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Asymptotic Methods for Asset Market Equilibrium Analysis

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Kenneth L. Judd
Sy-Ming Guu

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Abstract

General equilibrium analysis is difficult when asset markets are incomplete. We make the simplifying assumption that uncertainty is small and use bifurcation methods to compute Taylor series approximations for asset demand and asset market equilibrium. A computer must be used to derive these approximations since they involve large amounts of algebraic manipulation. To illustrate this method, we apply it to analyzing the allocative, price, and welfare effects of introducing a new derivative security. We find that the introduction of any derivative will raise the value of the risky asset relative to bonds.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 8135.

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Date of creation: Feb 2001
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Handle: RePEc:nbr:nberwo:8135

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Find related papers by JEL classification:
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques
D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets

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  2. Karl Schmedders, 2000. "Monopolistic Security Design In Finance Economies," Computing in Economics and Finance 2000 129, Society for Computational Economics. [Downloadable!]
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  3. Samuelson, Paul A, 1970. "The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances, and Higher Moments," Review of Economic Studies, Blackwell Publishing, vol. 37(4), pages 537-42, October. [Downloadable!] (restricted)
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  5. Elul Ronel, 1995. "Welfare Effects of Financial Innovation in Incomplete Markets Economies with Several Consumption Goods," Journal of Economic Theory, Elsevier, vol. 65(1), pages 43-78, February. [Downloadable!] (restricted)
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  7. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November. [Downloadable!] (restricted)
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  8. Hart, Oliver D., 1975. "On the optimality of equilibrium when the market structure is incomplete," Journal of Economic Theory, Elsevier, vol. 11(3), pages 418-443, December. [Downloadable!] (restricted)
  9. Schmedders, Karl, 1998. "Computing equilibria in the general equilibrium model with incomplete asset markets," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1375-1401, August. [Downloadable!] (restricted)
  10. Tesar, Linda L., 1995. "Evaluating the gains from international risksharing," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 42(1), pages 95-143, June. [Downloadable!] (restricted)
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  12. Gaspar, Jess & L. Judd, Kenneth, 1997. "Solving Large-Scale Rational-Expectations Models," Macroeconomic Dynamics, Cambridge University Press, vol. 1(01), pages 45-75, January. [Downloadable!]
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  13. Brown, Donald J & DeMarzo, Peter M & Eaves, B Curtis, 1996. "Computing Equilibria When Asset Markets Are Incomplete," Econometrica, Econometric Society, vol. 64(1), pages 1-27, January. [Downloadable!] (restricted)
  14. Michael Magill & Martine Quinzii, 2002. "Theory of Incomplete Markets, Volume 1," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262632543.
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  1. Bovenberg, A Lans & Uhlig, Harald, 2006. "Pension Systems and the Allocation of Macroeconomic Risk," CEPR Discussion Papers 5949, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  2. Devereux, Michael B & Sutherland, Alan, 2007. "Country Portfolio Dynamics," CEPR Discussion Papers 6208, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  3. Jinill Kim & Yun-kwong Kwok, 2007. "Higher-Order Properties of the ‘Exchange Rate Dynamics Redux’ Model," Computational Economics, Springer, vol. 30(4), pages 371-380, November. [Downloadable!] (restricted)
  4. Michael B. Devereux & Alan Sutherland, 2007. "Solving for Country Portfolios in Open Economy Macro Models," Working Papers 162007, Hong Kong Institute for Monetary Research. [Downloadable!]
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  5. Fousseni Chabi-Yo & Eric Ghysels & Eric Renault, 2008. "On Portfolio Separation Theorems with Heterogeneous Beliefs and Attitudes towards Risk," Working Papers 08-16, Bank of Canada. [Downloadable!]
  6. S. B. Aruoba & Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2005. "Comparing Solution Methods for Dynamic Equilibrium Economies," Levine's Bibliography 122247000000000855, UCLA Department of Economics. [Downloadable!]
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  7. Michael B. Devereux & Alan Sutherland, 2008. "Country portfolios in open economy macro models," Globalization and Monetary Policy Institute Working Paper 09, Federal Reserve Bank of Dallas. [Downloadable!]
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  8. Cédric Tille & Eric van Wincoop, 2007. "International capital flows," Staff Reports 280, Federal Reserve Bank of New York. [Downloadable!]
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  9. Jinill Kim & Andrew T. Levin & Tack Yun, 2007. "Diagnosing and treating bifurcations in perturbation analysis of dynamic macro models," Finance and Economics Discussion Series 2007-14, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  10. Michael B Devereux & Alan Sutherland, 2007. " Country Portfolio Dynamics," CDMA Conference Paper Series 0706, Centre for Dynamic Macroeconomic Analysis. [Downloadable!]
  11. Harald Uhlig, 2007. "Explaining Asset Prices with External Habits and Wage Rigidities in a DSGE Model," SFB 649 Discussion Papers SFB649DP2007-003a, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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