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Bayesian estimation of the infrequency of purchase model with an application to food demand in the UK

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  • Tiffin, R
  • Arnoult, M

Abstract

A Bayesian method of estimating multivariate sample selection models is introduced and applied to the estimation of a demand system for food in the UK to account for censoring arising from infrequency of purchase. We show how it is possible to impose identifying restrictions on the sample selection equations and that, unlike a maximum likelihood framework, the imposition of adding up at both latent and observed levels is straightforward. We find that higher income households consume proportionately more meat and more fresh fruit and vegetables. Regional differences in fruit and vegetable consumption are marked with the highest levels of consumption in London and the South East. The presence of children in a household reduces levels of vegetable consumption. Households employed in the professional or managerial sectors have higher levels of fruit and vegetable consumption. Age has an influence on the consumption of fats and sugars, with consumption declining amongst older households and on the types of fruit and vegetables consumed with younger households preferring more ready meals and prepared fruit and vegetables.

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File URL: http://mpra.ub.uni-muenchen.de/18836/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 18836.

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Date of creation: 26 Aug 2008
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Handle: RePEc:pra:mprapa:18836

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Keywords: Bayesian estimation; Demand system; Infrequency of purchase;

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  1. Wales, T. J. & Woodland, A. D., 1983. "Estimation of consumer demand systems with binding non-negativity constraints," Journal of Econometrics, Elsevier, vol. 21(3), pages 263-285, April.
  2. Cragg, John G, 1971. "Some Statistical Models for Limited Dependent Variables with Application to the Demand for Durable Goods," Econometrica, Econometric Society, vol. 39(5), pages 829-44, September.
  3. Stewart, Hayden & Yen, Steven T., 2004. "Changing household characteristics and the away-from-home food market: a censored equation system approach," Food Policy, Elsevier, vol. 29(6), pages 643-658, December.
  4. Steven T. Yen & Biing-Hwan Lin & David M. Smallwood, 2003. "Quasi- and Simulated-Likelihood Approaches to Censored Demand Systems: Food Consumption by Food Stamp Recipients in the United States," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 85(2), pages 458-478.
  5. Blundell, Richard & Meghir, Costas, 1987. "Bivariate alternatives to the Tobit model," Journal of Econometrics, Elsevier, vol. 34(1-2), pages 179-200.
  6. J. Scott Shonkwiler & Steven T. Yen, 1999. "Two-Step Estimation of a Censored System of Equations," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 81(4), pages 972-982.
  7. Daniel J. Phaneuf & Catherine L. Kling & Joseph A. Herriges, 2000. "Estimation and Welfare Calculations in a Generalized Corner Solution Model with an Application to Recreation Demand," The Review of Economics and Statistics, MIT Press, vol. 82(1), pages 83-92, February.
  8. Amemiya, Takeshi, 1974. "Multivariate Regression and Simultaneous Equation Models when the Dependent Variables Are Truncated Normal," Econometrica, Econometric Society, vol. 42(6), pages 999-1012, November.
  9. Deaton, A., 1988. "Price Elasticities From Survey Data: Extensions And Indonesian Results," Papers 138, Princeton, Woodrow Wilson School - Development Studies.
  10. Heien, Dale & Wessells, Cathy Roheim, 1990. "Demand Systems Estimation with Microdata: A Censored Regression Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(3), pages 365-71, July.
  11. Steven T. Yen, 2005. "A Multivariate Sample-Selection Model: Estimating Cigarette and Alcohol Demands with Zero Observations," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 87(2), pages 453-466.
  12. L. Wade, 1988. "Review," Public Choice, Springer, vol. 58(1), pages 99-100, July.
  13. Steven T. Yen & Biing-Hwan Lin, 2006. "A Sample Selection Approach to Censored Demand Systems," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 88(3), pages 742-749.
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