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

  • Victor Aguirregabiria

    (University of Chicago)

  • Pedro Mira

    (CEMFI)

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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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. 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.
  2. Hotz, V Joseph & Miller, Robert A, 1993. "Conditional Choice Probabilities and the Estimation of Dynamic Models," Review of Economic Studies, Wiley Blackwell, vol. 60(3), pages 497-529, July.
  3. Newey, Whitney K., 1984. "A method of moments interpretation of sequential estimators," Economics Letters, Elsevier, vol. 14(2-3), pages 201-206.
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  5. Ariel Pakes & Paul McGuire, 1994. "Computing Markov-Perfect Nash Equilibria: Numerical Implications of a Dynamic Differentiated Product Model," RAND Journal of Economics, The RAND Corporation, vol. 25(4), pages 555-589, Winter.
  6. Browning, Martin & Hansen, Lars Peter & Heckman, James J., 1999. "Micro data and general equilibrium models," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 8, pages 543-633 Elsevier.
  7. 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.
  8. V. Joseph Hotz & Robert A. Miller & Seth Sanders & Jeffrey Smith, 1992. "A Simulation Estimator for Dynamic Models of Discrete Choice," Working Papers 9205, Harris School of Public Policy Studies, University of Chicago.
  9. James Heckman & Lance Lochner & Christopher Taber, 1998. "Explaining Rising Wage Inequality: Explanations With A Dynamic General Equilibrium Model of Labor Earnings With Heterogeneous Agents," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 1(1), pages 1-58, January.
  10. Michael P. Keane & Kenneth I. Wolpin, 1994. "The solution and estimation of discrete choice dynamic programming models by simulation and interpolation: Monte Carlo evidence," Staff Report 181, Federal Reserve Bank of Minneapolis.
  11. repec:cup:cbooks:9780521405515 is not listed on IDEAS
  12. repec:cup:cbooks:9780521477444 is not listed on IDEAS
  13. 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.
  14. Miller, Robert A, 1984. "Job Matching and Occupational Choice," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 1086-120, December.
  15. repec:att:wimass:9106 is not listed on IDEAS
  16. 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.
  17. Ariel Pakes, 1986. "Patents as Options: Some Estimates of the Value of Holding European Patent Stocks," NBER Working Papers 1340, National Bureau of Economic Research, Inc.
  18. 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.
  19. repec:cup:cbooks:9780521477451 is not listed on IDEAS
  20. 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.
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