Costas Arkolakis

Appendix to:
Market Penetration Costs and the New Consumers Margin in International Trade

• Model fit for alternative calibrations
  • Jointly estimating θ/(σ-1) and β. (Errors as function of parameters, model fit)

  Here I look at the relative fit of the model for different parameters β
  and θ/(σ-1). The data used are the average (total) sales of
  French firms in France grouped into categories depending on
  the number of destinations they sell and in particular
  1, 2-3, 4-7, 8-15, 16-31, 32-63, 64+ destinations. The picture of the fit
  refers to weighted absolute deviations of the model with the data. A 2%
  deviations means that the model on average has a 2% difference from the
  data along the 7 groups. The picture on the model fit refers to the relative
  fit of the model to the data on the calibration picture that I use in the paper
  using the parameter that minimizes the weighted squared difference of the
  model to the data across the ranges of the data in the first picture.
  An important note of the results: The model attains a good fit for a variety
  of combinations of \beta and θ/(σ-1). (But never β close to 0). The
  intuition can be illustrated with a simple example: A firm might have high
  sales because it sell to many consumers or a lot per consumer. Since
  the data dont have information on that I cannot separetely identify the
  two parameters that govern these margins (β and θ/(σ-1) respectively).
  In the paper I find β conditional on the estimates of θ/(σ-1) coming from
  the fixed cost model.

  • Distribution of sales and trade growth in trade liberalization for combinations of β and θ/(σ-1) that give a good fit in the calibration exercise (see above)

  • Conditional estimation

* For terminology and references used, see paper.
Source for firm level data, Eaton, Kortum, and Kramarz and for goods data, OECD.

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