Increasing productivity dispersion: Evidence from light manufacturing in Brazil

Large productivity dispersion within narrowly defined sectors is widely documented. However, across studies, several statistics are used to assess dispersion and there is not enough discussion about differences among them. Using firm-level data for the textile and furniture sectors in Brazil over the 2003-2009 period, we estimated different TFP measures according to four methods: Ordinary Least Squares (OLS for short), the stochastic frontier model of Battese and Coelli (1988, 1992)(STCH for short), the control function approach of Levinsohn and Petrin (2003) (LP for short), and the corrected control function approach of Ackerberg et al. (2015) (ACF for short). Next, we calculated three dispersion statistics: Standard Deviation (SD); Coefficient of Variation (CV); and Interquartile Range (IQR). After confirming the existence of large productivity dispersion within the studied sectors, we analyzed if the dispersion is increasing or decreasing over time. For both sectors, SD and CV convey an increasing productivity dispersion message, but they do so at different rates (CV is seven times higher than SD). On the contrary, IQR suggests less productivity dispersion over time for textiles and mixed results for furnitures. Overall, in terms of characterizing the increasing productivity dispersion, the CV statistic combined with the ACF method define an upper bound while the IQR with LP method define a lower bound. Considering these results, the article underlines that there are non-trivial differences in the use of dispersion statistics. Thus, their use could not be interchangeable and should consider methodological issues, behavior in the tails of the firm productivity distribution, sample sizes and scenarios of divergence/convergence, among others.