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Heterogeneous dynamics, aggregation and the persistence of economic shocks

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  • Laura Mayoral
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    Abstract

    It has been recently emphasized that, if individuals have heterogeneous dynamics, estimates of shock persistence based on aggregate data are significatively higher than those derived from its disaggregate counterpart. However, a careful examination of the implications of this statement on the various tools routinely employed to measure persistence is missing in the literature. This paper formally examines this issue. We consider a disaggregate linear model with heterogeneous dynamics and compare the values of several measures of persistence across aggregation levels. Interestingly, we show that the average persistence of aggregate shocks, as measured by the impulse response function (IRF) of the aggregate model or by the average of the individual IRFs, is identical on all horizons. This result remains true even in situations where the units are (short-memory) stationary but the aggregate process is long-memory or even nonstationary. In contrast, other popular persistence measures, such as the sum of the autoregressive coefficients or the largest autoregressive root, tend to be higher the higher the aggregation level. We argue, however, that this should be seen more as an undesirable property of these measures than as evidence of different average persistence across aggregation levels. The results are illustrated in an application using U.S. inflation data.

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    File URL: http://research.barcelonagse.eu/tmp/working_papers/400.pdf
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    Bibliographic Info

    Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 400.

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    Date of creation: Oct 2009
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    Handle: RePEc:bge:wpaper:400

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    Related research

    Keywords: PPP puzzle; Real exchange rates; Heterogeneous dynamics; Fractional integration; aggregation bias;

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    References

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    1. Ignazio Angeloni & Luc Aucremanne & Michael Ehrmann & Jordi Galí & Andrew Levin & Frank Smets, 2005. "New Evidence on Inflation Persistence and Price Stickiness in the Euro Area: Implications for Macro Modelling," Working Papers 242, Barcelona Graduate School of Economics.
    2. Kuersteiner, Guido M., 2005. "Automatic Inference For Infinite Order Vector Autoregressions," Econometric Theory, Cambridge University Press, vol. 21(01), pages 85-115, February.
    3. Jean Imbs & Haroon Mumtaz & Morton O. Ravn & Helene Rey, 2002. "PPP Strikes Back: Aggregation and the Real Exchange Rate," NBER Working Papers 9372, National Bureau of Economic Research, Inc.
    4. Kilian, Lutz & Gonçalves, Sílvia, 2002. "Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form," Discussion Paper Series 1: Economic Studies 2002,26, Deutsche Bundesbank, Research Centre.
    5. Zaffaroni, Paolo, 2004. "Contemporaneous aggregation of linear dynamic models in large economies," Journal of Econometrics, Elsevier, vol. 120(1), pages 75-102, May.
    6. Pesaran, M.H. & Smith, R., 1992. "Estimating Long-Run Relationships From Dynamic Heterogeneous Panels," Cambridge Working Papers in Economics 9215, Faculty of Economics, University of Cambridge.
    7. 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.
    8. International Monetary Fund, 1999. "Neglected Heterogeneity and Dynamics in Cross-Country Savings Regressions," IMF Working Papers 99/128, International Monetary Fund.
    9. Forni, Mario & Lippi, Marco, 1997. "Aggregation and the Microfoundations of Dynamic Macroeconomics," OUP Catalogue, Oxford University Press, number 9780198288008, September.
    10. Jan Kmenta & James B. Ramsey, 1980. "Evaluation of Econometric Models," NBER Books, National Bureau of Economic Research, Inc, number kmen80-1, October.
    11. Koop, Gary & Pesaran, M. Hashem & Potter, Simon M., 1996. "Impulse response analysis in nonlinear multivariate models," Journal of Econometrics, Elsevier, vol. 74(1), pages 119-147, September.
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