Economics 244, Spring 2001, University of California, Berkeley

ECONOMICS 244: APPLIED ECONOMETRICS.
DISCRETE CHOICE METHODS WITH SIMULATION
Spring Semester 2008
Instructor: Kenneth Train

Lecture Topics and Readings

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Textbook for the course: Discrete Choice Methods with Simulation

Topic Assigned Readings
January 24
Introduction &
Drawing from Densities Textbook, Ch.1 and Sections 9.1-9.2

January 31
Properties of Discrete Choice Model; Logit
Do problem set 1 Textbook, Chs. 2 and 3
D. McFadden, "Conditional Logit Analysis of Qualitative Choice Behavior," in P. Zarembka (ed.), Frontiers of Econometrics, New York, NY, Academic Press, 1974
K. Train, "A Validation Test of a Disaggregate Mode Choice Model," Transportation Research, Vol. 12, pp. 167-174, 1978.

February 7
Numerical Maximization
Do problem set 2 Textbook, Ch. 8
P. Ruud, An Introduction to Classical Econometric Theory, New York, Oxford University Press, 2000, Chapter 16 and Section 14.7.

February 14
GEV/Nested Logit
Do problem set 3 Textbook, Ch. 4

D. McFadden, "Modeling the Choice of Residential Location," in A. Karlquist, et al. (eds.), Spatial Interaction Theory and Planning Models, Amsterdam, North-Holland Publishing Company, 1978.
K. Train, Qualitative Choice Analysis, Cambridge, MA, MIT Press, 1986, Ch. 8: Automobile Ownership and Use
K. Train, D. McFadden, and M. Ben-Akiva, "The Demand for Local Telephone Service: A Fully Discrete Model of Residential Calling Patterns and Service Choices," RAND Journal of Economics, Vol. 18, No. 1, pp. 109-123, 1987.

February 21
Probit, part 1 Textbook, Ch. 5
J. Hausman and D. Wise, "A Conditional Probit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogenous Preferences," Econometrica, Vol. 48, No. 2, pp. 403-426, 1978.
S. Lerman and C. Manski, "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, Cambridge, MA, MIT Press, 1981.
M. Ben-Akiva and D. Bolduc, "Multinomial Probit with a Logit Kernel and a General Parametric Specification of the Covariance Structure," working paper, 1996, Department d'Economique, Universite Laval, Quebec, Canada.

February 28
Probit, part 2
Do problem set 4 A. Boersch-Supan and V. Hajivassiliou, "Smooth Unbiased Multivariate Probability Simulators for Maximum Likelihood Estimation of Limited Dependent Variables," Journal of Econometrics, Vol. 58, pp. 347-368, 1993.
V. Hajivassiliou, D. McFadden, and P. Ruud, "Simulation of Multivariate Normal Rectangle Probabilities and Their Derivatives," Journal of Econometrics, Vol. 72, No. 1-2, pp. 85-134, 1996.

March 6
Mixed Logit
Do problem set 5 Textbook, Ch. 6
D. Revelt and K. Train, "Mixed Logit with Repeated Choices," Review of Economics and Statistics, Vol. LXXX, No. 4, pp. 647-657, 1998. Preprint version is viewable here, but not the published reprint.
D. Brownstone and K. Train, "Forecasting New Product Penetration with Flexible Substitution Patterns," Journal of Econometrics, Vol. 89, No. 1-2, pp. 109-129, 1998/99.
D. McFadden and K. Train, "Mixed MNL Models of Discrete Response,"Journal of Applied Econometrics, Vol. 15, No. 5, pp. 447-470, 2000. Preprint version is viewable here, but not the published reprint.
K. Train, "Recreation Demand Models with Taste Variation," Land Economics, Vol. 74, No. 2, pp. 230-239, 1998. Preprint version is viewable here, but not the published reprint.
M. Ben-Akiva, Denis Bolduc, and Joan Walker, "Specification, Identification, and Estimation of the Logit Kernel (or Continuous Mixed Logit) Model", DRAFT, February 2001.

Macrch 13
Conditional Distributions of Individual-level Parameters Textbook, Ch. 11
D. Revelt and K. Train, "Customer-Specific Taste Parameters and Mixed Logit," working paper no. E00-274, Department of Economics University of California, Berkeley, 2000.

March 20
Other models: variations on our themes Textbook, Ch. 7

April 3
Simulation Assisted Classical Estimation: MSL, MSM, MSS Textbook, Ch. 10
D. McFadden, "Lectures on Simulation-Assisted Statistical Inference," [PostScript] presented at EC² Conference, Florence, Italy, 1996.
D. McFadden, "A Method of Simulated Moments for Estimation of Discrete Choice Models without Numerical Integration," Econometrica, Vol. 57, No. 5, pp. 995-1026, 1989.
A. Pakes and D. Pollard, "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Vol. 57, No. 5, pp. 1027-1057, 1989.
L.-F. Lee, "On the Efficiency of Methods of Simulated Moments and Simulated Likelihood Estimation of Discrete Response Models," Econometric Theory, Vol. 8, No. 4, pp. 518-552, 1992.
V. Hajivassiliou and D. McFadden, "The Method of Simulated Scores with Application to Models of External Debt Crises," Econometrica, Vol. 66, No. 4, pp. 863-896, 1998.
M. Keane, "A Computationally Practical Simulation Estimator for Panel Data," Econometrica, Vol. 62, No. 1, pp. 95-116, 1994.
V. Hajivassiliou and P. Ruud, "Classical Estimation Methods for LDV Models using Simulation," in Handbook of Econometrics, R. Engle and D. McFadden (eds.), New York, NY, Elsevier Science, 1994.

April 10
Variance reduction: antithetics and Halton draws Textbook, Section 9.3
C. Bhat, "Quasi-Random Maxium Simulated Likelihood Estimation of the Mixed Multinomial Logit Model," Transportation Research, Part B, Vol. 35, pp. 677-693, 2001. Preprint version is viewable here, but not the published reprint.
K. Train, "Halton Sequences for Mixed Logit," working paper no. E00-278, Department of Economics, University of California, Berkeley, 2000.
C. Bhat, "Simulation Estimation of Discrete Choice Models Using Randomized and Scrambled Halton Sequences Transportation Research, Part B, Vol. 37, No. 9, pp. 837-855, 2003.
S. Hess, K. Train, and J. Polak, "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, Vol. 40, No. 2, pp. 147-167, 2006. Preprint version is viewable here, but not the published reprint.
K. Train and Z. Sandor, "Quasi Simulation of Discrete Choice Models," Transportation Research, Part B, Vol. 38, pp. 313-327, 2004. Preprint version is viewable here, but not the published reprint.

April 17
Hierarchical Bayes
Do problem set 6 Textbook, Ch 12
S. Chib and E. Greenberg, "Understanding the Metropolis-Hastings Algorithm," The American Statistician, Vol. 49, pp. 327-335, 1995. Reproduced with permission from The American Statistician. Copyright 1995 by the American Statistical Association. All rights reserved
Sawtooth Software, "The CBC/HB System for Hierarchical Bayes Estimation,".
J. Huber and K. Train, "On the Similarity of Classical and Bayesian Estimates of Individual Mean Partworths," Marketing Letters, Vol. 12, No. 3, pp. 257-267, 2001. Preprint version is viewable here, but not the published reprint.
J. Albert and S. Chib, "Bayesian Analysis of Binary and Polychomotomous Response Data," Journal of the American Statistical Association, Vol. 88, No. 422, pp.669-679, 1993.
R. McCulloch and P. Rossi, "An Exact Likelihood Analysis of the Multinomial Probit Model," Journal of Econometrics, Vol. 64, No. 1-2, pp. 207-240, 1994.
G. Allenby and P. Rossi, "Marketing Models of Consumer Heterogeneity," Journal of Econometrics, Vol. 89, No. 1-2, pp. 57-78, 1998/99.

April 24
Endogeneity: BLP, Control functions, Latent instruments Textbook, forthcoming second edition, Ch. 13
S. Berry, "Estimating Discrete Choice Models of Product Differentiation," The Rand Journal of Economics, Vol. 25, No. 2, pp. 242-262, 1994.
S. Berry, A. Pakes, and J. Levinsohn, "Automobile Prices in Equilibrium," Econometrica,Vol. 63, No. 4, pp. 841-890, 1995.
S. Berry, A. Pakes, and J. Levinsohn, "Differentiated Products Demand Systems from a Combination of Micro and Macro Data: The New Vehicle Market," Journal of Political Economy, Vol. 112, No. 1, pp. 68-105, 2004.
K. Train and C. Winston, Vehicle Choice Behavior and the Declining Market of US Automakers, Internatinal Economic Review, Vol. 48, No. 4, pp. 1469-1496, 2007
A. Petrin and K. Train, Omitted Product Attributes in Differentiated Product Markets, working paper.

May 1
EM algorithms Textbook, forthcoming second edition, Ch. 14
K. Train, EM Algorithms for Nonparametric Estimation of Mixing Distributions, Journal of Choice Modeling, forthcoming.
K. Train, A Recursive Estimator for Random Coefficient Models, working paper.

Topic	Assigned Readings
January 24 Introduction & Drawing from Densities	Textbook, Ch.1 and Sections 9.1-9.2
January 31 Properties of Discrete Choice Model; Logit Do problem set 1	Textbook, Chs. 2 and 3 D. McFadden, "Conditional Logit Analysis of Qualitative Choice Behavior," in P. Zarembka (ed.), Frontiers of Econometrics, New York, NY, Academic Press, 1974 K. Train, "A Validation Test of a Disaggregate Mode Choice Model," Transportation Research, Vol. 12, pp. 167-174, 1978.
February 7 Numerical Maximization Do problem set 2	Textbook, Ch. 8 P. Ruud, An Introduction to Classical Econometric Theory, New York, Oxford University Press, 2000, Chapter 16 and Section 14.7.
February 14 GEV/Nested Logit Do problem set 3	Textbook, Ch. 4 D. McFadden, "Modeling the Choice of Residential Location," in A. Karlquist, et al. (eds.), Spatial Interaction Theory and Planning Models, Amsterdam, North-Holland Publishing Company, 1978. K. Train, Qualitative Choice Analysis, Cambridge, MA, MIT Press, 1986, Ch. 8: Automobile Ownership and Use K. Train, D. McFadden, and M. Ben-Akiva, "The Demand for Local Telephone Service: A Fully Discrete Model of Residential Calling Patterns and Service Choices," RAND Journal of Economics, Vol. 18, No. 1, pp. 109-123, 1987.
February 21 Probit, part 1	Textbook, Ch. 5 J. Hausman and D. Wise, "A Conditional Probit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogenous Preferences," Econometrica, Vol. 48, No. 2, pp. 403-426, 1978. S. Lerman and C. Manski, "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, Cambridge, MA, MIT Press, 1981. M. Ben-Akiva and D. Bolduc, "Multinomial Probit with a Logit Kernel and a General Parametric Specification of the Covariance Structure," working paper, 1996, Department d'Economique, Universite Laval, Quebec, Canada.
February 28 Probit, part 2 Do problem set 4	A. Boersch-Supan and V. Hajivassiliou, "Smooth Unbiased Multivariate Probability Simulators for Maximum Likelihood Estimation of Limited Dependent Variables," Journal of Econometrics, Vol. 58, pp. 347-368, 1993. V. Hajivassiliou, D. McFadden, and P. Ruud, "Simulation of Multivariate Normal Rectangle Probabilities and Their Derivatives," Journal of Econometrics, Vol. 72, No. 1-2, pp. 85-134, 1996.
March 6 Mixed Logit Do problem set 5	Textbook, Ch. 6 D. Revelt and K. Train, "Mixed Logit with Repeated Choices," Review of Economics and Statistics, Vol. LXXX, No. 4, pp. 647-657, 1998. Preprint version is viewable here, but not the published reprint. D. Brownstone and K. Train, "Forecasting New Product Penetration with Flexible Substitution Patterns," Journal of Econometrics, Vol. 89, No. 1-2, pp. 109-129, 1998/99. D. McFadden and K. Train, "Mixed MNL Models of Discrete Response,"Journal of Applied Econometrics, Vol. 15, No. 5, pp. 447-470, 2000. Preprint version is viewable here, but not the published reprint. K. Train, "Recreation Demand Models with Taste Variation," Land Economics, Vol. 74, No. 2, pp. 230-239, 1998. Preprint version is viewable here, but not the published reprint. M. Ben-Akiva, Denis Bolduc, and Joan Walker, "Specification, Identification, and Estimation of the Logit Kernel (or Continuous Mixed Logit) Model", DRAFT, February 2001.
Macrch 13 Conditional Distributions of Individual-level Parameters	Textbook, Ch. 11 D. Revelt and K. Train, "Customer-Specific Taste Parameters and Mixed Logit," working paper no. E00-274, Department of Economics University of California, Berkeley, 2000.
March 20 Other models: variations on our themes	Textbook, Ch. 7
April 3 Simulation Assisted Classical Estimation: MSL, MSM, MSS	Textbook, Ch. 10 D. McFadden, "Lectures on Simulation-Assisted Statistical Inference," [PostScript] presented at EC² Conference, Florence, Italy, 1996. D. McFadden, "A Method of Simulated Moments for Estimation of Discrete Choice Models without Numerical Integration," Econometrica, Vol. 57, No. 5, pp. 995-1026, 1989. A. Pakes and D. Pollard, "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Vol. 57, No. 5, pp. 1027-1057, 1989. L.-F. Lee, "On the Efficiency of Methods of Simulated Moments and Simulated Likelihood Estimation of Discrete Response Models," Econometric Theory, Vol. 8, No. 4, pp. 518-552, 1992. V. Hajivassiliou and D. McFadden, "The Method of Simulated Scores with Application to Models of External Debt Crises," Econometrica, Vol. 66, No. 4, pp. 863-896, 1998. M. Keane, "A Computationally Practical Simulation Estimator for Panel Data," Econometrica, Vol. 62, No. 1, pp. 95-116, 1994. V. Hajivassiliou and P. Ruud, "Classical Estimation Methods for LDV Models using Simulation," in Handbook of Econometrics, R. Engle and D. McFadden (eds.), New York, NY, Elsevier Science, 1994.
April 10 Variance reduction: antithetics and Halton draws	Textbook, Section 9.3 C. Bhat, "Quasi-Random Maxium Simulated Likelihood Estimation of the Mixed Multinomial Logit Model," Transportation Research, Part B, Vol. 35, pp. 677-693, 2001. Preprint version is viewable here, but not the published reprint. K. Train, "Halton Sequences for Mixed Logit," working paper no. E00-278, Department of Economics, University of California, Berkeley, 2000. C. Bhat, "Simulation Estimation of Discrete Choice Models Using Randomized and Scrambled Halton Sequences Transportation Research, Part B, Vol. 37, No. 9, pp. 837-855, 2003. S. Hess, K. Train, and J. Polak, "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, Vol. 40, No. 2, pp. 147-167, 2006. Preprint version is viewable here, but not the published reprint. K. Train and Z. Sandor, "Quasi Simulation of Discrete Choice Models," Transportation Research, Part B, Vol. 38, pp. 313-327, 2004. Preprint version is viewable here, but not the published reprint.
April 17 Hierarchical Bayes Do problem set 6	Textbook, Ch 12 S. Chib and E. Greenberg, "Understanding the Metropolis-Hastings Algorithm," The American Statistician, Vol. 49, pp. 327-335, 1995. Reproduced with permission from The American Statistician. Copyright 1995 by the American Statistical Association. All rights reserved Sawtooth Software, "The CBC/HB System for Hierarchical Bayes Estimation,". J. Huber and K. Train, "On the Similarity of Classical and Bayesian Estimates of Individual Mean Partworths," Marketing Letters, Vol. 12, No. 3, pp. 257-267, 2001. Preprint version is viewable here, but not the published reprint. J. Albert and S. Chib, "Bayesian Analysis of Binary and Polychomotomous Response Data," Journal of the American Statistical Association, Vol. 88, No. 422, pp.669-679, 1993. R. McCulloch and P. Rossi, "An Exact Likelihood Analysis of the Multinomial Probit Model," Journal of Econometrics, Vol. 64, No. 1-2, pp. 207-240, 1994. G. Allenby and P. Rossi, "Marketing Models of Consumer Heterogeneity," Journal of Econometrics, Vol. 89, No. 1-2, pp. 57-78, 1998/99.
April 24 Endogeneity: BLP, Control functions, Latent instruments	Textbook, forthcoming second edition, Ch. 13 S. Berry, "Estimating Discrete Choice Models of Product Differentiation," The Rand Journal of Economics, Vol. 25, No. 2, pp. 242-262, 1994. S. Berry, A. Pakes, and J. Levinsohn, "Automobile Prices in Equilibrium," Econometrica,Vol. 63, No. 4, pp. 841-890, 1995. S. Berry, A. Pakes, and J. Levinsohn, "Differentiated Products Demand Systems from a Combination of Micro and Macro Data: The New Vehicle Market," Journal of Political Economy, Vol. 112, No. 1, pp. 68-105, 2004. K. Train and C. Winston, Vehicle Choice Behavior and the Declining Market of US Automakers, Internatinal Economic Review, Vol. 48, No. 4, pp. 1469-1496, 2007 A. Petrin and K. Train, Omitted Product Attributes in Differentiated Product Markets, working paper.
May 1 EM algorithms	Textbook, forthcoming second edition, Ch. 14 K. Train, EM Algorithms for Nonparametric Estimation of Mixing Distributions, Journal of Choice Modeling, forthcoming. K. Train, A Recursive Estimator for Random Coefficient Models, working paper.