Structural Models Involving Highly Dimensional Fixed Point Problems: An Asymptotically Efficient Two-Stage Estimator
AbstractIn 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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- 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.
- 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.
- 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.
- Michael P. Keane & Kenneth I. Wolpin, 1994.
"The solution and estimation of discrete choice dynamic programming models by simulation and interpolation: Monte Carlo evidence,"
181, Federal Reserve Bank of Minneapolis.
- 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.
- V. Joseph Hotz & Robert A. Miller & Seth Sanders & Jeffrey Smith, 1992.
"A Simulation Estimator for Dynamic Models of Discrete Choice,"
9205, Harris School of Public Policy Studies, University of Chicago.
- 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.
- Hotz, J.V. & Miller, R.A. & Sanders, S. & Smith, J., 1992. "A Simulation Estimator for Dynamic Models of Discrete Choice," GSIA Working Papers 1992-13, Carnegie Mellon University, Tepper School of Business.
- Hotz, V.J. & Miller, R.A., 1991.
"Conditional Choice Probabilities and the Estimation of Dynamic Models,"
GSIA Working Papers
1992-12, Carnegie Mellon University, Tepper School of Business.
- 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.
- 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.
- 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
- 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.
- Andrew B. Abel & Janice C. Eberly, 1995.
"Optimal Investment with Costly Reversibility,"
NBER Working Papers
5091, National Bureau of Economic Research, Inc.
- 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.
- Newey, Whitney K., 1984. "A method of moments interpretation of sequential estimators," Economics Letters, Elsevier, vol. 14(2-3), pages 201-206.
- 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.
- 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.
- 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.
- 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.
- Miller, Robert A, 1984. "Job Matching and Occupational Choice," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 1086-120, December.
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