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Heterogeneous dynamics, aggregation and the persistence of economic shocks



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.

Suggested Citation

  • Laura Mayoral, 2009. "Heterogeneous dynamics, aggregation and the persistence of economic shocks," UFAE and IAE Working Papers 786.09, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  • Handle: RePEc:aub:autbar:786.09

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    Cited by:

    1. Jondeau, Eric & Pelgrin, Florian, 2014. "Estimating aggregate autoregressive processes when only macro data are available," Economics Letters, Elsevier, vol. 124(3), pages 341-347.
    2. M. Dolores Gadea & Laura Mayoral, 2009. "Aggregation is not the solution: the PPP puzzle strikes back," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(6), pages 875-894.
    3. Laura Mayoral & Maria Dolores Gadea, 2009. "Analyzing aggregate real exchange rate persistence through the lens of sectoral data," UFAE and IAE Working Papers 787.09, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).

    More about this item


    Heterogeneous dynamics; aggregation; persistence; impulse response function; sum of the autoregressive coefficients; U.S. inflation persistence.;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • F31 - International Economics - - International Finance - - - Foreign Exchange
    • O11 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Macroeconomic Analyses of Economic Development

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