4. Deaton, Angus, 1991. "Saving and Liquidity Constraints," Econometrica, Econometric Society, vol. 59(5), pages 1221-1248, September.
    5. Gersovitz, Mark, 1988. "Saving and development," Handbook of Development Economics, in: Hollis Chenery & T.N. Srinivasan (ed.), Handbook of Development Economics, edition 1, volume 1, chapter 10, pages 381-424, Elsevier.
    6. Nicholas Kaldor, 1955. "Alternative Theories of Distribution," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(2), pages 83-100.
    7. Hyeng Keun Koo, 1998. "Consumption and Portfolio Selection with Labor Income: A Continuous Time Approach," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 49-65, January.
    8. Shankha Chakraborty & Mausumi Das, 2005. "Mortality, Human Capital and Persistent Inequality," Journal of Economic Growth, Springer, vol. 10(2), pages 159-192, June.
    9. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
    10. Stephen P. Zeldes, 1989. "Optimal Consumption with Stochastic Income: Deviations from Certainty Equivalence," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 104(2), pages 275-298.
    11. Banerjee, Abhijit V & Newman, Andrew F, 1993. "Occupational Choice and the Process of Development," Journal of Political Economy, University of Chicago Press, vol. 101(2), pages 274-298, April.
    12. Ray, Debraj & Streufert, Peter A, 1993. "Dynamic Equilibria with Unemployment Due to Undernourishment," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 61-85, January.
    13. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    14. Hey, John D, 1984. "Optimal Consumption When Income Follows a Markov Process," Bulletin of Economic Research, Wiley Blackwell, vol. 36(2), pages 109-118, November.
    15. David Cutler & Angus Deaton & Adriana Lleras-Muney, 2006. "The Determinants of Mortality," Journal of Economic Perspectives, American Economic Association, vol. 20(3), pages 97-120, Summer.
    16. Mark Huggett, 2004. "Precautionary Wealth Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 769-781.
    17. Oded Galor & Joseph Zeira, 1993. "Income Distribution and Macroeconomics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(1), pages 35-52.
    18. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(3), pages 659-684.
    19. Besley, Timothy, 1995. "Savings, credit and insurance," Handbook of Development Economics, in: Hollis Chenery & T.N. Srinivasan (ed.), Handbook of Development Economics, edition 1, volume 3, chapter 36, pages 2123-2207, Elsevier.
    20. Carroll, Christopher D., 2009. "Precautionary saving and the marginal propensity to consume out of permanent income," Journal of Monetary Economics, Elsevier, vol. 56(6), pages 780-790, September.
    21. Sadoulet, Elisabeth & Fukui, Seiichi & Janvry, Alan de, 1994. "Efficient share tenancy contracts under risk: The case of two rice-growing villages in Thailand," Journal of Development Economics, Elsevier, vol. 45(2), pages 225-243, December.
    22. Kimball, Miles S & Mankiw, N Gregory, 1989. "Precautionary Saving and the Timing of Taxes," Journal of Political Economy, University of Chicago Press, vol. 97(4), pages 863-879, August.
    23. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    24. Gersovitz, Mark, 1983. "Savings and Nutrition at Low Incomes," Journal of Political Economy, University of Chicago Press, vol. 91(5), pages 841-855, October.
    25. Carroll, Christopher D & Kimball, Miles S, 1996. "On the Concavity of the Consumption Function," Econometrica, Econometric Society, vol. 64(4), pages 981-992, July.
    26. Christopher D. Carroll, 2001. "A Theory of the Consumption Function, with and without Liquidity Constraints," Journal of Economic Perspectives, American Economic Association, vol. 15(3), pages 23-45, Summer.
    27. Chatterjee, Satyajit & Ravikumar, B., 1999. "Minimum Consumption Requirements: Theoretical And Quantitative Implications For Growth And Distribution," Macroeconomic Dynamics, Cambridge University Press, vol. 3(4), pages 482-505, December.
    28. Karen E. Dynan & Jonathan Skinner & Stephen P. Zeldes, 2004. "Do the Rich Save More?," Journal of Political Economy, University of Chicago Press, vol. 112(2), pages 397-444, April.
    29. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March.
    30. Behrman, Jere R. & Deolalikar, Anil B., 1988. "Health and nutrition," Handbook of Development Economics, in: Hollis Chenery & T.N. Srinivasan (ed.), Handbook of Development Economics, edition 1, volume 1, chapter 14, pages 631-711, Elsevier.
    31. Sheshinski, Eytan, 1989. "A simple model of optimum life-cycle consumption with earnings uncertainty," Journal of Economic Theory, Elsevier, vol. 49(1), pages 169-178, October.
    32. Huggett, Mark, 1993. "The risk-free rate in heterogeneous-agent incomplete-insurance economies," Journal of Economic Dynamics and Control, Elsevier, vol. 17(5-6), pages 953-969.
    33. Caballero, Ricardo J., 1990. "Consumption puzzles and precautionary savings," Journal of Monetary Economics, Elsevier, vol. 25(1), pages 113-136, January.
    34. Benveniste, L M & Scheinkman, J A, 1979. "On the Differentiability of the Value Function in Dynamic Models of Economics," Econometrica, Econometric Society, vol. 47(3), pages 727-732, May.
    35. Dora Costa & Richard H. Steckel, 1997. "Long-Term Trends in Health, Welfare, and Economic Growth in the United States," NBER Chapters, in: Health and Welfare during Industrialization, pages 47-90, National Bureau of Economic Research, Inc.
    36. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    37. Pierre-Olivier Gourinchas & Jonathan A. Parker, 2002. "Consumption Over the Life Cycle," Econometrica, Econometric Society, vol. 70(1), pages 47-89, January.
    38. Toche, Patrick, 2005. "A tractable model of precautionary saving in continuous time," Economics Letters, Elsevier, vol. 87(2), pages 267-272, May.
    39. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, December.
    40. Christopher D. Carroll & Patrick Toche, 2009. "A Tractable Model of Buffer Stock Saving," NBER Working Papers 15265, National Bureau of Economic Research, Inc.
    41. Christopher D. Carroll, 1997. "Buffer-Stock Saving and the Life Cycle/Permanent Income Hypothesis," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(1), pages 1-55.
    42. Glomm, Gerhard & Palumbo, Michael G., 1993. "Optimal intertemporal consumption decisions under the threat of starvation," Journal of Development Economics, Elsevier, vol. 42(2), pages 271-291, December.
    43. Thomas Piketty, 1997. "The Dynamics of the Wealth Distribution and the Interest Rate with Credit Rationing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(2), pages 173-189.
    44. Gary D. Thompson & Paul N. Wilson, 1994. "Ejido Reforms in Mexico: Conceptual Issues and Potential Outcomes," Land Economics, University of Wisconsin Press, vol. 70(4), pages 448-465.
    45. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    46. Lester G. Telser, 1955. "Safety First and Hedging," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(1), pages 1-16.
    47. Fogel, Robert William, 1993. "New findings on secular trends in nutrition and mortality: Some implications for population theory," Handbook of Population and Family Economics, in: M. R. Rosenzweig & Stark, O. (ed.), Handbook of Population and Family Economics, edition 1, volume 1, chapter 9, pages 433-481, Elsevier.
    48. Flemming, J. S., 1978. "Aspects of optimal unemployment insurance : Search, leisure, savings and capital market imperfections," Journal of Public Economics, Elsevier, vol. 10(3), pages 403-425, December.
    49. Schechtman, Jack, 1976. "An income fluctuation problem," Journal of Economic Theory, Elsevier, vol. 12(2), pages 218-241, April.
    50. Pyle, David H & Turnovsky, Stephen J, 1970. "Safety-First and Expected Utility Maximization in Mean-Standard Deviation Portfolio Analysis," The Review of Economics and Statistics, MIT Press, vol. 52(1), pages 75-81, February.
    51. Schechtman, Jack & Escudero, Vera L. S., 1977. "Some results on "an income fluctuation problem"," Journal of Economic Theory, Elsevier, vol. 16(2), pages 151-166, December.
    52. Deaton, Angus, 1992. "Understanding Consumption," OUP Catalogue, Oxford University Press, number 9780198288244, Decembrie.
    53. van Kooten, G Cornelis & Young, Douglas L & Krautkraemer, Jeffrey A, 1997. "A Safety-First Approach to Dynamic Cropping Decisions," European Review of Agricultural Economics, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 24(1), pages 47-63.
    Full references (including those not matched with items on IDEAS)

    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. Sattinger, Michael, 2013. "Safety first consumption," Journal of Economic Theory, Elsevier, vol. 148(1), pages 306-321.
    2. Wang, Chong & Wang, Neng & Yang, Jinqiang, 2016. "Optimal consumption and savings with stochastic income and recursive utility," Journal of Economic Theory, Elsevier, vol. 165(C), pages 292-331.
    3. Wang, Neng, 2007. "An equilibrium model of wealth distribution," Journal of Monetary Economics, Elsevier, vol. 54(7), pages 1882-1904, October.
    4. Wang, Neng, 2006. "Generalizing the permanent-income hypothesis: Revisiting Friedman's conjecture on consumption," Journal of Monetary Economics, Elsevier, vol. 53(4), pages 737-752, May.
    5. Wang, Neng, 2004. "Precautionary saving and partially observed income," Journal of Monetary Economics, Elsevier, vol. 51(8), pages 1645-1681, November.
    6. Richard M. H. Suen, 2011. "Concave Consumption Function and Precautionary Wealth Accumulation," Working papers 2011-23, University of Connecticut, Department of Economics.
    7. Emilio Fernandez-Corugedo, 2002. "Soft liquidity constraints and precautionary saving," Bank of England working papers 158, Bank of England.
    8. Bar Light, 2018. "Precautionary Saving in a Markovian Earnings Environment," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 29, pages 138-147, July.
    9. repec:ptu:bdpart:r201610 is not listed on IDEAS
    10. Markus K. Brunnermeier & Thomas M. Eisenbach & Yuliy Sannikov, 2012. "Macroeconomics with Financial Frictions: A Survey," Levine's Working Paper Archive 786969000000000384, David K. Levine.
    11. Valério Ercolani, 2016. "The precautionary saving: theories, measurements and policies," Economic Bulletin and Financial Stability Report Articles and Banco de Portugal Economic Studies, Banco de Portugal, Economics and Research Department.
    12. Orazio P. Attanasio, 1998. "Consumption Demand," NBER Working Papers 6466, National Bureau of Economic Research, Inc.
    13. Fulford, Scott L., 2013. "The effects of financial development in the short and long run: Theory and evidence from India," Journal of Development Economics, Elsevier, vol. 104(C), pages 56-72.
    14. Emilio Fernandez-Corugedo, 2004. "Consumption Theory," Handbooks, Centre for Central Banking Studies, Bank of England, number 23, April.
    15. Adrien Auclert, 2019. "Monetary Policy and the Redistribution Channel," American Economic Review, American Economic Association, vol. 109(6), pages 2333-2367, June.
    16. Jalan, Jyotsna & Ravallion, Martin, 2001. "Behavioral responses to risk in rural China," Journal of Development Economics, Elsevier, vol. 66(1), pages 23-49, October.
    17. repec:hal:wpspec:info:hdl:2441/5l6uh8ogmqildh09h6m8hj429 is not listed on IDEAS
    18. Céline Antonin, 2009. "Age, revenu et comportements d'épargne des ménages : une analyse théorique et empirique sur la période 1978-2006," Sciences Po publications info:hdl:2441/5l6uh8ogmqi, Sciences Po.
    19. Daria Pignalosa, 2019. "On the role of the utility function in the estimation of preference parameters," Metroeconomica, Wiley Blackwell, vol. 70(4), pages 793-820, November.
    20. Fulford, Scott L., 2015. "The surprisingly low importance of income uncertainty for precaution," European Economic Review, Elsevier, vol. 79(C), pages 151-171.
    21. Wang, Neng, 2009. "Optimal consumption and asset allocation with unknown income growth," Journal of Monetary Economics, Elsevier, vol. 56(4), pages 524-534, May.
    22. Kovacs, Agnes & Rondinelli, Concetta & Trucchi, Serena, 2021. "Permanent versus transitory income shocks over the business cycle," European Economic Review, Elsevier, vol. 139(C).

    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:47:y:2011:i:4:p:409-416. 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.