Thinking about the firm-size distribution

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[Note: This post isn't about international economics. I'll use an example from trade to comment on a feature of the US real-estate market.]

In a letter to the Economist, the president of the National Association of Realtors writes:

[I]t is not true that large brokers dominate the industry. In fact, the real-estate industry consists mostly of independent contractors and small firms. Eight out of ten realtors work as independent contractors for their firms.

The second sentence appears to be a non-sequitur, unless one thinks that existence is informative about dominance. It’s not. In their first glance, antitrust authorities would look at concentration ratios or Herfindahl–Hirschman indices, because dominance is about economic outcomes, such as market shares, not mere existence.

According to Bernard, Jensen, Redding, and Schott’s JEP survey, four percent of the 5.5 million US firms export. That makes 220,000 exporters. The top ten percent, just 22,000 exporters, are responsible for 96% of US exports. Would we say that “larger exporters do not dominate exporting because the exporting set of firms consists mostly of small exporters”? Of course not.

When thinking about the sales distribution, we care about the exponent of the power law characterizing it, not merely the fact that its support includes small sizes.

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