No. 247

January 2005

SMALL BUSINESS

RESEARCH

SUMMARY

Firm Size Dynamics of Industries:

Stochastic Growth Processes, Large Fluctuations, and 

the Population of Firms as a Complex System 

By Daniel Teitelbaum and Robert Axtell, NuTech Solutions, Inc., Arlington, VA

under contract no. SBAHQ-03-Q-0015 (2005, 22 pages)

This Small Business Research Summary (ISSN 1076-8904) summarizes one of a series of research papers prepared under contracts

issued by the U.S. Small Business Administration’s Office of Advocacy. The opinions and recommendations of the authors of this study do

not necessarily reflect official policies of the SBA or other agencies of the U.S. government. For more information, write to the Office of

Advocacy at 409 Third Street S.W., Washington, DC 20416, or visit the office’s Internet site at www.sba.gov/advo.

Purpose

With the emergence of various longitudinal data

sources for firms, studies on business size distributions, business turnover, and business growth/decline

have had a resurgence among the academic community. This study was conducted to better understand

the dynamic nature of the growth and decline of firms

in various size classes and industries.

Overall Findings

Firm growth rates do not fit the often assumed normal

distribution. As a result, there are more slow-growing

firms, more fast-growing firms, and fewer mediumgrowing firms than are generally modeled by economists. This finding held for all industries analyzed

and growth rates were unrelated to establishment size.

Highlights

• The distribution of the growth of firms mapped a

pyramid shape of the Laplace distribution rather than

the inverted u-shape of normal distribution. Hence,

business growth tends more to the tails (or extreme

gains and losses) and less to the median than is commonly believed.

• Looking at the North American Industry

Classification Systems' (NAICS) 20 major industry

sectors revealed differing mean growth rates but similar distributions and variances. Particularly surprising was the similar results from two industries that

had negative mean growth rates. The finance industry

was unique in that its pyramid shape had convex

curved sides. This may have been a result of the time

period chosen as equity markets were exploding

from 1998 to 1999.

• Both small and large size classes exhibited similar

distributions of growth rates and variances. The similar variance findings differed from previous research.

• This research is an exciting first step into growth

analysis that generated some interesting questions

such as would more detailed industry classes produce differing results, would these results hold up for

the growth distribution of firms by age instead of

size and is there persistence among the growth of

establishments over time? 

• With the findings from this report, economists

will have to reevaluate their econometric tools when

modeling the growth of businesses. 

Scope and Methodology

The researchers utilized special tabulations from the

U.S. Census Bureau's Statistics of U.S. Business

(SUSB). SUSB excludes farms but includes nearly

all employer firms in the U.S. Establishments (or

business locations) surviving from 1998 to 1999

were the basis for the study which employed a

method to approximate firm size associated with the

establishments. Establishments that opened and

closed during the period were not included in the

analysis. Note that the Office of Advocacy is a partial funder of the SUSB. 
The log of growth rates for establishments were

charted and checked with a Kolmogorov-Smirnov

goodness-of-fit test to determine statistically if they

more closely matched a normal or Laplace distribution. 

This report was peer-reviewed consistent with

Advocacy's data quality guidelines. More information on this process can be obtained by contacting

the Director of Economic Research at

advocacy@sba.gov or (202) 205-6533.

Ordering Information

The full text of this report and summaries of other

studies performed under contract to the U.S. Small

Business Administration’s Office of Advocacy are

available at www.sba.gov/advo/research. Copies are

also available from:

National Technical Information Service

U.S. Department of Commerce

5285 Port Royal Road

Springfield, VA 22161

(800) 553-6847 or (703) 605-6000

(703) 487-4639 (TDD)

www.ntis.gov

NTIS order number: PB2005-101701

Pricing information:

Paper copy A03 ($26.50)

Microfiche A01 ($14.00)

CD-ROM A00 ($18.95)

Download A00 ($ 8.95)

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