Estimation with Numerical Integration on Sparse Grids
For the estimation of many econometric models, integrals without analytical solutions have to be evaluated. Examples include limited dependent variables and nonlinear panel data models. In the case of one-dimensional integrals, Gaussian quadrature is known to work efficiently for a large class of problems. In higher dimensions, similar approaches discussed in the literature are either very specific and hard to implement or suffer from exponentially rising computational costs in the number of dimensions - a problem known as the "curse of dimensionality" of numerical integration. We propose a strategy that shares the advantages of Gaussian quadrature methods, is very general and easily implemented, and does not suffer from the curse of dimensionality. Monte Carlo experiments for the random parameters logit model indicate the superior performance of the proposed method over simulation techniques.
|Date of creation:||Apr 2006|
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- Bhat, Chandra R., 2001. "Quasi-random maximum simulated likelihood estimation of the mixed multinomial logit model," Transportation Research Part B: Methodological, Elsevier, vol. 35(7), pages 677-693, August.
- McFadden, Daniel, 1989.
"A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration,"
Econometric Society, vol. 57(5), pages 995-1026, September.
- Daniel McFadden, 1987. "A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration," Working papers 464, Massachusetts Institute of Technology (MIT), Department of Economics.
- Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-96, March.
- Geweke, John, 1996.
"Monte carlo simulation and numerical integration,"
Handbook of Computational Economics,
in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 15, pages 731-800
- Vassilis A. Hajivassiliou & Axel Borsch-Supan, 1990.
"Smooth Unbiased Multivariate Probability Simulators for Maximum Likelihood Estimation of Limited Dependent Variable Models,"
Cowles Foundation Discussion Papers
960, Cowles Foundation for Research in Economics, Yale University.
- Borsch-Supan, Axel & Hajivassiliou, Vassilis A., 1993. "Smooth unbiased multivariate probability simulators for maximum likelihood estimation of limited dependent variable models," Journal of Econometrics, Elsevier, vol. 58(3), pages 347-368, August.
- Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
- Train,Kenneth E., 2009.
"Discrete Choice Methods with Simulation,"
Cambridge University Press, number 9780521747387, September.
- Hess, Stephane & Train, Kenneth E. & Polak, John W., 2006. "On the use of a Modified Latin Hypercube Sampling (MLHS) method in the estimation of a Mixed Logit Model for vehicle choice," Transportation Research Part B: Methodological, Elsevier, vol. 40(2), pages 147-163, February.
- Hajivassiliou, Vassilis A & Ruud, Paul A., 1993.
"Classical Estimation Methods for LDV Models Using Simulation,"
Department of Economics, Working Paper Series
qt3cg196fr, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
- Hajivassiliou, Vassilis A. & Ruud, Paul A., 1986. "Classical estimation methods for LDV models using simulation," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 40, pages 2383-2441 Elsevier.
- Vassilis A. Hajivassiliou & Paul A. Ruud, 1993. "Classical Estimation Methods for LDV Models Using Simulation," Cowles Foundation Discussion Papers 1051, Cowles Foundation for Research in Economics, Yale University.
- Vassilis A. Hajivassiliou and Paul A. Ruud., 1993. "Classical Estimation Methods for LDV Models Using Simulation," Economics Working Papers 93-219, University of California at Berkeley.
- V.A. Hajivassiliou & P. A. Ruud, 1993. "Classical Estimation Methods for LDV Models Using Simulation," Econometrics 9311002, EconWPA.
- Butler, J S & Moffitt, Robert, 1982. "A Computationally Efficient Quadrature Procedure for the One-Factor Multinomial Probit Model," Econometrica, Econometric Society, vol. 50(3), pages 761-64, May.
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