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 Wto 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 0.2to0.6.
Wang, Chong, Neng Wang, and Jinqiang Yang. "Optimal consumption and savings with stochastic income and recursive utility." Journal of Economic Theory 165 (2016): 292-331.
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