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On Aggregation of Linear Dynamic Models

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Abstract

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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Bibliographic Info

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

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Related research

Keywords: Aggregation; Heterogeneous dynamic models; Long memory; Life cycle models under habit formation;

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References

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  1. Lutkepohl, Helmut, 1984. "Linear transformations of vector ARMA processes," Journal of Econometrics, Elsevier, vol. 26(3), pages 283-293, December.
  2. Rose, David E., 1977. "Forecasting aggregates of independent Arima processes," Journal of Econometrics, Elsevier, vol. 5(3), pages 323-345, May.
  3. 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.
  4. Muellbauer, John, 1975. "Aggregation, Income Distribution and Consumer Demand," Review of Economic Studies, Wiley Blackwell, vol. 42(4), pages 525-43, October.
  5. Stoker, Thomas M, 1984. "Completeness, Distribution Restrictions, and the Form of Aggregate Functions," Econometrica, Econometric Society, vol. 52(4), pages 887-907, July.
  6. Christoffersen & Diebold, . "Further Results on Forecasting and Model Selection Under Asymmetric Loss," Home Pages _059, University of Pennsylvania.
  7. Van Garderen, K. J. & Lee, K. & Pesaran M., 1998. "Cross-sectional Aggregation of Non-linear Models," Cambridge Working Papers in Economics 9803, Faculty of Economics, University of Cambridge.
  8. 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.
  9. Lewbel, Arthur, 1994. "Aggregation and Simple Dynamics," American Economic Review, American Economic Association, vol. 84(4), pages 905-18, September.
  10. Johansen, Leif, 1972. "Simple and general nonsubstitution theorems for input-output models," Journal of Economic Theory, Elsevier, vol. 5(3), pages 383-394, December.
  11. Christopher D. Carroll & David N. Weil, 1993. "Saving and growth: a reinterpretation," Working Paper Series / Economic Activity Section 140, Board of Governors of the Federal Reserve System (U.S.).
  12. Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July.
  13. 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.
  14. 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.
  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. 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.
  17. 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.
  18. 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.
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Citations

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Cited by:
  1. Arvid Raknerud, 2001. "A State Space Approach for Estimating VAR Models for Panel Data with Latent Dynamic Components," Discussion Papers 295, Research Department of Statistics Norway.
  2. 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.
  3. Alessandra dal Colle Stievano, 2004. "Finance-Growth Nexus in open economies with outliers," Money Macro and Finance (MMF) Research Group Conference 2004 4, Money Macro and Finance Research Group.

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