Aguirregabiria, Victor and Magesan, Arvind
(2013):
*Euler Equations for the Estimation of Dynamic Discrete Choice Structural.*

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## Abstract

We derive marginal conditions of optimality (i.e., Euler equations) for a general class of Dynamic Discrete Choice (DDC) structural models. These conditions can be used to estimate structural parameters in these models without having to solve for or approximate value functions. This result extends to discrete choice models the GMM-Euler equation approach proposed by Hansen and Singleton (1982) for the estimation of dynamic continuous decision models. We first show that DDC models can be represented as models of continuous choice where the decision variable is a vector of choice probabilities. We then prove that the marginal conditions of optimality and the envelope conditions required to construct Euler equations are also satisfied in DDC models. The GMM estimation of these Euler equations avoids the curse of dimensionality associated to the computation of value functions and the explicit integration over the space of state variables. We present an empirical application and compare estimates using the GMM-Euler equations method with those from maximum likelihood and two-step methods.

Item Type: | MPRA Paper |
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Original Title: | Euler Equations for the Estimation of Dynamic Discrete Choice Structural |

Language: | English |

Keywords: | Dynamic discrete choice structural models; Euler equations; Choice probabilities. |

Subjects: | C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C35 - Discrete Regression and Qualitative Choice Models ; Discrete Regressors ; Proportions C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis |

Item ID: | 46056 |

Depositing User: | Victor Aguirregabiria |

Date Deposited: | 10 Apr 2013 20:38 |

Last Modified: | 09 Oct 2019 16:38 |

References: | Ackerberg, D., X. Chen, and J. Hahn (2012): "A Practical Asymptotic Variance Estimator for Two-Step Semiparametric Estimators," The Review of Economics and Statistics, 94(2): 481--498. Adda, J. and R. Cooper (2000): "Balladurette and Juppette: A Discrete Analysis of Scrapping Subsidies," Journal of Political Economy, 108, 778-806. Aguirregabiria, V. and P. Mira (2002): "Swapping the nested fixed point algorithm: A class of estimators for discrete Markov decision models," Econometrica, 70, 1519-1543. Aguirregabiria, V. and P. Mira (2007): "Sequential estimation of dynamic discrete games," Econometrica, 75, 1-53. Anderson, S., A. De Palma, and J-F Thisse (1992): "Discrete choice theory of product differentiation." MIT press. Arcidiacono, P. and R. Miller (2011): "CCP Estimation of Dynamic Discrete Choice Models with Unobserved Heterogeneity," Econometrica, 79, 1823--1867. Bajari, P., L. Benkard and J. Levin (2007). Estimating dynamic models of imperfect competition. Econometrica 75, 1331-1370. Cho,.S. (2011): "An Empirical Model of Mainframe Computer Investment," Journal of Applied Econometrics, 26(1), 122-150. Das, M. (1992): "A Micro-econometric Model of Capital Utilization and Retirement: The Case of the Cement Industry," Review of Economic Studies, 59, 277-297. Fernández-Villaverde, J., J. Rubio-Ramírez, and M. Santos, 2006, Convergence Properties of the Likelihood of Computed Dynamic Models. Econometrica 74, 93-119. Geweke, J. (1996): "Monte Carlo simulation and numerical integration," in H. Amman, D. Kendrick, and J. Rust (eds.) Handbook of Computational Economics, chapter 15, pages 731-800. North-Holland. Amsterdam. Geweke, J. and M. Keane (2000): "Bayesian Inference for Dynamic Discrete Choice Models without the Need for Dynamic Programming." In book Simulation Based Inference and Econometrics: Methods and Applications, Mariano, Schuermann and Weeks (eds.), Cambridge University Press, 100-131. Geweke, J. and M. Keane, 2001. "Computationally intensive methods for integration in econometrics," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 56, pages 3463-3568. Elsevier. Gourieroux, C., and Monfort, A., 1997, Simulation-based econometric methods. Oxford University Press, USA. Gourieroux, C., & Monfort, A. (1993). Simulation-based inference: A survey with special reference to panel data models. Journal of Econometrics, 59(1), 5-33. Hajivassiliou, V. and P. Ruud (1994). Classical Estimation Methods for LDV Models Using Simulation, in The Handbook of Econometrics, Volume 4, D. McFadden and R. Engle (eds.). North-Holland: Amsterdam. Hansen, L. P., and K. J. Singleton (1982): "Generalized instrumental variables estimation of nonlinear rational expectations models," Econometrica, 50, 1269-1286. Hotz, J., and R.A. Miller (1993). Conditional choice probabilities and the estimation of dynamic models. Review of Economic Studies 60, 497-529. Hotz, J., R.A. Miller, S. Sanders, and J. Smith (1994). A simulation estimator for dynamic models of discrete choice. Review of Economic Studies 61, 265-89. Kasahara, H., and K. Shimotsu (2008): "Pseudo-likelihood estimation and bootstrap inference for structural discrete Markov decision models," Journal of Econometrics, 146(1), 92--106. Kasahara, H. (2009): "Temporary Increases in Tariffs and Investment: The Chilean Case," Journal of Business and Economic Statistics, 27(1), 113-127. Kennet, M. (1994) "A Structural Model of Aircraft Engine Maintenance," Journal of Applied Econometrics, 9, 351-368. Lerman, S. and C. Manski (1981). "On the Use of Simulated Frequencies to Approximate Choice Probabilities," in C. Manski and D. McFadden (eds.), Structural Analysis of Discrete Data with Econometric Applications, MIT Press, Cambridge, MA. McFadden, D., 1981, "Econometric Models of Probabilistic Choice," in C. Manski and D. McFadden (eds.), Structural Analysis of Discrete Data with Econometric Applications, MIT Press, Cambridge, MA. McFadden, D. (1989). "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, 57(5), 995-1026. Newey, W.K. (1984): "A Method of Moments Interpretation of Sequential Estimators," Economics Letters 14, pp. 201-206. Newey, W.K. (1994): "The Asymptotic Variance of Semiparametric Estimators," Econometrica, 62, 1349-1382. Newey, W.K. and D. F. McFadden (1994): "Large sample estimation and hypothesis testing", in R.F. Engle III and D.F. McFadden (eds.), The Handbook of Econometrics, vol. 4. North-Holland, Amsterdam. Miranda, M., and G. Schnitkey (1995): "An empirical model of asset replacement in dairy production," Journal of Applied Econometrics, 10, S41--S55. Norets, A. (2012), "Estimation of Dynamic Discrete Choice Models Using Artificial Neural Network Approximations," Econometric Reviews, 31, 84-106. Pakes, A., 1994, Dynamic structural models, problems and prospects, in C. Sims (ed.) Advances in Econometrics. Sixth World Congress, Cambridge University Press. Pakes, A. and D. Pollard (1989). "Simulation and the Asymptotics of Optimization Estimators," Econometrica, 57(5), 1027-57. Pesendorfer, M. and Schmidt-Dengler (2008). Asymptotic Least Squares Estimators for Dynamic Games. The Review of Economic Studies. Forthcoming. Powell, W. B. (2007). Approximate Dynamic Programming: Solving the curses of dimensionality (Vol. 703). Wiley-Interscience. Rust, J. (1987): "Optimal replacement of GMC bus engines: An empirical model of Harold Zurcher," Econometrica, 55, 999-1033. Rust, J. (1992): "Do People Behave According to Bellman's Principle of Optimality?" Working Paper E-92-10. The Hoover Institute. Stanford University. Rust, J. (1994): "Structural estimation of Markov decision processes," in R. E. Engle and McFadden (eds.) Handbook of Econometrics Volume 4, North-Holland. Rust, J. (1996): "Numerical dynamic programming in economics," Handbook of computational economics, 1, 619-729. Rust, J. and G. Rothwell (1995): "Optimal Response to a Shift in Regulatory Regime: The Case of the US Nuclear Power Industry," Journal of Applied Econometrics, 10, S75-S118. Stern, S. (1997). Simulation-based estimation. Journal of Economic Literature, 35, 2006--2039. Stokey, N., R. Lucas, and E. Prescott (1989): "Recursive methods in economic dynamics," Harvard University Press. Sturm, R. (1991): "A Structural Economic Model of Operating Cycle Management in European Nuclear Power Plants," manuscript, RAND Corporation. Wolpin, K. (1984). An Estimable Dynamic Stochastic Model of Fertility and Child Mortality. Journal of Political Economy, 92, 852-874. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/46056 |