Does

Gibrat’s

Law

Apply

to

Nonprofits?

Teresa

D.

Harrison

and

Christopher

A.

Laincz

April

2008

Abstract

We

test

whether

Gibrat’s

Law

holds

for

nonprofits

(NPs).

Gibrat’s

Law

implies

that

growth

rates

are

independent

of

firm

size

and

the

firm

size

distribution

is

log-normal.

We

nonparametrically

estimate

the

distributions

and

generally

find

them

to

be

right-skewed.

We

then

test

Gibrat’s

Law

in

a

regression-based

analysis

and

find

that

smaller

NPs

grow

faster

than

larger

firms

and

growth

rates

are

serially

correlated.

Finally,

we

test

Gibrat’s

Law

on

selected

disaggregated

sectors

of

two

types

-

sectors

dominated

by

NPs

and

sectors

that

compete

with

for-profits.

Though

not

conclusive,

we

do

not

detect

any

systematic

differences

between

the

two

groups.

1

Introduction

Nonprofits

(NPs)

accounted

for

over

8%

of

US

wages

and

salaries

in

2005

(Urban

In-

stitute,

2007)

and

the

total

number

of

public

charities

increased

by

45%

through

the

1990s

compared

with

only

12.6%

for

all

firms

(Harrison

and

Laincz,

2007).

However,

the

rapidly

growing

NP

sector

remains

little

understood

despite

its

importance

in

providing

public

goods

including

health

and

education.

Using

tax

return

data

and

“Gibrat’s

Law

of

Proportionate

Effect”

as

a

benchmark,

we

analyze

the

relationship

between

NP

size

and

growth.

Gibrat’s

Law

(GL)

postulates

that

firm

growth

rates

are

independent

of

size

and

the

resulting

size

distribution

is

log-

normal.

Numerous

studies

have

rejected

GL

for

the

manufacturing

sector,

finding:

(i)

right-skewed

distributions;

(ii)

small

firms

grow

faster

than

larger

ones;

and

(iii)

serial

correlation

(Lotti

et

al.,

2003).

In

contrast,

Audretsch

et

al.

(2004)

argue

the

service

sector

should

differ

because

the

failure

of

GL

in

manufacturing

stems

from

sunk

entry

costs

and

firms’

need

to

“rush”

to

reach

a

sufficient

scale

for

survival.

They

present

evidence

for

independence

between

size

and

growth

using

Dutch

service

data.

Thus,

GL

may

apply

to

NPs

because

they

are

almost

exclusively

service

sector

en-

tities.

However,

NPs

face

a

non-redistribution

constraint

(NRC),

i.e.

no

“profits”

may

be

distributed.

That

constraint

also

applies

at

exit,

because

upon

liquidation

all

assets

must

be

used

for

charitable

purposes.

Therefore,

the

NRC

implies

that

all

start-up

costs

are

sunk

because

they

are

unrecoverable

through

exit.

If

sunk

costs

play

a

large

role,

risk-averse

NPs

would

be

inclined

to

start

small

but

grow

rapidly.

2

Methodology

and

Data

We

implement

two

empirical

strategies.

First,

if

GL

holds,

then

firm

size

should

follow

a

log-normal

distribution.

We

nonparametrically

estimate

the

size

distribution

using

a

Gaussian

kernel

and

the

cross-validation

least-squares

method

for

optimal

bandwidth

1

Manuscript