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Aggregation of Firm-Level Exports and Imports

Abstract​

In this paper, we present a technique to trace the aggregation of firm-level exports and imports into national aggregates.

  • Sectoral Fluctuations: We clarify the linear relations that link sectoral fluctuations to aggregate fluctuations of an economy.
  • Aggregation of Agents: We study the aggregation of groups of fluctuating agents within parts of the aggregate. This allows for a precise reconstruction of the aggregation of fluctuations from the micro to the macro level.

We utilize firm-level export and import data from France Customs over the period 1997-2013 to constrain the theoretical derivations to practical parameter regions, simplifying a generally difficult problem. Empirically constrained computational tests confirm that each analytical expression in this paper is true, either exactly or approximately.

Key Insights​

  • Postponement of the Law of Large Numbers: Idiosyncratic variance decays more slowly than 1/N1/N with the population size NN due to large, multiplicative micro fluctuations. This can be accounted for as a comovement among agents.
  • Concentration Effects: This phenomenon is distinct from situations where concentration allows groups of a few large firms to drive the aggregate towards their level of volatility.