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Structural Models Involving Highly Dimensional Fixed Point Problems: An Asymptotically Efficient Two-Stage Estimator

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  • Victor Aguirregabiria

    (University of Chicago)

  • Pedro Mira

    (CEMFI)

Abstract

In this paper we consider a class of structural econometric models in which the distribution of the endogenous variables can be defined as the solution of a fixed-point problem. We propose a two-stage estimator which avoids repeated solution of the fixed point problem. The idea behind our estimator builds on previous work by Hotz and Miller (1993), Manski (1993) and Aguirregabiria and Mira (1999) in the context of dynamic discrete choice models. The first stage involves non-parametric estimation of the distribution of endogenous variables. In the second stage a pseudo-likelihood function is maximized. Given parameter values, the pseudo-likelihood function is computed by a single iteration on the fixed point operator, using the first stage non-parametric estimates as starting values. Our two-stage estimator is the value of the structural parameters that maximizes this pseudo-likelihood function. We state regularity conditions for consistency of this estimator and provide additional sufficient conditions under which the two-stage estimator can be used instead of a maximum likelihood estimator with no loss of asymptotic efficiency. We also show that these sufficient conditions will be satisfied if a Newton operator is used to solve the fixed point problem. Finally, we study the performance of this estimator in finite samples for several specific examples: a dynamic programming discrete choice model, a model of oligopolistic competition in a differentiated product market and a model of irreversible investment.

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 1702.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:1702

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  1. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521405515, April.
  2. Hotz, V Joseph & Robert A. Miller & Seth Sanders & Jeffrey Smith, 1994. "A Simulation Estimator for Dynamic Models of Discrete Choice," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 265-89, April.
  3. Pakes, Ariel S, 1986. "Patents as Options: Some Estimates of the Value of Holding European Patent Stocks," Econometrica, Econometric Society, vol. 54(4), pages 755-84, July.
  4. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521477451, April.
  5. V. Joseph Hotz & Robert A. Miller, 1992. "Conditional Choice Probabilities and the Estimation of Dynamic Models," Working Papers 9202, Harris School of Public Policy Studies, University of Chicago.
  6. Keane, Michael P & Wolpin, Kenneth I, 1994. "The Solution and Estimation of Discrete Choice Dynamic Programming Models by Simulation and Interpolation: Monte Carlo Evidence," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 648-72, November.
  7. repec:att:wimass:9106 is not listed on IDEAS
  8. James J. Heckman & Lance Lochner & Christopher Taber, 1998. "Explaining Rising Wage Inequality: Explorations with a Dynamic General Equilibrium Model of Labor Earnings with Heterogeneous Agents," NBER Working Papers 6384, National Bureau of Economic Research, Inc.
  9. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September.
  10. Ariel Pakes & Paul McGuire, 1992. "Computing Markov perfect Nash equilibria: numerical implications of a dynamic differentiated product model," Discussion Paper / Institute for Empirical Macroeconomics 58, Federal Reserve Bank of Minneapolis.
  11. Martin Browning & Lars Peter Hansen & James J. Heckman, 1999. "Micro Data and General Equilibrium Models," Discussion Papers 99-10, University of Copenhagen. Department of Economics.
  12. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521471626, April.
  13. Newey, Whitney K., 1984. "A method of moments interpretation of sequential estimators," Economics Letters, Elsevier, vol. 14(2-3), pages 201-206.
  14. Ariel Pakes & Paul McGuire, 1997. "Stochastic Algorithms for Dynamic Models: Markov Perfect Equilibrium, and the 'Curse' of Dimensionality," Cowles Foundation Discussion Papers 1144, Cowles Foundation for Research in Economics, Yale University.
  15. Bentolila, Samuel & Bertola, Giuseppe, 1990. "Firing Costs and Labour Demand: How Bad Is Eurosclerosis?," Review of Economic Studies, Wiley Blackwell, vol. 57(3), pages 381-402, July.
  16. Miller, Robert A, 1984. "Job Matching and Occupational Choice," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 1086-120, December.
  17. Abel, Andrew B & Eberly, Janice C, 1996. "Optimal Investment with Costly Reversibility," Review of Economic Studies, Wiley Blackwell, vol. 63(4), pages 581-93, October.
  18. Manski, Charles F., 1993. "Dynamic choice in social settings : Learning from the experiences of others," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 121-136, July.
  19. Ericson, Richard & Pakes, Ariel, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," Review of Economic Studies, Wiley Blackwell, vol. 62(1), pages 53-82, January.
  20. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521477444, April.
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