
on Discrete Choice Models 
By:  Qian Chen (School of Public Finance & Public Policy, Central University of Finance & Economics, People's Republic of China); David E. Giles (Department of Economics, University of Victoria) 
Abstract:  We examine the finite sample properties of the maximum likelihood estimator for the binary logit model with random covariates. Analytic expressions for the firstorder bias and secondorder mean squared error function for the maximum likelihood estimator in this model are derived, and we undertake some numerical evaluations to analyze and illustrate these analytic results for the single covariate case. For various data distributions, the bias of the estimator is signed the same as the covariate’s coefficient, and both the absolute bias and the mean squared errors increase symmetrically with the absolute value of that parameter. The behaviour of a biasadjusted maximum likelihood estimator, constructed by subtracting the (maximum likelihood) estimator of the firstorder bias from the original estimator, is examined in a Monte Carlo experiment. This biascorrection is effective in all of the cases considered, and is recommended when the logit model is estimated by maximum likelihood with small samples. 
Keywords:  Logit model, bias, mean squared error, bias correction, random covariates 
JEL:  C01 C13 C25 
Date:  2009–08–05 
URL:  http://d.repec.org/n?u=RePEc:vic:vicewp:0906&r=dcm 
By:  Heller, Yuval 
Abstract:  In many situations a decision maker has incomplete psychological preferences, and the weak axiom of revealed preference (WARP) is often violated. In this paper we relax WARP, and replace it with convex axiom of revealed noninferiority (CARNI). An alternative x is revealed inferior to y if x is never chosen when y is in the convex hull of the choice set. CARNI requires that an alternative is chosen if it is not inferior to all other alternatives in the convex hull of the choice set. We apply CARNI in two models and axiomatize nonbinary choice correspondences. In the first model we impose the standard axioms of expected utility model, except that WARP is replaced by CARNI. We prove that it has a multipleutility representation: There is a unique convex set of vNM utilities, such that an alternative is chosen if and only if it is best with respect to one of the utilities in this set. In the second model we impose the axioms of the subjective expected utility, relax WARP in a similar way, and get multipleprior representation: There is a unique convex set of priors over the state of nature, such that an alternative is chosen if and only if it is best with respect to one of these priors. Both representations are closelyrelated to psychological insights of justifiable choice: The decision maker has several ways to evaluate acts, each with a different justification. Observable payoffirrelevant information during the choice triggers her to use a specific “anchoring” justification for the evaluation of the alternatives. 
Keywords:  uncertainty; multiple priors; multiple utilities; incomplete preferences; anchoring; framing; nonbinary choice. 
JEL:  D81 
Date:  2009–06–10 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:15645&r=dcm 
By:  Craig E. Landry; Paul Hindsley; Okmyung Bin; Jamie B. Kruse; John C. Whitehead; Kenneth R. Wilson 
Abstract:  The city of New Orleans suffered extensive damage as a result of Hurricane Katrina. Katrina overwhelmed the natural and built environment, inundating the city. As rebuilding proceeds, decisions on investment in protective measures will include the choice of lines of defense and the storm severity that design criteria should meet. An exhaustive list of protective measures has been studied in planning documents such as the Louisiana Coastal Protection and Restoration Technical Report (2009), with public comment solicited in town hall meetings. In this study we employ a different approach to examine public sentiment towards the selection and investment in protective measures. Our study utilizes a stated choice experiment with a stratified sample to investigate individuals’ willingnesstopay for rebuilding New Orleans’ manmade storm defenses, restoring natural storm protection, and improving evacuation options through a modernized transportation system. We target residents of the New Orleans metropolitan area as well as other US citizens. Our results indicate that individuals are willingtopay for increased storm protection for New Orleans, but the allocation of these resources differs among residents of the New Orleans metro area and other US citizens. Key Words: storm surge mitigation, conjoint analysis, willingness to pay, Hurricane Katrina, flood control, stated choice, rebuilding New Orleans, recovery 
JEL:  H43 Q51 R53 
Date:  2009 
URL:  http://d.repec.org/n?u=RePEc:apl:wpaper:0918&r=dcm 
By:  Steven T. Berry (Cowles Foundation, Yale University); Philip A. Haile (Cowles Foundation, Yale University) 
Abstract:  We consider identification of nonparametric random utility models of multinomial choice using "micro data," i.e., observation of the characteristics and choices of individual consumers. Our model of preferences nests random coefficients discrete choice models widely used in practice with parametric functional form and distributional assumptions. However, the model is nonparametric and distribution free. It allows choicespecific unobservables, endogenous choice characteristics, unknown heteroskedasticity, and highdimensional correlated taste shocks. Under standard "large support" and instrumental variables assumptions, we show identifiability of the random utility model. We demonstrate robustness of these results to relaxation of the large support condition and show that when it is replaced with a weaker "common choice probability" condition, the demand structure is still identified. We show that key maintained hypotheses are testable. 
Keywords:  Nonparametric identification, Discrete choice demand, Differentiated products 
JEL:  C35 
Date:  2009–09 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:1718&r=dcm 
By:  Franco Mariuzzo (The Geary Institute University College Dublin); Patrick Paul Walsh (SPIRe and The Geary Institute University College Dublin); Ciara Whelan (Univesity College Dublin) 
Abstract:  Since retail stores tend to host a subset of products available in the market, Ackerberg and Rysman (2005) allow logit errors to represent idiosyncratic unobserved consumer preferences over retail stores and products. Having product level data on store coverage we are able to estimate their logit, nested logit and random coefficients logit models of product demand jointly with cost, in a structural model of equilibrium, for Carbonated Soft Drink products. As Ackerberg and Rysmanâ€™ (2005) Monte Carlo study suggests; using standard logit errors does lead to predictable biases in estimated price elasticities and welfare. A counterfactual that imposes full coverage of stores by products, in our structural equilibrium, increases the estimated price elasticities and welfare. Competition in markets is more curtailed than assumed when one works with standard logit errors. 
Keywords:  Carbonated Soft Drinks, Differentiated products, discrete choice, Store coverage, structural model, price elasticities, welfare. 
JEL:  L11 L62 
Date:  2009–07–21 
URL:  http://d.repec.org/n?u=RePEc:ucd:wpaper:200922&r=dcm 