Testing the Adding up Condition in Demand Systems

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DOI: 10.4236/ojs.2017.72022    318 Downloads   427 Views  

ABSTRACT

A test of the adding up condition in demand systems is crucial for determining whether a share format is admissible when the number of sample goods is smaller than the number of commodity choices available to consumers. This test requires the estimation of a demand system in a quantity format. It cannot be performed when a demand system is specified in share format. The share specification of any demand system is like a straight jacket: once worn, it forces the error covariance matrix to be singular and the adding up condition to hold whether or not the data generating process warrants it. The empirical verification of the adding up hypothesis uses a five-commodity sample selected from the Canadian Family Expenditure Survey with 4847 observations. Three specifications are considered: AIDS (Almost Ideal Demand System), QUAIDS (Quadratic AIDS) and EASI (Exact Affine Stone Index). The hypothesis is rejected in all three cases with a high level of confidence.

Cite this paper

Paris, Q. and Caracciolo, F. (2017) Testing the Adding up Condition in Demand Systems. Open Journal of Statistics, 7, 290-304. doi: 10.4236/ojs.2017.72022.

References

[1] Stone, R. (1954) Linear Expenditure Systems and Demand Analysis: An Application to the Pattern of British Demand. The Economic Journal, 64, 511-527.
https://doi.org/10.2307/2227743
[2] Barten, A.P. (1964) Consumer Demand Functions under Conditions of Almost Additive Preferences. Econometrica, 32, 1-38.
[3] Barten, A.P. (1968) Estimating Demand Functions. Econometrica, 36, 213-251.
[4] Pollak, R.A. and Wales, T.J. (1969) Estimation of the Linear Expenditure System. Econometrica, 37, 611-628.
[5] Barten, A.P. (1977) The System of Consumer Demand Functions Approach: A Review. Econometrica, 45, 23-50.
[6] LaFrance, J.T. and Hanemann, W.M. (1989) The Dual Structure of Incomplete Demand Systems. American Journal of Agricultural Economics, 71, 262-274.
https://doi.org/10.2307/1241583
[7] Barten, A.P. (1969) Maximum Likelihood Estimation of a Complete System of Demand Equations. European Economic Review, 1, 7-73.
[8] Deaton, A. and Muellbauer, J. (1980) An Almost Ideal Demand System. American Economic Review, 70, 312-326.
[9] Banks, J., Blundell, R. and Lewbel, A. (1997) Quadratic Engel Curves and Consumer Demand. Review of Economics and Statistics, 79, 527-539.
https://doi.org/10.1162/003465397557015
[10] Lewbel, A. and Pendakur, K. (2009) Tricks and Hicks: The EASI Demand System. American Economic Review, 99, 827-863.
https://doi.org/10.1257/aer.99.3.827
[11] Worswick, G.D.N. and Champernowne, D.G. (1954-1955) A Note on the Adding-Up Criterion. The Review of Economic Studies, 22, 57-59.
https://doi.org/10.2307/2296224
[12] Berndt, E.R. and Savin, N.E. (1975) Estimation and Hypothesis Testing in Singular Equation Systems with Autoregressive Disturbances. Econometrica, 43, 937-958.
[13] Moschini, G. (1998) The Semiflexible Almost Ideal Demand System. European Economic Review, 42, 349-364.
[14] Alston, J.M., Chalfant, J.A. and Piggott, N.E. (2001) Incorporating Demand Shifters in the Almost Ideal Demand System. Economics Letters, 70, 73-78.
[15] Fisher, D., Fleissig, A.R. and Serletis, A. (2001) An Empirical Comparison of Flexible Demand System Functional Forms. Journal of Applied Econometrics, 16, 59-80.
https://doi.org/10.1002/jae.585
[16] Cranfield, J.A.L., Eales, J.S., Hertel, T.W. and Preckel, P.V. (2003) Model Selection When Estimating and Predicting Consumer Demands Using International, Cross Section Data. Empirical Economics, 28, 353-364.
https://doi.org/10.1007/s001810200135
[17] Barnett, W.A. and Serletis, A. (2008) Consumer Preferences and Demand Systems. Journal of Econometrics, 147, 210-224.
[18] Liu, H., Parton, K.A., Zhou, Z.Y. and Cox, R. (2009) At-Home Meat Consumption in China: An Empirical Study. Australian Journal of Agricultural and Resource Economics, 53, 485-501.
https://doi.org/10.1111/j.1467-8489.2009.00463.x
[19] Brown, B.W. and Walker, M.B. (1989) The Random Utility Hypothesis and Inference in Demand Systems. Econometrica, 57, 815-829.
[20] Gorman, W.M. (1981) Some Engel Curves. In: Deaton, A., Ed., Essays in the Theory and Measurement of Consumer Behaviour: In Honour of Sir Richard Stone, Cambridge University Press, Cambridge, 7-30.
https://doi.org/10.1017/cbo9780511984082.003
[21] Besley, D.A., Kuh, E. and Welsch, R.E. (1980) Regression Diagnostics. Identifying Influential Data and Sources of Collinearity. Wiley Interscience, New York.
https://doi.org/10.1002/0471725153

  
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