Box–Cox Quantile Regression and the Distribution of Firm Sizes

José A. F. Machado*, José Mata

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


Using the Box–Cox quantile regression model, we analyse the size distribution of firms in Portuguese manufacturing during the 1980s. Specifically, we estimate the effect of selected industry attributes on the location, scale, skewness and kurtosis of the conditional size distributions of firms. We find that industry attributes affect the size of firms in the same direction across the distribution, but the effects of these variables are typically much greater at the largest quantiles. Over time the distribution shifted towards smaller firms, due mainly to the way the economy responds to industry characteristics rather than to changes of the level of these characteristics. The prediction of lognormality, implied by Gibrat's Law, is soundly rejected by the observed distribution of firm sizes. However, we found that, at least in 1983, lognormality is a reasonable description of the conditional size distribution.
Original languageEnglish
JournalJournal of Applied Econometrics
Issue number3
Pages (from-to)253-274
Number of pages22
Publication statusPublished - 2000
Externally publishedYes

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