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On the Stochastic Steady-State Behavior of Optimal Asset Accumulation in the Presence of Random Wage Fluctuations and Incomplete Markets

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  • Richard H. Clarida

Abstract

We establish rigorously the existence and properties of the stationary probability distribution which characterizes the accumulation of non-contingent financial claims by a risk averse individual who confronts random wage fluctuations and incomplete insurance markets. We show that there exists a unique, almost-everywhere continuous stationary cumulative distribution function which characterizes the accumulation of non-contingent financial claims in a stochastic steady-state. This distribution is shown to possess a single mass point coinciding with the non-negative, finite borrowing limit faced by the individual. We establish that the stationary distribution which characterizes the asset accumulation of low time preference individuals is at least as large, in the sense of first-degree stochastic dominance, as that of individuals with higher rates of time preference. We prove that, so long as individuals are allowed to borrow in amounts which can be repayed with probability one, additive differences in the probability distribution governing random wage earnings imply inversely proportional additive differences in the stationary probability distributions which govern the accumulation of non-contingent financial claims.

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File URL: http://cowles.econ.yale.edu/P/cd/d07a/d0701.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 701.

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Length: 31 pages
Date of creation: Apr 1984
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Handle: RePEc:cwl:cwldpp:701

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  1. Danthine, Jean-Pierre & Donaldson, John B, 1981. "Stochastic Properties of Fast vs. Slow Growing Economies," Econometrica, Econometric Society, vol. 49(4), pages 1007-33, June.
  2. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  3. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
  4. Mendelssohn, Roy & Sobel, Matthew J., 1980. "Capital accumulation and the optimization of renewable resource models," Journal of Economic Theory, Elsevier, vol. 23(2), pages 243-260, October.
  5. 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.
  6. Hadar, Josef & Russell, William R., 1971. "Stochastic dominance and diversification," Journal of Economic Theory, Elsevier, vol. 3(3), pages 288-305, September.
  7. Lucas, Robert E, Jr, 1980. "Equilibrium in a Pure Currency Economy," Economic Inquiry, Western Economic Association International, vol. 18(2), pages 203-20, April.
  8. Sibley, David S., 1975. "Permanent and transitory income effects in a model of optimal consumption with wage income uncertainty," Journal of Economic Theory, Elsevier, vol. 11(1), pages 68-82, August.
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