Measuring Productivity Dispersion: A Parametric Approach Using the Lévy Alpha-Stable Distribution

64 Pages Posted: 22 Oct 2019

See all articles by Jangho Yang

Jangho Yang

University of Waterloo; INET & Oxford Martin School

Torsten Heinrich

Oxford Martin Programme on Technological and Economic Change, Oxford Martin School, University of Oxford; University of Oxford - Institute for New Economic Thinking at the Oxford Martin School; University of Bremen

Julian Winkler

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School

Francois Lafond

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School; University of Oxford - Mathematical Institute

Pantelis Koutroumpis

Oxford Martin Programme of Technological and Economic Change; University of Oxford - Institute for New Economic Thinking at the Oxford Martin School; Imperial College Business School

J. Doyne Farmer

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School; Santa Fe Institute

Date Written: September 30, 2019

Abstract

Productivity levels and growth are extremely heterogeneous among firms. A vast literature has developed to explain the origins of productivity shocks, their dispersion, evolution and their relationship to the business cycle. We examine in detail the distribution of labor productivity levels and growth, and observe that they exhibit heavy tails. We propose to model these distributions using the four parameter Lévy stable distribution, a natural candidate deriving from the generalised Central Limit Theorem. We show that it is a better fit than several standard alternatives, and is remarkably consistent over time, countries and sectors. In all samples considered, the tail parameter is such that the theoretical variance of the distribution is infinite, so that the sample standard deviation increases with sample size. We find a consistent positive skewness, a markedly different behaviour between the left and right tails, and a positive relationship between productivity and size. The distributional approach allows us to test different measures of dispersion and find that productivity dispersion has slightly decreased over the past decade.

Keywords: productivity, dispersion, distribution, heavy-tail, Lévy stable distribution

JEL Classification: D2, O3, J24, R12

Suggested Citation

Yang, Jangho and Heinrich, Torsten and Winkler, Julian and Lafond, Francois and Koutroumpis, Pantelis and Farmer, J. Doyne, Measuring Productivity Dispersion: A Parametric Approach Using the Lévy Alpha-Stable Distribution (September 30, 2019). Available at SSRN: https://ssrn.com/abstract=3468301 or http://dx.doi.org/10.2139/ssrn.3468301

Jangho Yang

University of Waterloo ( email )

Waterloo, Ontario N2L 3G1
Canada

INET & Oxford Martin School ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

Torsten Heinrich (Contact Author)

Oxford Martin Programme on Technological and Economic Change, Oxford Martin School, University of Oxford ( email )

University of Oxford
34 Broad Street
Oxford, OX1 3BD
United Kingdom

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School ( email )

Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

University of Bremen ( email )

ierp, FB7
Max von Laue Str. 1
D-28359 Bremen, Bremen 28359
Germany

Julian Winkler

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School ( email )

Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

Francois Lafond

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School ( email )

Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

University of Oxford - Mathematical Institute ( email )

Andrew Wiles Building
Radcliffe Observatory Quarter (550)
Oxford, OX2 6GG
United Kingdom

Pantelis Koutroumpis

Oxford Martin Programme of Technological and Economic Change ( email )

University of Oxford
34 Broad Street
Oxford, OX1 3BD
United Kingdom
01865610388 (Phone)
OX1 3BD (Fax)

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School ( email )

Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

Imperial College Business School ( email )

South Kensington Campus
Exhibition Road
London SW7 2AZ, SW7 2AZ
United Kingdom

J. Doyne Farmer

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School ( email )

Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

HOME PAGE: http://www.inet.ox.ac.uk/people/view/4

Santa Fe Institute ( email )

1399 Hyde Park Road
Santa Fe, NM 87501
United States
505-984-8800 (Phone)
505-982-0565 (Fax)

HOME PAGE: http://www.santafe.edu/~jdf/

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