Measuring productivity dispersion: a parametric approach using the Lévy alpha-stable distribution

Growth, development, and structural change at the firm-level: The example of the PR China

“…To understand the development of firm-level distributions, scholars have instead focussed on firms of different age groups, their survival, and their shifts over time (Cabral and Mata, 2003). Important findings include that the form of the distribution does not change over time (Yang et al, 2019) or with age (Cabral and Mata, 2003;Angelini and Generale, 2008), that surviving firms are slightly larger (Cabral and Mata, 2003), and that they increase their productivity (making within-firm productivity gains important at the aggregate level) (Bartelsman et al, 2013;Li and Rama, 2015). Cabral and Mata (2003) report that surviving firms in a Portuguese data set have less long tails and lower skew; however, if the statistical process which the firm size follows in reality is heavy-tailed with low exponents 3 , these moments may not exist and Cabral and Mata's findings may be statistical artifacts (Yang et al, 2019).…”

“…This has been explained with both structural factors, such as constraints on credit availability (Bloom et al, 2010;Cabral and Mata, 2003), and also internal factors of the firm population of developing countries, such as bad management and reluctance to delegate decision-making (Bloom et al, 2010;Chaffai et al, 2012). More recently, it has been found that productivities (both labor productivity and total factor productivity, TFP) are heavy-tailed with tail exponents below 2.0 such that most dispersion measures, including the ones used in this line of research, are not meaningful (Yang et al, 2019).…”

“…An important characteristic of firm-level distributions in developed countries is that no significant changes are observed with either time (Yang et al, 2019) or firm age (Cabral and Mata, 2003). Developing countries, however, may be very different.…”

“…While other distributional models have been suggested for labor productivity (Yu et al (2015) consider Asymmetric Exponential Power (AEP) distributions and Gaussian normal distributions), the mounting evidence for heavy tails in both labor productivity and labor productivity change (Yang et al, 2019) suggests the Lévy alpha-stable distribution (Nolan, 1998(Nolan, , 2019 as a distributional model. Lévy alpha-stable distributions generalize Gaussian normal distributions, 2 but have heavy tails for almost all parameter values.…”

“…It also relates to the debate on granular origins of aggregate fluctuations (Gabaix, 2011;Schwarzkopf et al, 2010) and the question of how characteristics of labor productivity distributions in firm populations should be quantified and interpreted. The characteristics of labor productivity dispersion measures and the consequences for these economic questions are studied comprehensively in Yang et al (2019).…”