Abstract
The firm size distribution is highly skewed to the right and often follows a power law. In practice, it is common that firm size and firm age data are aggregated and released as grouped data to avoid disclosure of confidential information. We investigate multiple parametric methods for firm size and firm age modeling based on grouped data, and propose to estimate the joint distribution of firm size and firm age using the Plackett copula. The goodness-of-fit of the estimated marginal distributions are benchmarked with respect to the fit to the whole data and to the upper tails, respectively. The utilization of the proposed methods are demonstrated via an application to the 1977-2014 US firm data. Results show that the generalized lambda distribution has overall better performance in modeling both firm size and firm age data. The exponentiated Weibull distribution also works well in modeling the firm size data. As a by-product, the estimated parameter of the Plackett copula provides a measure of the association between firm size and firm age.
Highlights
Firms of different sizes and ages play different roles on employment, innovative activities, economic growth and other aspects of social and economic life
It was reported that firm size and age have a negative effect on firm growth for manufacturing firms [1,2,3,4,5], mining, wholesale and retail firms [6], and firms in the fields of construction, trade and service industries [7,8,9,10]
Firm age is computed for all firms in the Longitudinal Business Database (LBD) from the age of the establishments belonging to that particular firm, and the establishment age is computed by taking the difference between the current year of operation and the year the establishment first reports positive employment in the LBD
Summary
Firms of different sizes and ages play different roles on employment, innovative activities, economic growth and other aspects of social and economic life. 14,000 Japanese manufacturing firms extracted from the “MITI Basic Survey of Business Structure and Activities (SBSA)” survey [15] He found that firm size and firm age have negative effects on firm growth, and they have positive effects on a firm’s survivability. Firm age is computed for all firms in the Longitudinal Business Database (LBD) from the age of the establishments belonging to that particular firm, and the establishment age is computed by taking the difference between the current year of operation and the year the establishment first reports positive employment in the LBD Both the firm size and firm age data have been aggregated into classes and are top-coded. More firm size and age data have been released for 2015 and 2016 in the BDS firm and establishment data tables
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