Optimal consumption and savings with stochastic income and recursive utility

We develop a tractable incomplete-markets model with an earnings process Y subject to permanent shocks and borrowing constraints. Financial frictions cause the marginal (certainty equivalent) value of wealth W to be greater than unity and decrease with liquidity w = W/Y . Additionally, financial frictions cause consumption to decrease with this endogenously determined marginal value of liquidity. Risk aversion and the elasticity of inter-temporal substitution play very different roles on consumption and the dispersion of w. Permanent earnings shocks, especially large discrete stochastic jumps, make consumption smoothing quantitatively difficult to achieve. Borrowing constraints and permanent discrete jump shocks can generate empirically plausible values for marginal propensities to consume in the range of 0.2 to 0.6. © 2016 Elsevier Inc. All rights reserved. ✩ We thank Cristina De Nardi, Lars Peter Hansen, Dirk Krueger, Ricardo Lagos, Tom Sargent, Stijn Van Nieuwerburgh, Suresh Sundaresan, Amir Yaron, Steve Zeldes, two anonymous referees, and seminar participants at Columbia University for helpful comments. Neng Wang acknowledges support by the National Natural Science Foundation of China (#71472117) and the Chazen Institute of International Business at Columbia Business School. Jinqiang Yang acknowledges support by National Natural Science Foundation of China (#71202007, #71522008), New Century Excellent Talents in University (#NCET-13-0895), Fok Ying Tong Education Foundation (#151086), and the Program for Innovative Research Team of Shanghai University of Finance and Economics (#2016110241). * Corresponding author at: Columbia Business School, New York, NY, United States. E-mail addresses: [email protected] (C. Wang), [email protected] (N. Wang), [email protected] (J. Yang). http://dx.doi.org/10.1016/j.jet.2016.04.002 0022-0531/© 2016 Elsevier Inc. All rights reserved. C. Wang et al. / Journal of Economic Theory 165 (2016) 292–331 293 JEL classification: G11; G31; E2