, Econometric models of probabilistic choice, Structural Analysis of Discrete Data with Econometric Applications, 1981.
A theory of the perturbed consumer with general budgets, 2012. ,
Estimating Industry Conduct in Differentiated Products Markets, 2019. ,
Measuring market power in the ready-to-eat cereal industry, Econometrica, vol.69, pp.307-342, 2001. ,
On the surjectivity of the mapping between utilities and choice probabilities, Quantitative Economics, vol.4, pp.149-155, 2013. ,
Mergers, brand competition, and the price of a pint, European Economic Review, vol.48, pp.617-643, 2004. ,
Improving the performance of random coefficients demand models: the role of optimal instruments, Journal of Econometrics, vol.179, pp.83-98, 2014. ,
Model selection tests for nonlinear dynamic models, The Econometrics Journal, vol.5, pp.1-39, 2002. ,
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, Probabilistic choice (models) as a result of balancing multiple goals, vol.57, p.3069, 2013.
, Notes: Summary statistics across 500 Monte Carlo replications. The bias is measured by the mean error. The mean square error (MSE) measures the accuracy
, Notes: Summary statistics across 500
The bias is measured by the mean error. The mean square error (MSE) measures the accuracy ,
, Notes: Summary statistics across 500
The bias is measured by the mean error. The mean square error (MSE) measures the accuracy ,
, Notes: Summary statistics across 500
The bias is measured by the mean error. The mean square error (MSE) measures the accuracy ,
Identification With Additively Separable Heterogeneity, Econometrica, vol.87, pp.1021-1054, 2019. ,
, Discrete choice theory of product differentiation, 1992.
Weak instruments in IV regression: Theory and practice, 2018. ,
Large market asymptotics for differentiated product demand estimators with economic models of supply, Econometrica, vol.84, pp.1961-1980, 2016. ,
Common ownership and competition in the ready-to-eat cereal industry, 2018. ,
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Optimal product variety in radio markets, The RAND Journal of Economics, vol.47, pp.463-497, 2016. ,
Connected substitutes and invertibility of demand, Econometrica, vol.81, pp.2087-2111, 2013. ,
Identification in differentiated products markets, Annual review of Economics, vol.8, pp.27-52, 2016. ,
Voluntary export restraints on automobiles: Evaluating a trade policy, American Economic Review, vol.63, pp.400-430, 1995. ,
Additional information for:Comments on Alternative models of demand for automobiles by Charlotte Wojcik, Economics Letters, vol.74, pp.43-51, 2001. ,
Estimating discrete-choice models of product differentiation, The RAND Journal of Economics, vol.25, pp.242-262, 1994. ,
Identification in differentiated products markets using market level data, Econometrica, vol.82, pp.1749-1797, 2014. ,
Does merger simulation work? Evidence from the Swedish analgesics market, American Economic Journal: Applied Economics, vol.8, pp.125-64, 2016. ,
Liberalizing a distribution system: the European car market, Journal of the European Economic Association, vol.4, pp.216-251, 2006. ,
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A Paired Combinational Logit Model for Travel Demand Analysis, Selected Proceedings of the Fifth World Conference on Transport Research, vol.4, pp.295-309, 1989. ,
Market Counterfactuals and the Specification of Multi-Product Demand: A Nonparametric Approach, 2019. ,
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The Ready-to-eat Breakfast Cereal Industry in 1994 (A), 1996. ,
, Recherches sur les principes mathématiques de la théorie des richesses par Augustin Cournot, chez L. Hachette, 1838.
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Application of Duality Theory, Frontiers of Quantitative Economics, vol.2, 1974. ,
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Improving the numerical performance of static and dynamic aggregate discrete choice random coefficients demand estimation, Econometrica, vol.80, pp.2231-2267, 2012. ,
Mergers in a Model with Complementarity, 2018. ,
, The Inverse Product Differentiation Logit Model, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02183411
Measuring substitution patterns in differentiated products industries, 2017. ,
Valuing new goods in a model with complementarity: Online newspapers, The American Economic Review, vol.97, pp.713-744, 2007. ,
Product differentiation and oligopoly in international markets: The case of the US automobile industry, Econometrica, pp.891-951, 1995. ,
Tax design in the alcohol market, Journal of Public Economics, vol.172, pp.20-35, 2019. ,
Blurred boundaries: a flexible approach for segmentation applied to the car market, 2018. ,
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Competitive analysis with differenciated products, Annales d'Economie et de Statistique, pp.159-180, 1994. ,
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Identification and Estimation of Demand for Bundles: The Case of the RTE Cereal Industry, 2019. ,
Estimation of Random-Coefficient Demand Models: Two Empiricists' Perspective, Review of Economics and Statistics, vol.96, pp.34-59, 2014. ,
The paired combinatorial logit model: properties, estimation and application, Transportation Research Part B: Methodological, vol.34, pp.75-89, 2000. ,
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Conditional logit analysis of qualitative choice behavior, Frontiers in Econometrics, pp.105-142, 1974. ,
Mixed MNL models for discrete response, Journal of applied Econometrics, vol.15, pp.447-470, 2000. ,
Estimating Industry Conduct in Differentiated Products Markets, 2019. ,
Pass-Through and the Prediction of Merger Price Effects, The Journal of Industrial Economics, vol.64, pp.683-709, 2016. ,
Shape Restrictions for Structural Demand Estimation: Beyond the ARUM, 2019. ,
Not so demanding: Demand structure and firm behavior, American Economic Review, vol.107, pp.3835-74, 2017. ,
Mergers with Differentiated Products: The Case of the Ready-to-Eat Cereal Industry, The RAND Journal of Economics, vol.31, pp.307-342, 1997. ,
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Substitutes and complements, The New Palgrave Dictionary of Economics, vol.1, issue.8, pp.6434-6438, 2008. ,
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Quantifying the benefits of new products: The case of the minivan, Journal of political Economy, vol.110, pp.705-729, 2002. ,
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Spatial price competition: a semiparametric approach, Econometrica, vol.70, pp.1111-1153, 2002. ,
Just How Sensitive are Instrumental Variable Estimates?, Foundations and Trends in Accounting, vol.10, pp.204-237, 2016. ,
Improving the performance of random coefficients demand models: the role of optimal instruments, Journal of Econometrics, vol.179, pp.83-98, 2014. ,
Price competition in US brewing, The Journal of Industrial Economics, vol.56, pp.1-31, 2008. ,
Market definition with differentiated products: the Post/Nabisco cereal Merger, Antitrust LJ, vol.68, p.163, 2000. ,
Fast," robust", and approximately correct: estimating mixed demand systems, National Bureau of Economic Research, 2019. ,
Complementarity: An essay on the 40th anniversary of the Hicks-Allen revolution in demand theory, Journal of Economic literature, vol.12, pp.1255-1289, 1974. ,
A weak instrument F-test in linear IV models with multiple endogenous variables, Journal of Econometrics, vol.190, pp.212-221, 2016. ,
Does advertising overcome brand loyalty? Evidence from the breakfast-cereals market, Journal of Economics & Management Strategy, vol.13, pp.241-272, 2004. ,
High performance quadrature rules: How numerical integration affects a popular model of product differentiation, 2011. ,
Market power and joint dominance in UK brewing, The Journal of Industrial Economics, vol.52, pp.133-163, 2004. ,
International price discrimination in the European car market, The RAND Journal of Economics, pp.240-268, 1996. ,
Evidence on the accuracy of merger simulations, Review of Economics and Statistics, vol.95, pp.1584-1600, 2013. ,
Pass-through as an economic tool: Principles of incidence under imperfect competition, Journal of Political Economy, vol.121, pp.528-583, 2013. ,
Alternative models of demand for automobiles, Economics Letters, vol.68, pp.113-118, 2000. ,
Using Berry and Haile (2014)'s setting, he proposes to non-parametrically estimate inverse demand models, 2019. ,
, , 2012.
, The function G is homogeneous of degree one if, for all ? > 0, G (?s) = ?G (s)
, (iii) lim i?? |? x i f (x i )| = +? whenever x 1 , x 2 , . . . is a sequence in int (domf ) converging to a point x ? bd (domf ). A pair (int (domf ) , f ) is a convex function of Legendre type if int (domf ) is an open convex set and f is a strictly convex function on int (domf ) that is essentially smooth
, Let f : R J+1 ? R?{+?} be a proper convex function. Assume that f is continuous and essentially smooth.The following five conditions are equivalent 1. x * = ?f (x), x ? int, 1970.
,
,
, Assume that (int(domf ), f ) is a convex function of Legendre type. Then (int(domf * ), f * ) is also a convex function of Legendre type. Furthermore, the gradient mapping ? x f is a continuous bijection between int (domf ) and int (domf * ), with a continuous inverse mapping (? x f ) ?1 = ? x * f * , i.e., (? x f ) ?1 (x * ) = ? x * f * (x * ) for x * ? int (domf * ), Let f : R J+1 ? R ? {+?} be a continuous convex function, 1970.
, This is a consequence of the assumption that ? is fully supported on R J+1 , which, e.g., is satisfied by the logit and nested logit models. The following proposition, due to Daly and Zachary (1979) and restated by, their Theorem 3.1, states that Conditions (DZ i) -(DZ v) are necessary and sufficient for consistency with ARUM maximization, p.20, 1992.
, Proposition 5. The ARUM choice probabilities (19) satisfy Conditions (DZ i) -(DZ v). Conversely, any demand satisfying Conditions (DZ i) -(DZ v) can be derived as ARUM choice probabilities
, See Proofs of Theorem 3.1. in Anderson et al. (1992) or of Theorem 3 in Koning and Ridder, 2003.
, that Slutsky symmetry and positive definiteness is weaker than Slutsky symmetry and positivity. Koning and Ridder (2003) show that Slutsky J p ? symmetry and negative semidefiniteness is weaker than Slutsky symmetry and non-negativity (i.e., Equation (20) holds with weak inequality). As an illustration, they consider the simple J + 1 = 2 case (see their Appendix C), Their illustration can be easily extended to show that Slutsky J ? ? symmetry and positive definiteness is weaker than Slutsky symmetry and positivity, 2002.
Other papers have investigated the restrictions on demands that make them consistent with a random utility maximization (see e, The Daly-Zachary conditions are also known as the Daly-Zachary-McFadden conditions, due to McFadden, 1981. ,
Stochastic choice and preferences for randomization, Journal of Political Economy, vol.125, pp.40-68, 2017. ,
Hicksian Complementarity and Perturbed Utility Models, Identification With Additively Separable Heterogeneity, vol.87, pp.1021-1054, 2018. ,
A representative consumer theory of the logit model, Discrete choice theory of product differentiation, pp.461-466, 1988. ,
Which demand systems can be generated by discrete choice?, Journal of Economic Theory, vol.158, pp.293-307, 2015. ,
Connected substitutes and invertibility of demand, Econometrica, vol.81, pp.2087-2111, 2013. ,
Identification in differentiated products markets, Annual review of Economics, vol.8, pp.27-52, 2016. ,
Automobile prices in market equilibrium, Econometrica, vol.63, pp.841-890, 1995. ,
Estimating discrete-choice models of product differentiation, The RAND Journal of Economics, vol.25, pp.242-262, 1994. ,
Identification in differentiated products markets using market level data, Econometrica, vol.82, pp.1749-1797, 2014. ,
Income Effects and Rationalizability in Multinomial Choice Models, 2019. ,
, Convex optimization, 2004.
Deliberately stochastic, American Economic Review, vol.109, pp.2425-2470, 2019. ,
Duality in dynamic discretechoice models, Quantitative Economics, vol.7, pp.83-115, 2016. ,
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Market Counterfactuals and the Specification of Multi-Product Demand: A Nonparametric Approach, 2019. ,
Improved multiple choice models, Determinants of Travel Choice, pp.337-357, 1979. ,
Subsidies and time discounting in new technology adoption: Evidence from solar photovoltaic systems, American Economic Review, vol.109, pp.2137-72, 2019. ,
Discrete Choice and Rational Inattention: A General Equivalence Result, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-01501313
, The Inverse Product Differentiation Logit Model, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02183411
Stochastic choice and revealed perturbed utility, Econometrica, vol.83, pp.2371-2409, 2015. ,
Cupids invisible hand: Social surplus and identification in matching models, 2015. ,
On the global convergence of stochastic fictitious play, Econometrica, vol.70, pp.2265-2294, 2002. ,
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Discrete choice cannot generate demand that is additively separable in own price, Economics Letters, vol.116, pp.129-132, 2012. ,
Linear demand systems are inconsistent with discrete choice, The BE Journal of Theoretical Economics, p.10, 2010. ,
Discrete choice and stochastic utility maximization, The Econometrics Journal, vol.6, pp.1-27, 2003. ,
Demand Systems with and without Errors, American Economic Review, vol.91, pp.611-618, 2001. ,
Stochastic choice functions generated from deterministic preferences over lotteries, The economic journal, vol.95, pp.575-594, 1985. ,
Rational inattention to discrete choices: A new foundation for the multinomial logit model, American Economic Review, vol.105, pp.272-98, 2015. ,
Probabilistic choice and procedurally bounded rationality, Games and Economic Behavior, vol.41, pp.61-78, 2002. ,
Returns to scale, Euler's theorem, and the form of production functions, Econometrica, pp.275-279, 1969. ,
Conditional logit analysis of qualitative choice behavior, Structural Analysis of Discrete Data with Econometric Applications, 1973. ,
A theory of the perturbed consumer with general budgets, National Bureau of Economic Research, 2012. ,
, The Flexible Inverse Logit Model, 2019.
Quasi-linear integrability, Journal of Economic Theory, vol.169, pp.603-628, 2017. ,
Extending the bounds of rationality: Evidence and theories of preferential choice, Journal of Economic Literature, vol.44, pp.631-661, 2006. ,
, Convex analysis, 1970.
Complementarity: An essay on the 40th anniversary of the Hicks-Allen revolution in demand theory, Journal of Economic literature, vol.12, pp.1255-1289, 1974. ,
International price discrimination in the European car market, The RAND Journal of Economics, pp.240-268, 1996. ,