The Multivariate Rational Addiction Model
Author(s)
Michael K. Wohlgenant*
Affiliation(s)
Department of Agricultural & Resource Economics, North Carolina State University, Raleigh, USA.
Department of Agricultural & Resource Economics, North Carolina State University, Raleigh, USA.
ABSTRACT
This paper generalizes the model of Becker, Grossman, and Murphy (1994) to the multivariate case. The multivariate model generates Frisch demand functions where current consumption is related to prices of all goods, and lagged and future consumption of all goods. The theoretical restrictions are that current price effects (holding lagged and future consumption constant) are negative definite, and lagged and future consumption are proportional to one another, the proportionality factor being the consumer’s discount rate. The conditions for dynamic stability are derived, and the solution to the matrix difference equation is derived. General formulas for multivariate Frisch price elasticities with respect to different lengths of time are also derived. Finally, alternative econometric specifications are derived, showing how theoretical restrictions can be imposed to test the theory and to reduce the number of estimable parameters. It is also shown how the model can be modified to account for different discount rates by commodity when estimating the model using aggregate data.
This paper generalizes the model of Becker, Grossman, and Murphy (1994) to the multivariate case. The multivariate model generates Frisch demand functions where current consumption is related to prices of all goods, and lagged and future consumption of all goods. The theoretical restrictions are that current price effects (holding lagged and future consumption constant) are negative definite, and lagged and future consumption are proportional to one another, the proportionality factor being the consumer’s discount rate. The conditions for dynamic stability are derived, and the solution to the matrix difference equation is derived. General formulas for multivariate Frisch price elasticities with respect to different lengths of time are also derived. Finally, alternative econometric specifications are derived, showing how theoretical restrictions can be imposed to test the theory and to reduce the number of estimable parameters. It is also shown how the model can be modified to account for different discount rates by commodity when estimating the model using aggregate data.
KEYWORDS
Rational Addiction Model; Dynamic Frisch Demand Functions; Dynamic Consumer Demand; Habit Formation
Rational Addiction Model; Dynamic Frisch Demand Functions; Dynamic Consumer Demand; Habit Formation
Cite this paper
M. K. Wohlgenant, "The Multivariate Rational Addiction Model," Theoretical Economics Letters, Vol. 2 No. 5, 2012, pp. 459-464. doi: 10.4236/tel.2012.25086.
M. K. Wohlgenant, "The Multivariate Rational Addiction Model," Theoretical Economics Letters, Vol. 2 No. 5, 2012, pp. 459-464. doi: 10.4236/tel.2012.25086.
References
[1] G. Becker., M. Grossman and K. Murphy, “An Empirical Analysis of Cigarette Addiction,” American Economic Review, Vol. 84, No. 3, 1994, pp. 396-418. [2] M. Bask and M. Melkersson, “Rationally Addicted to Drinking and Smoking,” Applied Economics, Vol. 36, No. 4, 2004, pp. 373-381. doi:10.1080/00036840410001674295 [3] P. Pierani and S. Tiezzi, “Addiction and Interaction between Alcohol and Tobacco Consumption,” Empirical Economics, Vol. 37, No. 1, 2009, pp. 1-23. doi:10.1007/s00181-008-0220-3 [4] L. Phlips, “Applied Consumption Analysis,” North-Holland Publishing Co., Amsterdam, 1983. [5] R. Lucas, “Optimal Investment Policy and Flexible Accelerator,” International Economic Review, Vol. 8, No. 1, 1967, pp. 78-85. doi:10.2307/2525383 [6] T. Sargent, “Macroeconomic Theory,” Academic Press, New York, 1979. [7] W. Diewert and T. Wales, “Flexible Functional Forms and Global Curvature Conditions,” Econometrica, Vol. 55, No. 1, 1987, pp. 43-68. doi:10.2307/1911156
[1] G. Becker., M. Grossman and K. Murphy, “An Empirical Analysis of Cigarette Addiction,” American Economic Review, Vol. 84, No. 3, 1994, pp. 396-418. [2] M. Bask and M. Melkersson, “Rationally Addicted to Drinking and Smoking,” Applied Economics, Vol. 36, No. 4, 2004, pp. 373-381. doi:10.1080/00036840410001674295 [3] P. Pierani and S. Tiezzi, “Addiction and Interaction between Alcohol and Tobacco Consumption,” Empirical Economics, Vol. 37, No. 1, 2009, pp. 1-23. doi:10.1007/s00181-008-0220-3 [4] L. Phlips, “Applied Consumption Analysis,” North-Holland Publishing Co., Amsterdam, 1983. [5] R. Lucas, “Optimal Investment Policy and Flexible Accelerator,” International Economic Review, Vol. 8, No. 1, 1967, pp. 78-85. doi:10.2307/2525383 [6] T. Sargent, “Macroeconomic Theory,” Academic Press, New York, 1979. [7] W. Diewert and T. Wales, “Flexible Functional Forms and Global Curvature Conditions,” Econometrica, Vol. 55, No. 1, 1987, pp. 43-68. doi:10.2307/1911156