Partial Identification of Counter Factual Choice Probabilities

This article shows how to predict counterfactual discrete choice behavior when the presumed behavioral model partially identifies choice probabilities. The simple, general approach uses observable choice probabilities to partially infer the distribution of types in the population and then applies the results to predict behavior in unrealized choice settings. Two illustrative applications are given. One assumes only that persons have strict preferences. The other assumes strict preferences and utility functions that are linear in attribute bundles, with no restrictions on the shape of the distribution of preference parameters. Copyright 2007 by the Economics Department Of The University Of Pennsylvania And Osaka University Institute Of Social And Economic Research Association.

[1]  Charles F. Manski,et al.  Confidence Intervals for Partially Identified Parameters , 2003 .

[2]  J. Marschak Binary Choice Constraints on Random Utility Indicators , 1959 .

[3]  Alastair Scott,et al.  Quick Simultaneous Confidence Intervals for Multinomial Proportions , 1987 .

[4]  Rosa L. Matzkin Nonparametric and Distribution-Free Estimation of the Binary Threshold Crossing and the Binary Choice Models , 1992 .

[5]  D. McFadden Econometric Models of Probabilistic Choice , 1981 .

[6]  Francesca Molinari,et al.  Asymptotic Properties for a Class of Partially Identified Models , 2006 .

[7]  Guido W. Imbens,et al.  The Interpretation of Instrumental Variables Estimators in Simultaneous Equations Models with an Application to the Demand for Fish , 2000 .

[8]  Adam M. Rosen,et al.  Confidence Sets for Partially Identified Parameters that Satisfy a Finite Number of Moment Inequalities , 2006 .

[9]  E. S. Pearson,et al.  THE USE OF CONFIDENCE OR FIDUCIAL LIMITS ILLUSTRATED IN THE CASE OF THE BINOMIAL , 1934 .

[10]  L. Brown,et al.  Interval Estimation for a Binomial Proportion , 2001 .

[11]  C. Manski,et al.  On the Use of Simulated Frequencies to Approximate Choice Probabilities , 1981 .

[12]  D. McFadden Conditional logit analysis of qualitative choice behavior , 1972 .

[13]  Thierry Magnac,et al.  Identification and information in monotone binary models , 2007 .

[14]  A Agresti,et al.  On Small‐Sample Confidence Intervals for Parameters in Discrete Distributions , 2001, Biometrics.

[15]  T. Magnac,et al.  Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data , 2008 .

[16]  Joseph Glaz,et al.  Simultaneous Confidence Intervals and Sample Size Determination for Multinomial Proportions , 1995 .

[17]  Steven T. Berry,et al.  Automobile Prices in Market Equilibrium , 1995 .

[18]  C. Manski MAXIMUM SCORE ESTIMATION OF THE STOCHASTIC UTILITY MODEL OF CHOICE , 1975 .

[19]  J. Horowitz,et al.  Nonparametric Analysis of Randomized Experiments with Missing Covariate and Outcome Data , 2000 .

[20]  C. Manski,et al.  Inference on Regressions with Interval Data on a Regressor or Outcome , 2002 .

[21]  D. McFadden,et al.  MIXED MNL MODELS FOR DISCRETE RESPONSE , 2000 .

[22]  L. A. Goodman On Simultaneous Confidence Intervals for Multinomial Proportions , 1965 .

[23]  S. Afriat THE CONSTRUCTION OF UTILITY FUNCTIONS FROM EXPENDITURE DATA , 1967 .

[24]  D. Wise,et al.  A CONDITIONAL PROBIT MODEL FOR QUALITATIVE CHOICE: DISCRETE DECISIONS RECOGNIZING INTERDEPENDENCE AND HETEROGENEOUS PREFERENCES' , 1978 .

[25]  Peter C. Fishburn,et al.  Induced binary probabilities and the linear ordering polytope: a status report , 1992 .

[26]  C. Daganzo,et al.  Multinomial Probit and Qualitative Choice: A Computationally Efficient Algorithm , 1977 .

[27]  V. Chernozhukov,et al.  Estimation and Confidence Regions for Parameter Sets in Econometric Models , 2007 .

[28]  Bo E. Honoré,et al.  Bounds on Parameters in Panel Dynamic Discrete Choice Models , 2006 .

[29]  C. Manski Nonparametric Bounds on Treatment Effects , 1989 .

[30]  S. Cosslett DISTRIBUTION-FREE MAXIMUM LIKELIHOOD ESTIMATOR OF THE BINARY CHOICE MODEL1 , 1983 .

[31]  Saul Lach,et al.  Using Elicited Choice Probabilities to Estimate Random Utility Models: Preferences for Electricity Reliability , 2008 .

[32]  Daniel McFadden,et al.  Modelling the Choice of Residential Location , 1977 .

[33]  C. Blyth,et al.  Binomial Confidence Intervals , 1983 .

[34]  J. Glaz,et al.  Simultaneous confidence intervals for multinomial proportions , 1999 .

[35]  P. Samuelson Consumption Theory in Terms of Revealed Preference , 1948 .

[36]  George Casella,et al.  Refining binomial confidence intervals , 1986 .

[37]  C. Manski Monotone Treatment Response , 2009, Identification for Prediction and Decision.

[38]  C. Manski Identification of Binary Response Models , 1988 .

[39]  D. McFadden Revealed stochastic preference: a synthesis , 2005 .