PanelDataNotes-25

PanelDataNotes-25 - Econometric Analysis of Panel Data William Greene Department of Economics Stern School of Business 25 Modeling Heterogeneity in

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Unformatted text preview: Econometric Analysis of Panel Data William Greene Department of Economics Stern School of Business 25. Modeling Heterogeneity in Classical Discrete Choice: Contrasts with Bayesian Estimation William Greene Department of Economics Stern School of Business New York University 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. 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 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. 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 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 itj j=1 ex p(α +β'x ) Prob[c hoic e j |i,t] = ex p(α +β'x ) What’s Wrong with this MNL Model?What’s Wrong with this MNL Model?...
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This note was uploaded on 01/05/2012 for the course B 55.9912 taught by Professor Willamgreene during the Fall '11 term at NYU.

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PanelDataNotes-25 - Econometric Analysis of Panel Data William Greene Department of Economics Stern School of Business 25 Modeling Heterogeneity in

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