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Endogenous Prices in a Riemannian Geometry Framework

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Abstract

Economic agents decide often under different price conditions (named endogenous prices), and moreover these individual price systems may depend on their previous choices. Such a situation appears for instance for consumers' choices under constraints which imply virtual costs or when non-monetary resources add to the monetary budget constraint. In case where no market exist which regulates these prices and make them converge toward a common price for all agents, observed differences appear between the social distribution of consumer expenditures and their change over time which are modelized here using Riemannian geometry. Observations in a cross-sectional survey are supposed to constitute a Riemannian surface (where each point is associated with a particular price system). Social differences are measured along the geodesics of the Riemannian surface, while changes over time correspond to movements along their tangent spaces (characterized by constant endogenous prices). The Riemannian curvature of the consumptiion space is thus estimated comparing the derivatives over the surface (corresponding to cross-section differences) to those of the tangent plane (corresponding to the time changes). The Riemannian curvature being shown to be non-null for the Polish consumers surveyed in a four years Polish panel, implies that usual econometric methods based on a unique metric over the (cross-sectional) consumption space are inadequate to estimate geodesics (corresponding to optimal choices) on the Riemannian surface. The curvature of the survey can be linked to changes in latent endogenous prices over the Riemannian surface, which are for instance full prices in a domestic production framework. Finally, the Riemannian structure is used to study the path dependency of consumers' choices

Suggested Citation

  • François Gardes, 2021. "Endogenous Prices in a Riemannian Geometry Framework," Documents de travail du Centre d'Economie de la Sorbonne 21026, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  • Handle: RePEc:mse:cesdoc:21026
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    References listed on IDEAS

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    1. François Gardes, 2019. "The Estimation of Price Elasticities and the Value of Time in a Domestic Production Framework: an Application using French Micro-Data," Post-Print hal-03281830, HAL.
    2. Angrist, Joshua D. & Krueger, Alan B., 1999. "Empirical strategies in labor economics," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 23, pages 1277-1366, Elsevier.
    3. Mette Christensen, 2014. "Heterogeneity in Consumer Demands and the Income Effect: Evidence from Panel Data," Scandinavian Journal of Economics, Wiley Blackwell, vol. 116(2), pages 335-355, April.
    4. Neary, J. P. & Roberts, K. W. S., 1980. "The theory of household behaviour under rationing," European Economic Review, Elsevier, vol. 13(1), pages 25-42, January.
    5. Anil Alpman, 2016. "Implementing Rubin's alternative multiple-imputation method for statistical matching in Stata," Stata Journal, StataCorp LP, vol. 16(3), pages 717-739, September.
    6. Gardes, Francois & Langlois, Simon & Richaudeau, Didier, 1996. "Cross-section versus time-series income elasticities of Canadian consumption," Economics Letters, Elsevier, vol. 51(2), pages 169-175, May.
    7. François Gardes, 2019. "The Estimation of Price Elasticities and the Value of Time in a Domestic Production Framework: an Application using French Micro-Data," Annals of Economics and Statistics, GENES, issue 135, pages 89-120.
    8. François Gardes, 2019. "The Estimation of Price Elasticities and the Value of Time in a Domestic Production Framework: an Application using French Micro-Data," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03281830, HAL.
    9. Mundlak, Yair, 1978. "On the Pooling of Time Series and Cross Section Data," Econometrica, Econometric Society, vol. 46(1), pages 69-85, January.
    10. Anil Alpman & François Gardes & Noel Thiombiano, 2017. "Statistical Matching for Combining Time-Use Surveys with Consumer Expenditure Surveys: An Evaluation on Real Data," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01529699, HAL.
    11. Anil Alpman & François Gardes & Noel Thiombiano, 2017. "Statistical Matching for Combining Time-Use Surveys with Consumer Expenditure Surveys: An Evaluation on Real Data," Post-Print halshs-01529699, HAL.
    12. Duncan, G.J. & Gardes, F. & Gaubert, P. & Starzec, C., 1998. "A Comparison of Consumption Models Estimated on American and Polish Panel and Pseudo-Panel Data," Papiers du Laboratoire de Microéconomie Appliquée 1998-09, Université Panthéon-Sorbonne (Paris 1).
    13. Anil Alpman & François Gardes & Noël Thiombiano, 2017. "Statistical Matching for Combining Time-Use Surveys with Consumer Expenditure Surveys: An Evaluation on Real Data," Documents de travail du Centre d'Economie de la Sorbonne 17024, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    14. François Gardes, 2019. "The Estimation of Price Elasticities and the Value of Time in a Domestic Production Framework: an Application using French Micro-Data," PSE-Ecole d'économie de Paris (Postprint) hal-03281830, HAL.
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    More about this item

    Keywords

    Spatial autocorrelation; Riemannian geometry; curvature; virtual price; full price; path dependency;
    All these keywords.

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis

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