Suen, Richard M. H. (2011): Concave consumption function and precautionary wealth accumulation.

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Abstract
This paper examines the theoretical foundations of precautionary wealth accumulation in a multiperiod model where consumers face uninsurable earnings risk and borrowing constraints. We begin by characterizing the consumption function of individual consumers. We show that consumption function is concave when the utility function has strictly positive third derivative and the inverse of absolute prudence is a concave function. These conditions encompass all HARA utility functions with strictly positive third derivative as special cases. We then show that when consumption function is concave, a meanpreserving spread in earnings risk would encourage wealth accumulation at both the individual and aggregate levels.
Item Type:  MPRA Paper 

Original Title:  Concave consumption function and precautionary wealth accumulation 
Language:  English 
Keywords:  Consumption function, borrowing constraints, precautionary saving 
Subjects:  D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D81  Criteria for DecisionMaking under Risk and Uncertainty D  Microeconomics > D9  Intertemporal Choice > D91  Intertemporal Household Choice ; Life Cycle Models and Saving E  Macroeconomics and Monetary Economics > E2  Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E21  Consumption ; Saving ; Wealth 
Item ID:  34774 
Depositing User:  Richard M. H. Suen 
Date Deposited:  18. Nov 2011 00:56 
Last Modified:  06. Oct 2015 07:45 
References:  ABOWD, J. and CARD, D. (1989), "On the Covariance Structure of Earnings and Hours Change," Econometrica, 57, 411445. AIYAGARI, R. (1994), "Uninsured Idiosyncratic Risk and Aggregate Saving," Quarterly Journal of Economics, 109, 659684. ALVAREZ, F. and STOKEY, N. L. (1998), "Dynamic Programming with Homogeneous Functions," Journal of Economic Theory, 82, 167189. B INDER, M., PESARAN, M. H. and SAMIEI, S. H. (2000), "Solution of Nonlinear Rational Expectations Models with Applications to FiniteHorizon LifeCycle Models of Consumption," Computational Economics, 15, 2557. BLUNDELL, R., and PRESTON, I. (1998), "Consumption Inequality and Income Uncertainty," Quarterly Journal of Economics, 113, 603640. BROWNING, M. and LUSARDI, A. (1996), "Household Saving: Micro Theories and Micro Facts," Journal of Economic Literature, 34, 17971855. CABALLERO, R. J. (1991), "Earnings Uncertainty and Aggregate Wealth Accumulation," American Economic Review, 81, 859871. CARROLL, C. D. (1992), "The BufferStock Theory of Saving: Some Macroeconomic Evidence," Brookings Papers on Economic Activity, 2, 61156. CARROLL, C. D. (1997), "BufferStock Saving and the Life Cycle/Permanent Income Hypothesis," Quarterly Journal of Economics, 112, 155. CARROLL, C.D. (2009), "Precautionary Saving and the Marginal Propensity to Consume out of Permanent Income," Journal of Monetary Economics, 56, 780790. CARROLL, C.D. (2011), "Theoretical Foundations of Buffer Stock Saving," (Manuscript) CARROLL, C. D. and KIMBALL, M. S. (1996), "On the Concavity of the Consumption Function," Econometrica, 64, 981992. CARROLL, C. D. and KIMBALL, M. S. (2005), "Liquidity Constraints and Precautionary Saving," (Manuscript) CARROLL, C. D. and SAMWICK, A. A. (1997), "The Nature of Precautionary Wealth," Journal of Monetary Economics, 40, 4171. CARROLL, C. D. and SAMWICK, A. A. (1998), "How Important is Precautionary Saving?" Review of Economics and Statistics, 80, 410419. DEATON, A. (1991), "Saving and Liquidity Constraints," Econometrica, 59, 12211248. GHIGLINO, C. and VENDITTI, A. (2007), "Wealth Inequality, Preference Heterogeneity and Macroeconomic Volatility in TwoSector Economies," Journal of Economic Theory, 135, 414441. GOLLIER, C. (2001), "Wealth Inequality and Asset Pricing," Review of Economics Studies, 68, 181203. GOLLIER, C. and ZECKHAUSER, R. J. (2002), "Horizon Length and Portfolio Risk," Journal of Risk and Uncertainty, 24, 195212. GOURINCHAS, P.O. and PARKER, J. A. (2001), "The Empirical Importance of Precautionary Saving," American Economic Review Papers and Proceedings, 91, 406412. GOURINCHAS, P.O. and PARKER, J. A. (2002), "Consumption over the Life Cycle," Econometrica, 70, 4789. HARDY, G., LITTLEWOOD, J. E. and PÓLYA, G. (1952), Inequalities, 2nd Edition (Cambridge: Cambridge University Press) HEALTHCOTE, J., STORESLETTEN, K. and VIOLANTE, G. L. (2009), "Quantitative Macroeconomics with Heterogeneous Households," Annual Review of Economics, 1, 319354. HUGGETT, M. (2004), "Precautionary Wealth Accumulation", Review of Economics Studies, 71, 769781. HUGGETT, M. and OSPINA S. (2001) "Aggregate Precautionary Savings: When is the Third Derivative Irrelevant?" Journal of Monetary Economics, 48, 373396. HUGGETT, M. and VIDON, E. (2002), "Precautionary Wealth Accumulation: A Positive Third Derivative is not Enough," Economics Letters, 76, 323329. JOHNSON, D. S., PARKER, J. A., and SOULELES, N. S. (2006), "Household Expenditure and the Income Tax Rebates of 2001," American Economic Review, 96, 15891610. KIMBALL, M. S. (1990), "Precautionary Saving in the Small and in the Large," Econometrica, 58, 5373. LUDVIGSON, S. (1999), "Consumption and Credit: A Model of TimeVarying Liquidity Constraints," Review of Economics and Statistics, 81, 434447. MENDELSON, H. and AMIHUD, Y. (1982), "Optimal Consumption Policy under Uncertain Income," Management Science, 28, 683697. MOFFITT, R. A. and GOTTSCHALK, P. (2011), "Trends in the Covariance Structure of Earnings in the U.S.: 19691987," Journal of Economic Inequality, 9, 439459. PARKER, J. A. and PRESTON, B. (2005), "Precautionary Saving and Consumption Fluctuations," American Economic Review, 95, 11191143. PRIMICERI, G.E. and VAN RENS, T. (2009), "Heterogeneous LifeCycle Profiles, Income Risk and Consumption Inequality," Journal of Monetary Economics, 56, 2039. RABAULT, G. (2002), "When do Borrowing Constraints Bind? Some New Results on the Income Fluctuation Problem," Journal of Economic Dynamics and Control, 26, 217245. ROCKAFELLAR, R. T. (1970), Convex Analysis (Princeton: Princeton University Press). ROTHSCHILD, M. and STIGLITZ, J. (1970), "Increasing Risk I: A Definition," Journal of Economic Theory, 2, 225243. SCHECHTMAN, J. (1976), "An Income Fluctuation Problem," Journal of Economic Theory, 12, 218241. SCHECHTMAN, J. and ESCUDERO, V. L. S. (1977), "Some Results on an Income Fluctuation Problem," Journal of Economic Theory, 16, 151166. SOULELES, N. S. (1999), "The Response of Household Consumption to Income Tax Refunds," American Economic Review, 89, 947958. STOKEY, N. L., LUCAS, R. E. and PRESCOTT, E. C. (1989), Recursive Methods in Economic Dynamics, (Cambridge: Harvard University Press). STORESLETTEN, K., TELMER, C. I. and YARON, A. (2004a), "Consumption and Risk Sharing over the Life Cycle," Journal of Monetary Economics, 51, 609633. STORESLETTEN, K., TELMER, C. I. and YARON, A. (2004b), "Cyclical Dynamics in Idiosyncratic Labor Market Risk," Journal of Political Economy, 112, 695717. WEIL, P. (1993), "Precautionary Savings and the Permanent Income Hypothesis," Review of Economic Studies, 60, 367383. ZELDES, S. P. (1989), "Optimal Consumption with Stochastic Income: Deviations from Certainty Equivalence," Quarterly Journal of Economics, 104, 275298. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/34774 