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Understanding Equilibrium Models with a Small and a Large Number of Agents

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Author Info
Wouter J. Den Haan

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Abstract

In this paper, I compare a two-agent asset pricing model with the corresponding model with a continuum of agents. In a two-agent economy, interest rates respond to because each agent represents half of the population. These interest rate effects facilitate consumption smoothing. An agent in a two-agent economy, however, can never lend more than the other agent is allowed to borrow, which prevents him from building a buffer stock of assets. For most parameter values, the first effect is more important. For some parameter values, the interest rate effects in the two-agent economy are so strong that a relaxation of the borrowing constraint reduces an agent's utility. In contrast to these differences, I find that for most parameter values there are no large differences in average interest rates across the two types of economies. In addition, I analyze the business cycle behavior of interest rates in an incomplete markets economy with a continuum of agents. The dynamic response of interest rates to aggregate shocks is a lot more complicated than the response in a complete markets economy and the magnitude of the response is bigger.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 5792.

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Date of creation: Oct 1996
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Handle: RePEc:nbr:nberwo:5792

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Find related papers by JEL classification:
E21 - Macroeconomics and Monetary Economics - - Macroeconomics: Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Determination of Interest Rates; Term Structure of Interest Rates

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  1. Lettau, M. & Uhlig, H., 1997. "Preferences, consumption smoothing, and risk premia," Discussion Paper 60, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  2. Lawrence J. Christiano & Jonas D.M. Fisher, 1997. "Algorithms for solving dynamic models with occasionally binding constraints," Working Paper 9711, Federal Reserve Bank of Cleveland. [Downloadable!]
    Other versions:
  3. Alexis Anagnostopoulos, 2004. "Consumption and Debt Dynamics with (Rarely Binding) Borrowing Constraints," Economics Working Papers ECO2004/34, European University Institute. [Downloadable!]
  4. Dirk Krueger & Hanno Lustig, 2006. "When is Market Incompleteness Irrelevant for the Price of Aggregate Risk (and when is it not)?," NBER Working Papers 12634, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  5. Martin Lettau, 2001. "Idiosyncratic risk and volatility bounds, or can models with idiosyncratic risk solve the equity premium puzzle?," Staff Reports 130, Federal Reserve Bank of New York. [Downloadable!]
  6. Eva Carceles-Poveda, 2009. "Asset Prices and Business Cycles under Market Incompleteness," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 12(3), pages 405-422, July. [Downloadable!] (restricted)
    Other versions:
  7. Krüger, Dirk & Lustig, Hanno, 2006. "The Irrelevance of Market Incompleteness for the Price of Aggregate Risk," CEPR Discussion Papers 5936, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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