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On Aggregation of Linear Dynamic Models

This paper provides a general framework for aggregating linear dynamic models by deriving the aggregate model as an optimal prediction of the aggregate variable of interest with respect to an aggregate information set generated by current and past values of available aggregate observations. The paper shows how the results in the literature can be readily obtained using the proposed forecasting approach, and provides a number of important extensions and generalisations. In particular, it does not require the assumption of independence of the micro distributed lag coefficients, and establishes that in general the long-run coefficients obtained from the optimal aggregate relation are equal to the averages of the long-run coefficients from the micro relations. Finally, the approach advocated in the paper is applied to aggregation of life-cycle decision rules under habit formation, and the implications of the heterogeneity in habit formation coefficients across individuals for the analysis of aggregate consumption are investigated.

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File URL: http://www.econ.cam.ac.uk/faculty/pesaran/agglin_may02.pdf
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Paper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 9919.

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Date of creation: Dec 1999
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Handle: RePEc:cam:camdae:9919
Contact details of provider: Web page: http://www.econ.cam.ac.uk/index.htm

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  1. Harry H. Kelejian, 1980. "Aggregation and Disaggregation of Nonlinear Equations," NBER Chapters, in: Evaluation of Econometric Models, pages 135-152 National Bureau of Economic Research, Inc.
  2. Lippi, Marco, 1988. "On the dynamic shape of aggregated error correction models," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 561-585.
  3. Stoker, Thomas M, 1984. "Completeness, Distribution Restrictions, and the Form of Aggregate Functions," Econometrica, Econometric Society, vol. 52(4), pages 887-907, July.
  4. Christoffersen & Diebold, . "Further Results on Forecasting and Model Selection Under Asymmetric Loss," Home Pages _059, University of Pennsylvania.
  5. Carroll, Christopher D. & Weil, David N., 1994. "Saving and growth: a reinterpretation," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 40(1), pages 133-192, June.
  6. Johansen, Leif, 1972. "Simple and general nonsubstitution theorems for input-output models," Journal of Economic Theory, Elsevier, vol. 5(3), pages 383-394, December.
  7. Binder, Michael & Pesaran, M. Hashem, 2001. "Life-cycle consumption under social interactions," Journal of Economic Dynamics and Control, Elsevier, vol. 25(1-2), pages 35-83, January.
  8. Muellbauer, John, 1975. "Aggregation, Income Distribution and Consumer Demand," Review of Economic Studies, Wiley Blackwell, vol. 42(4), pages 525-43, October.
  9. Jeffrey C. Fuhrer, 2000. "Habit Formation in Consumption and Its Implications for Monetary-Policy Models," American Economic Review, American Economic Association, vol. 90(3), pages 367-390, June.
  10. Stoker, Thomas M, 1993. "Empirical Approaches to the Problem of Aggregation Over Individuals," Journal of Economic Literature, American Economic Association, vol. 31(4), pages 1827-74, December.
  11. Trivedi, Pravin K, 1985. "Distributed Lags, Aggregation, and Compounding: Some Econometric Implications," Review of Economic Studies, Wiley Blackwell, vol. 52(1), pages 19-35, January.
  12. van Garderen, Kees Jan & Lee, Kevin & Pesaran, M. Hashem, 2000. "Cross-sectional aggregation of non-linear models," Journal of Econometrics, Elsevier, vol. 95(2), pages 285-331, April.
  13. Rose, David E., 1977. "Forecasting aggregates of independent Arima processes," Journal of Econometrics, Elsevier, vol. 5(3), pages 323-345, May.
  14. Lutkepohl, Helmut, 1984. "Linear transformations of vector ARMA processes," Journal of Econometrics, Elsevier, vol. 26(3), pages 283-293, December.
  15. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
  16. Stoker, Thomas M, 1986. "Simple Tests of Distributional Effects on Macroeconomic Equations," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 763-95, August.
  17. Lewbel, Arthur, 1994. "Aggregation and Simple Dynamics," American Economic Review, American Economic Association, vol. 84(4), pages 905-18, September.
  18. Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July.
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