Modeling Consumer Decision Making and Discrete Choice Behavior

Stochastic Frontier ModelsWilliam GreeneStern School of BusinessNew York University0Introduction1Efficiency Measurement2Frontier Functions3Stochastic Frontiers4Production and Cost5Heterogeneity6Model Extensions7Panel Data8Applications

[Part 8] #/27Stochastic FrontierModelsApplications1Range of ApplicationsRegulated industries railroads, electricity, public servicesHealth care delivery nursing homes, hospitals, health care systems (WHO)Banking and FinanceMany, many (many) other industries. See Lovell and Schmidt survey[Part 8] #/27Stochastic FrontierModelsApplications2Discrete VariablesCount data frontierOutcomes inside the frontier: Preserve discrete outcomePatents (Hofler, R. A Count Data Stochastic Frontier Model,Infant Mortality (Fe, E., On the Production of Economic Bads)[Part 8] #/27Stochastic FrontierModelsApplications3Count FrontierP(y*|x)=Poisson Model for optimal outcome

Effects the distribution: P(y|y*,x)=P(y*-u|x)= a different count model for the mixture of two count variablesEffects the mean:E[y*|x]=(x) while E[y|x]=u (x) with 0 < u < 1. (A mixture model)Other formulations.[Part 8] #/27Stochastic FrontierModelsApplications4Alvarez, Arias, Greene Fixed ManagementYit = f(xit,mi*) where mi* = managementActual mi = mi* - ui. Actual falls short of idealTranslates to a random coefficients stochastic frontier modelEstimated by simulationApplication to Spanish dairy farms[Part 8] #/27Stochastic FrontierModelsApplications5Fixed Management as an Input Implies Time Variation in Inefficiency

[Part 8] #/27Stochastic FrontierModelsApplications6Random Coefficients Frontier Model

[Chamberlain/Mundlak: Correlation mi* (not mi-mi*) with xit][Part 8] #/27Stochastic FrontierModelsApplications7Estimated Model

First order production coefficients (standard errors). Quadratic terms not shown.[Part 8] #/27Stochastic FrontierModelsApplications8Inefficiency Distributions

Without Fixed ManagementWith Fixed Management[Part 8] #/27Stochastic FrontierModelsApplications9Holloway, Tomberlin, Irz: Coastal Trawl FisheriesApplication of frontier to coastal fisheriesHierarchical Bayes estimationTruncated normal model and exponentialPanel data applicationTime varying inefficiencyThe good captain effect vs. inefficiency[Part 8] #/27Stochastic FrontierModelsApplications10SportsKahane: Hiring practices in hockeyOutput=payroll, Inputs=coaching, franchise measuresEfficiency in payroll related to team performanceBattese/Coelli panel data translog modelKoop: Performance of baseball playersAggregate output: singles, doubles, etc.Inputs = year, league, teamPolicy relevance? (Just for fun)[Part 8] #/27Stochastic FrontierModelsApplications11Macro Performance Koop et al.Productivity Growth in a stochastic frontier modelCountry, year, Yit = ft(Kit,Lit)EitwitBayesian estimationOECD Countries, 1979-1988[Part 8] #/27Stochastic FrontierModelsApplications12Mutual Fund PerformanceStandard CAPMStochastic frontier addedExcess return=a+b*Beta +v uSub-model for determinants of inefficiencyBayesian frameworkPooled various different distribution estimates[Part 8] #/27Stochastic FrontierModelsApplications13Energy ConsumptionDerived input to household and community production

Cost analogy

Panel data, statewide electricity consumption: Filippini, Farsi, et al.[Part 8] #/27Stochastic FrontierModelsApplicationsHospitals Usually cost studiesMultiple outputs case mixQuality is a recurrent theme Complexity unobserved variableEndogeneityRosko: US Hospitals, multiple outputs, panel data, determinants of inefficiency = HMO penetration, payment policies, also includes indicators of heterogeneityAustralian hospitals: Fit both production and cost frontiers. Finds large cost savings from removing inefficiency.[Part 8] #/27Stochastic FrontierModelsApplications15Law FirmsStochastic frontier applied to service industryOutput=RevenueInputs=Lawyers, associates/partners ratio, paralegals, average legal experience, national firmAnalogy drawn to hospitals literature quality aspect of output is a difficult problem[Part 8] #/27Stochastic FrontierModelsApplications16FarmingHundreds of applicationsMajor proving ground for new techniquesMany high quality, very low level micro data setsODonnell/Griffiths Philippine rice farmsLatent class favorable or unfavorable climatePanel data production modelBayesian has a difficult time with latent class models. Classical is a better approach[Part 8] #/27Stochastic FrontierModelsApplications17Railroads and other Regulated IndustriesFilippini Maggi: Swiss railroads, scale effects etc. Also studied effect of different panel data estimatorsCoelli Perelman, European railroads. Distance function. Developed methodology for distance functionsMany authors: Electricity (C&G). Used as the standard test data for Bayesian estimators[Part 8] #/27Stochastic FrontierModelsApplications18BankingDozens of studiesWheelock and Wilson, U.S. commercial banksTurkish Banking systemBanks in transition countriesU.S. Banks Fed studies (hundreds of studies)Typically multiple output cost functionsDevelopment area for new techniques Many countries have very high quality data available[Part 8] #/27Stochastic FrontierModelsApplications19SewersNew York State sewage treatment plants200+ statewide, several thousand employeesUsed fixed coefficients technologylnE = a + b*lnCapacity + v u; b < 1 implies economies of scale (almost certain)Fit as frontier functions, but the effect of market concentration was the main interest[Part 8] #/27Stochastic FrontierModelsApplications20Summary[Part 8] #/27Stochastic FrontierModelsApplications21Inefficiency

[Part 8] #/27Stochastic FrontierModelsApplications22MethodologiesData Envelopment AnalysisHUGE User baseLargely atheoreticalApplications in management, consulting, etc.Stochastic Frontier ModelingMore theoretically based model basedMore active technique development literatureEqually large applications pool[Part 8] #/27Stochastic FrontierModelsApplications23SFA ModelsNormal Half NormalTruncationHeteroscedasticityHeterogeneity in the distribution of uiNormal-Gamma, Exponential, RayleighClassical vs. Bayesian applicationsFlexible functional forms for inefficiencyThere are yet others in the literature[Part 8] #/27Stochastic FrontierModelsApplications24Modeling SettingsProduction and Cost ModelsMultiple output modelsCost functionsDistance functions, profits and revenue functions[Part 8] #/27Stochastic FrontierModelsApplications25Modeling IssuesAppropriate model frameworkCost, production, etc.Functional formHow to handle observable heterogeneity where do we put the zs?Panel dataIs inefficiency time invariant?Separating heterogeneity from inefficiencyDealing with endogeneityAllocative inefficiency and the Greene problem[Part 8] #/27Stochastic FrontierModelsApplications26Range of ApplicationsRegulated industries railroads, electricity, public servicesHealth care delivery nursing homes, hospitals, health care systems (WHO, AHRQ)Banking and FinanceMany other industries. See Lovell and Schmidt Efficiency and Productivity 27 page bibliography. Table of over 200 applications since 2000[Part 8] #/27Stochastic FrontierModelsApplications27