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PanelDataNotes-25

PanelDataNotes-25 - Econometric Analysis of Panel Data...

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Econometric Analysis of Panel Data William Greene Department of Economics Stern School of Business
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25. Modeling Heterogeneity in Classical Discrete Choice: Contrasts with Bayesian Estimation William Greene Department of Economics Stern School of Business New York University
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Abstract      T his study examines some aspects of mixed (random parameters)  logit modeling.  We present some familiar results in specification  and classical estimation of the random parameters model. We then  describe several extensions of the mixed logit model developed in  recent papers.  The relationship of the mixed logit model to  Bayesian treatments of the simple multinomial logit model is noted,  and comparisons and contrasts of the two methods are described.   The techniques described here are applied to two data sets, a  stated/revealed choice survey of commuters and one simulated  data set on brand choice.
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Random Parameters Models of Discrete Choice E conometric Methodology for Discrete Choice  Models Classical Estimation and Inference Bayesian Methodology M odel Building Developments The Mixed Logit Model Extensions of the Standard Model Modeling Individual Heterogeneity ‘Estimation’ of Individual Taste Parameters
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Useful References C lassical Train, K.,  Discrete Choice Methods with Simulation , Cambridge, 2003.  (Train) Hensher, D., Rose, J., Greene, W.,  Applied Choice Analysis Cambridge, 2005. Hensher, D., Greene, misc. papers, 2003-2005,  http://www.stern.nyu.edu/~wgreene B ayesian Allenby, G., Lenk, P., “Modeling Household Purchase Behavior with  Logistic Normal Regression,”  JASA , 1997. Allenby, G., Rossi, P., “Marketing Models of Consumer  Heterogeneity,”  Journal of Econometrics , 1999. (A&R) Yang, S., Allenby, G., “A Model for Observation, Structural, and  Household Heterogeneity in Panel Data,” Marketing Letters, 2000.
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A Random Utility Model Random Utility Model for Discrete Choice Among J alternatives at time t by person i. U itj = α j + β x itj + ε ijt α j = Choice specific constant x itj = Attributes of choice presented to person (Information processing strategy . Not all attributes will be evaluated. E.g., lexicographic utility functions over certain attributes.) β = ‘Taste weights,’ ‘Part worths,’ marginal utilities ε ijt = Unobserved random component of utility Mean=E[ ε ijt] = 0; Variance=Var[ ε ijt] = σ 2
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The Multinomial Logit Model    Independent type 1 extreme value (Gumbel): F( ε itj )  =  1 – Exp(-Exp( ε itj ))  Independence  across utility functions Identical variances σ 2  =  π 2 /6 Same taste parameters  for all individuals t j it j J (i) j it j j=1 ex p(α + β'x ) Prob[c hoic e j | i, t ] = ex p(α + β'x )
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What’s Wrong with this MNL Model?
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  • Fall '11
  • WillamGreene
  • Estimation theory, Likelihood function, Randomness, Bayesian inference, Bayes factor, Multinomial logit

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