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Estimation of Unit Values in Cross Sections without Quantity Information and Implications for Demand and Welfare Analysis

  • Vincenzo Atella


    (University of Rome II - Faculty of Economics)

  • Martina Menon

    (University of Verona - Economic Sciences)

  • Federico Perali


    (University of Verona - Economic Sciences and University of Verona - Department of Economics)

Household surveys frequently record only expenditure information. The lack of information about quantities purchased precludes the possibility of deriving household specific unit values. The aggregate price indexes derived from sources exogenous to the household survey are often not sufficient to identify all parameters and to provide plausible estimates. We use a theoretical result developed by Lewbel (1989) to construct "pseudo" unit values by 1) reproducing the variability of crosssectional price variation using the variability of the budget shares, and 2) adding the variability to the aggregate price indexes published by the national statistical institute. The study estimates a complete quadratic demand system using a time series of cross-sections of Italian household budgets including, in turn, aggregate price indexes and "pseudo" unit values. The results show that the matrix of compensated price elasticities is negative semidefinite only if "pseudo" unit values are used. In order to have a counterfactual experiment, we then consider a household survey with actual unit values and compare them with "pseudo" unit values. The experiment shows that in most cases "pseudo" values maintain the relevant characteristics of the distribution of actual unit values. Overall, we conclude that "pseudo" unit values are better than aggregate price indexes for sound demand and welfare analysis.

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Paper provided by Tor Vergata University, CEIS in its series CEIS Research Paper with number 12.

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Date of creation: 18 Apr 2003
Date of revision:
Handle: RePEc:rtv:ceisrp:12
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  1. BLACKORBY, Charles & BOSSERT, Walter, 2004. "Interpersonal Comparisons of Well-Being," Cahiers de recherche 06-2004, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  2. Deaton, Angus, 1987. "Estimation of own- and cross-price elasticities from household survey data," Journal of Econometrics, Elsevier, vol. 36(1-2), pages 7-30.
  3. Lahatte, Agenor & Miquel, Ruth & Laisney, Francois & Preston, Ian, 1998. "Demand systems with unit values:: A comparison of two specifications," Economics Letters, Elsevier, vol. 58(3), pages 281-290, March.
  4. Coondoo, D. & Majumder, A. & Ray, E,, 2001. "On the Method of Calculating Regional Prices Differentials with Illustrative Evidence from India," Papers 2001-09, Tasmania - Department of Economics.
  5. John K. Dagsvik & Leif Brubakk, 1998. "Price Indexes for Elementary Aggregates Derived from Behavioral Assumptions," Discussion Papers 234, Statistics Norway, Research Department.
  6. Arthur Lewbel, 1989. "Identification and Estimation of Equivalence Scales under Weak Separability," Review of Economic Studies, Oxford University Press, vol. 56(2), pages 311-316.
  7. D. Coondoo & A. Majumder & R. Ray, 2001. "On a Method of Calculating Regional Price Differentials with Illustrative Evidence from India," ASARC Working Papers 2001-06, The Australian National University, Australia South Asia Research Centre.
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