Testing aggregation consistency across geography and commodities*
Qinghua Liu
Search for more papers by this authorC. Richard Shumway
Search for more papers by this authorQinghua Liu
Search for more papers by this authorC. Richard Shumway
Search for more papers by this authorAbstract
Consistent aggregation of production data across commodities and Western USA states was tested using Lewbel's generalised composite commodity theorem. The applicability of the generalised composite commodity theorem for testing consistent geographic aggregation was demonstrated and applied to two groups of states. Consistent commodity aggregation was tested in each state for two output groups and three input groups and in one state for a larger number of groups. Most tests for commodity aggregation supported consistent aggregation of inputs but not outputs. Consistent geographic aggregation was supported for each output and input category across Pacific Northwest states but only for inputs across all Western states.
Footnotes
References
- Asche, F., Bremnes, H. and Wessells, C.R. 1999, ‘Product aggregation, market integration, and relationships between prices: an application to world salmon markets’, American Journal of Agricultural Economics, vol. 81, pp. 568–581.
- Ball, V.E. 1988, ‘Modeling supply response in a multiproduct framework’, American Journal of Agricultural Economics, vol. 70, pp. 813–825.
- Barnett, W.A. 1979, ‘Theoretical foundations for the Rotterdam Model’, Review of Economic Studies, vol. 46, pp. 109–130.
- Blundell, R. and Robin, J.M. 2000, ‘Latent separability: grouping goods without weak separability’, Econometrica, vol. 75, pp. 53–84.
- Capalbo, S.M. and Denny, M.G.S. 1986, ‘Testing long-run productivity model for the Canadian and US agricultural sectors’, American Journal of Agricultural Economics, vol. 68, pp. 615–625.
- Chambers, R.G. 1988, Applied Production Analysis: A Dual Approach, Cambridge University Press, New York.
- Chambers, R.G. and Pope, R.D. 1996, ‘Aggregable price-taking firms’, European Economic Review, vol. 40, pp. 417–428.
- Chavas, J.P. and Cox, T.L. 1988, ‘A nonparametric analysis of agricultural technology’, American Journal of Agricultural Economics, vol. 70, pp. 303–310.
- Davis, G.C. 2003, ‘The generalized composite commodity theorem: stronger support in the presence of data limitations’, Review of Economics and Statistics, vol. 85, pp. 476–480.
- Davis, G.C., Lin, N. and Shumway, C.R. 2000, ‘Aggregation without separability: tests of U.S. and Mexican agricultural production data’, American Journal of Agricultural Economics, vol. 82, pp. 214–230.
- Debreu, G. 1959, Theory of Value: An Axiomatic Analysis of Economic Equilibrium, Cowles Foundation Monograph 17, Yale University, New Haven, CT.
- Dickey, D.A. and Fuller, W.A. 1979, ‘Distribution of the estimators for autoregressive time series with a unit root’, Journal of the American Statistics Association, vol. 74, pp. 427–431.
- Eales, J., Hyde, J. and Schrader, L.F. 1998, ‘A note on dealing with poultry in demand analysis’, Journal of Agricultural and Resource Economics, vol. 23, pp. 558–567.
- Fackler, P.L. and Goodwin, B.K. 2001, ‘Spatial price analysis’, in B. Gardner and G. Rausser (eds), Handbook of Agricultural Economics, vol. 1, Elsevier Science B.V., Amsterdam.
-
Gorman, W.M.
1953, ‘Community preference fields’, Econometrica, vol. 21, pp. 63–80.
10.2307/1906943 Google Scholar
- Gorman, W.M. 1959, ‘Separable utility and aggregation’, Econometrica, vol. 27, pp. 469–481.
- Granger C.W.J. and Hallman, J. 1989, ‘The algebra of I(1)’, Finance and Economics Discussion Series, paper 45, Division of Research and Statistics Federal Reserve Board, Washington, DC.
- Hicks, J.R. 1936, Value and Capital, Oxford University Press, Oxford.
- Hellerstein, D. 1995, ‘Welfare estimation using aggregate and individual-observation models: a comparison using Monte Carlo techniques’, American Journal of Agricultural Economics, vol. 77, pp. 620–630.
- Karagiannis, G. and Mergos, G.J. 2002,Estimating theoretically consistent demand systems using cointegration techniques with application to Greek food data’, Economics Letters, vol. 74, pp. 137–143.
- Lau, L. 1977, ‘Existence conditions for aggregate demand functions: the case of multiple indices’, IMSS technical report no. 249R, Stanford University, Stanford, CA.
-
Leontief, W.
1936, ‘Composite commodities and the problem of index numbers’, Econometrica, vol. 4, pp. 39–59.
10.2307/1907120 Google Scholar
- Leontief, W. 1947, ‘Introduction to a theory of the internal structure of functional relationships’, Econometrica, vol. 15, pp. 361–373.
- Lewbel, A. 1996, ‘Aggregation without separability: a generalized composite commodity theorem’, American Economic Review, vol. 86, pp. 524–543.
- Lim, H. and Shumway, C.R. 1992a, ‘Separability in state-level agricultural technology’, American Journal of Agricultural Economics vol. 74, pp. 120–131.
- Lim, H. and Shumway, C.R. 1992b, ‘Profit maximization, returns to scale, and measurement error’, Review of Economics and Statistics, vol. 74, pp. 430–438.
- MacKinnon, J. 1994, ‘Approximate asymptotic distribution functions for unit-root and cointegration tests’, Journal of Business and Economic Statistics, vol. 12, pp. 167–176.
- MacKinnon, J. 1996, ‘Numerical distribution functions for unit root and cointegration tests’, Journal of Applied Econometrics, vol. 11, pp. 601–618.
- Muellbauer, J. 1975, ‘Aggregation, income distribution, and consumer demand’, Review of Economic Studies, vol. 62, pp. 525–543.
- Pesaran, M.H., Pierse, R.G. and Kumar, M.S. 1989, ‘Econometric analysis of aggregation in the context of linear prediction models’, Econometrica, vol. 57, pp. 861–888.
- Polson, R.A. and Shumway, C.R. 1990, ‘Structure of south central agricultural production’, Southern Journal of Agricultural Economics, vol. 22, pp. 153–163.
- Pope, R.D. and Chambers, R.G. 1989, ‘Price aggregation when price-taking firms’ prices vary’, Review of Economic Studies, vol. 56, pp. 297–309.
- Ray, S.C. 1982, ‘A translog cost function analysis of U.S. agriculture 1939–77’, American Journal of Agricultural Economics, vol. 64, pp. 490–498.
- Russell, T. 1982,Exact aggregation as a corollary of Richmond's Theorem’, Economics Letters, vol. 9, pp. 311–314.
-
Sckokai, P. and
Moro, D.
‘Direct separability in multi-output technologies: an application to the Italian agricultural sector’, European Review of Agricultural Economics, vol. 23, pp. 95–116.
10.1093/erae/23.1.95 Google Scholar
- Shumway, C.R. 1983,Supply, demand, and technology in a multiproduct industry: Texas field crops’, American Journal of Agricultural Economics, vol. 65, pp. 748–760.
- Shumway, C.R. and Davis, G.C. 2001, ‘Does consistent aggregation really matter?’, Australian Journal of Agricultural Economics vol. 45, pp. 161–149.
- Simes, R.J. 1986, ‘An improved Bonferroni procedure for multiple tests of significance’, Biometrika, vol. 73, pp. 751–754.
- Stoker, T.M. 1986, ‘Simple tests of distributional effects on macroeconomic equations’, Journal of Political Economy, vol. 94, pp. 763–795.
- Weaver, R.D. 1977, ‘The theory and measurement of provisional agricultural production decisions’, PhD Thesis, University of Wisconsin, Madison.
-
Williams, S.P. and
Shumway, C.R.
1998a, ‘Aggregation of data and profit maximization in Mexican agriculture’, Applied Economics, vol. 30, pp. 235–244.
10.1080/000368498326038 Google Scholar
- Williams, S.P. and Shumway, C.R. 1998b, ‘Testing for behaviour objective and aggregation opportunities in U.S. agricultural data’, American Journal of Agricultural Economics, vol. 80, pp. 195–207.