BLS WORKING PAPERS 

 

U.S. Department of Labor 

U.S. Bureau of Labor Statistics 

Office of Productivity and Technology 

Industry Competition and Total Factor Productivity Growth 

Michael D. Giandrea, U.S. Bureau of Labor Statistics 

Working Paper 399

September 2006

All views expressed in this paper are those of the author and do not necessarily reflect the views or policies of the 

U.S. Bureau of Labor Statistics. 
Industry Competition and Total Factor Productivity Growth

Michael D. Giandrea, Ph.D. 

U.S. Bureau of Labor Statistics 

Office of Productivity and Technology 

Postal Square Building, Room 2180 

2 Massachusetts Ave., NE 

Washington, DC 20212-0001 

Email: giandrea.michael@bls.gov

Phone: (202) 691-5628 

August 25, 2006 

* All views expressed in this paper are those of the author and do not necessarily 

reflect the views or policies of the U.S. Bureau of Labor Statistics. The author 

would like to thank Frank Gollop for his assistance and advice, and James 

Monahan for his assistance with the Longitudinal Research Database. Any errors 

are the author’s responsibility. 
- 2 -

Industry Competition and Total Factor Productivity Growth

Michael D. Giandrea 

August 25, 2006 

Abstract 

This paper analyzes the impact of changes in the competitive market structure on an 

industry's total factor productivity (TFP) growth. The impact of horizontal mergers on 

TFP growth is of particular interest. The number of proposed horizontal mergers among 

U.S. firms totaled 28,818 from 1996 to 2005, while the number of U.S. Department of 

Justice investigations of proposed mergers totaled 1,303 during the same time period. 

The impact of mergers upon total factor productivity growth is rightly a topic for 

consideration. Merger participants routinely claim that mergers will result in welfare 

improving efficiency gains. If true, these gains should translate into increased TFP 

growth. This paper estimates this effect and others after presenting a model of TFP 

growth as a function of changes in the competitive market structure of an industry, 

changes in production diversification measured at the establishment level, and changes in 

output per establishment and the number of establishments. Mergers are found to have a 

positive impact upon TFP growth, accounting for 0.36 percentage points of total factor 

productivity growth between census years. 

JEL Classification: D2, L1, L4. 

 
- 3 -

 

1. Introduction 

This paper considers the processes by which changes in an industry's market 

structure affect total factor productivity. Its uniqueness lies in the development 

and application of a model explaining productivity changes at the four-digit SIC 

industry level as a function of changes in industry output, changes in 

diversification of production in establishments, and changes in the industry's 

market structure. 

Changes in market structure due to mergers among competitors and the 

consequences of these mergers on total factor productivity growth are of 

particular interest. This is an especially important topic when one considers 

recent merger trends. The Hart-Scott-Rodino Act of 1976 requires notification of 

intended mergers if the parties involved in the mergers are of sufficient size. The 

United States Department of Justice Antitrust Division reports in its workload 

statistics a total of 28,818 Hart-Scott-Rodino merger notifications from 1996 

through 2005 with a peak of 4,926 in 2000. The number of investigations into 

these proposed mergers totaled 1,303 from 1996 through 2005 with a high of 220 

in 1997.1

Most, if not all, mergers are undertaken by firms that anticipate lower average 

costs or increased profits as a result. These increased profits may arise from 

economies of scale or synergies in production, distribution, management, and 

advertising. At the same time, however, mergers can lead to increased market 

power and potential anti-competitive effects. This paper will assess whether 

economies of scale and synergies resulting from mergers impact productivity 

growth, and, if so, the significance of that impact. 

The current literature has not investigated the relationships among all the 

changes in market structure and productivity, but typically focused on only 

mergers or entry and exit. This paper considers all the reasons why industry 

market structure changes over time. In addition to mergers, the paper investigates 

factors loosely described as industry evolution or changes in competitive 

1

 Workload statistics are available from the U.S. Department of Justice website at 

http://www.usdoj.gov/atr/public/workstats.pdf. 
- 4 -

structure. These factors include births and deaths of establishments, changes in 

the market shares of existing and continuing establishments, and changes in 

establishment output. An industry’s competitive structure evolves over time as 

new establishments enter an industry and old establishments exit. Entry occurs 

when new establishments are built or when changes to an existing establishment's 

product line result in its classification in a different industry. Exit of an 

establishment from an industry occurs either with the closure of an establishment 

or the transfer of an establishment from one industry to another due to a change in 

the product line. An explanation of changes in competitive structure due to births, 

deaths, mergers, and changing market shares is presented in Section 3. 

This paper reaches a number of conclusions related to changes in market 

structure and productivity growth. Model estimation finds that mergers had a 

positive impact on total factor productivity growth and that this effect was 

predominant in nondurable goods industries and concentrated industries. This 

latter result poses a particular problem for antitrust authorities who are especially 

concerned with the anticompetitive effects of mergers in concentrated markets. 

Estimation also determined that births of new firms resulted in faster productivity 

growth. This may have been due to increased competition spurring existing firms 

to compete more vigorously and more efficiently, or from the utilization of stateof-the-art capital and production techniques by new firms. 

In the existing literature, ownership change was considered by Healy et al. 

(1990) who studied the fifty largest mergers among U.S. firms between 1979 and 

1983. They observed that the firms that participated in these mergers realized 

faster asset productivity growth than other firms in the industry. McGuckin, 

Nguyen, and Reznek (1995) investigated establishment ownership change within 

SIC 20, Food and Kindred Products, between 1977 and 1987, to determine the 

effect of ownership change on productivity growth, wage growth, and 

employment. They found that ownership change was positively associated with 

both productivity and wage growth, but that the effects were smaller for large 
- 5 -

firms. Their analysis also showed that establishments that experienced ownership 

change were more likely to survive than those that did not. 

McGuckin and Nguyen (1995a) utilized an unbalanced panel of 

establishments in SIC 20 to find that both employment and productivity were 

positively related to ownership change for the representative establishment, but 

negatively related to establishment closings for large establishments. McGuckin 

and Nguyen (1995b) also investigated the effect that acquisitions of 

establishments had on both the acquiring firm and the acquired establishment. In 

their analysis of SIC 20, they found that the productivity growth of acquired 

establishments increased while acquiring firms suffered slower productivity 

growth. 

Extensive literature exists studying both the entry and exit of firms. Baldwin 

and Gorecki (1991) used Canadian establishment level data from the 1970s to 

investigate the exit rates and growth paths of establishments based on different 

types of entry and exit. Johnson and Parker (1994) analyzed the births of new 

establishments and the deaths of old establishments to detect the effects on future 

births and deaths. They explained possible interactions between births and 

deaths, and determined which variables have an effect on births and deaths. 

Finally, Baily et al. (1992) explored the heterogeneity of productivity within fourdigit industries. They concluded that entry and exit of establishments had little 

effect on industry output growth. Using a neoclassical production function they 

determined that increasing output shares of high productivity establishments, and 

decreasing shares of output in low productivity establishments, were the primary 

causes of industry output growth. 

This paper builds on various aspects of these works and others. I develop a 

model where total factor productivity growth is affected by the changes in the 

competitive structure of an industry and the changes in the level and composition 

of industry output. I begin by adding functional form to the analyses in 

McGuckin and Nguyen (1995a, 1995b) and others to better explain the process of 

how industry evolution, measured at the establishment level, affects productivity 
growth. I also utilize a larger data set than the above papers which allows me to 

investigate all manufacturing industries over more than two decades. From this 

model and extensive data set, I find that changes in market structure in general, 

and changes in market structure due to mergers in particular, impact TFP growth. 

2. Theoretical Framework 

The analysis of productivity growth begins with a 4-digit industry cost 

function given by 

= (p HDTQC ),,,,, (1) 

Where industry subscripts are suppressed. Industry cost is determined by a 

number of variables, including a vector of input prices, p, where the four factors 

of production are capital, k, production workers, l, energy, e, and materials, m. 

Factor markets are assumed to be competitive. The 4-digit industry output, given 

by Q, is the real total value of shipments in the time period. The level of 

technology is given by T. As is the custom, technology is measured in terms of 

time, t, such that, T=et

. D is an index of production diversification. Finally, H

represents the level of competition that exists in the 4-digit industry. I will argue 

that the competitive structure of an industry can change for any of four reasons: 

deaths of existing companies, births of new companies, mergers among 

competitors, and changes in market share of existing firms. These changes will 

be explained in detail in Section 3. 

The ideal level of output may be chosen endogenously in a model of profit 

maximization that is external to this cost function and is not considered here. 

Therefore, I assume that output is exogenous. Industry output is calculated as the 

product QE·E, where QE is the average output of an establishment in the industry 

and E is the number of establishments in the industry. The industry cost function 

is restated as 

( HDTEQC ).,,,,, = p E (2) 

An index describing the level of diversification within a firm was developed 

by Gollop and Monahan (1991). The index illustrates phenomena that exist due 

- 6 -
- 7 -

to the manner in which output data are measured. A 4-digit industry's output 

consists of the production of 5-digit products classified within the industry. The 

industry is comprised of firms, each of which owns one or more production 

establishments. The level of diversification will quantitatively account for three 

issues relating to a firm's output. 

First, a representative firm in a 4-digit industry may produce goods classified 

across a large or small number of 5-digit product categories. For example, Firm 

A's entire output may consist of production of a single 5-digit product within a 4-

digit industry. Firm B, on the other hand, may produce output that is classified 

across ten separate 5-digit product categories. The diversification index accounts 

for this difference in the number of products produced by the firms, such that a 

firm is viewed as increasingly diversified as its number of products increases. 

Second, the index quantifies the different firm characteristics depending upon 

the distribution of output across a number of separate 5-digit product categories. 

Firm B may produce ten separate 5-digit products where one of the ten products 

accounts for 91% of the firm's total output and each of the nine remaining 

products accounts for only 1%. A hypothetical, and far more diversified, Firm C 

may also produce ten separate 5-digit products where each product accounts for 

10% of total output. Gollop’s and Monahan's diversification index accounts for 

this difference in distribution across 5-digit product categories. 

Third, the diversification index quantifies a heterogeneity factor among firms 

that produce multiple 5-digit products. Other things equal, a firm producing a 

number of products with very similar inputs to production is less diversified than 

a firm producing the same number of products requiring very different inputs to 

production. When aggregating numerous 5-digit products into a 4-digit industry, 

significant information that had previously been lost is recovered through the 

diversification index. Each of these three components of the diversification index 

could affect the industry cost function. Gollop (1997) demonstrated that 

production specialization, measured as a reduction in the diversification index, 

had a significant effect on productivity growth measured at the 2-digit industry 
level. He found that a 10% reduction in diversification within an industry 

increased TFP growth by 1.48 percentage points, thereby supporting the argument 

that increased specialization measured at the establishment level led to increased 

productivity growth. 

By logarithmically differentiating equation (2) with respect to time, I obtain 

an expression of the growth in industry production cost in terms of the component 

variables given by 

, ln

ln

lnln

ln

lnln

ln

ln

ln

ln

ln ln

ln

ln ln

ln

ln ln

dt

Hd

H

C

dt

Dd

D

C

dt

Td

T

C

dt

Ed

E

C

dt

Qd

Q

C

dt

pd

p

C

dt

Cd E

h E

h

h

∂

∂

+

∂

∂

+

∂

∂

+

∂

∂

+

∂

∂

+

∂

∂ = ∑

 (3)

for each 4-digit industry. Moreover, h indexes k, l, e, and m in equation (3) and 

throughout the paper. Applying Shephard's lemma to equation (3) allows an 

economic explanation for each of the partial derivatives. The industry cost 

elasticities of each input price are equal to that input's share of total cost. 

Capital's share of input cost is given by 

. ln

ln

k

k

k C

kp

p

C == β ∂

∂ (4) 

Similarly, the industry cost shares of production labor, energy, and materials, and 

are given respectively by 

, ln

ln

l

l

l C

lp

p

C == β ∂

∂ (5) 

, ln

ln e

e

e C

ep

p

C == β ∂

∂ (6) 

and 

. ln

ln m

m

m C

mp

p

C == β ∂

∂ (7) 

The cost elasticity of average establishment output is representative of scale 

economies and is given by 

. ln

ln

QE QE

C = β ∂

∂ (8) 

- 8 -
If QE β takes a value less (greater) than one, then the industry exhibits economies 

(diseconomies) of scale. Other things equal, if cost changes proportionately less 

(more) than average establishment output, then production displays economies 

(diseconomies) of scale. If QE β takes a value equal to one, then the production 

function locally displays constant returns to scale. 

The cost elasticity of the number of establishments within a 4-digit industry is 

given by 

. ln

ln

E E

C = β ∂∂ (9) 

By holding the level of competition, H, fixed with respect to equation (9), the 

number of firms is effectively held constant. Therefore, equation (9) is the 

elasticity of establishments per firm, which measures multiple establishment 

economies. A value of β E that is less (greater) than one implies economies 

(diseconomies) of increasing the number of establishments per firm. 

Technology is defined using census years where T=et such that dtT =∂ 1ln

and the average rate of technical change between census years is given by 

. ln

ln

T T

C = β ∂∂ − (10) 

The average rate of technical change takes a negative sign since an increase in 

technology leads to a reduction in cost. 

The elasticity of cost with respect to the diversification index is given by 

. ln

ln

D D

C = β ∂

∂ (11) 

Other things equal, β D describes the relationship between changes in industry 

cost and changes in the establishment-based measurement of production 

diversification. 

 Finally, consider the variable of particular interest in this paper, the measure 

of 4-digit industry competition. The elasticity of cost with respect to changes in 

competition is given by 

- 9 -
. ln

ln

H H

C = β ∂∂ (12) 

In Section 3 I consider in detail the development of this variable and how it 

changes over time. 

In order to derive total factor productivity growth from the 4-digit industry 

cost growth function described by equation (3), replace the partial elasticities to 

obtain 

. ln ln ln

ln ln ln ln

dt

Hd

dt

Dd

dt

Td

dt

Ed

dt

Qd

dt

pd

t

C

T D H

E

E

Q

h

h

h E

β β β

β β β

− + +

= + +

∂

∂ ∑

 (13) 

From each side of equation (13) subtract the cost-share weighted input price 

growth rates, the growth rate of average establishment output, and the growth rate 

of the number of establishments to obtain 

( ) ( )

. ln ln ln

ln 1 ln 1

ln ln ln ln

dt

Hd

dt

Dd

dt

Td

dt

Ed

dt

Qd

dt

Ed

dt

Qd

dt

pd

dt

Cd

T D H

E

E

Q

h E

h

h

E

β β β

β β

β

− + +

−= −+

−∑ −−

 (14) 

Multiply each side of equation (14) by negative one to obtain the negative of the 

growth rate of cost less the cost-share weighted growth of input prices, the growth 

rate of average establishment output, and the growth rate of the number of 

establishments given by 

( ) ( )

. ln ln ln

ln 1 ln 1

ln ln ln ln

dt

Hd

dt

Dd

dt

Td

dt

Ed

dt

Qd

dt

Ed

dt

Qd

dt

pd

dt

Cd

T D H

E

E

Q

h E

h

E

β β β

β β

β

+ − −

−= −+

⎥

⎦

⎤ ⎢

⎣

⎡ −− ∑ −−

 (15) 

The left-hand side of equation (15) is the expression for total factor productivity, 

i.e. the reduction in industry cost not accounted for by a reduction in input prices 

or industry output. Therefore, equation (15) becomes 

- 10 -
( ) ( )

. ln ln ln

ln 1 ln 1

dt

Hd

dt

Dd

dt

Td

dt

Ed

dt

Qd PFT

T D H

E

E

QE

β β β

β β

+ − −

& −= −+

 (16) 

The intuition behind the right-hand side variables becomes clearer upon 

inspection of equation (16). For example, an increase in the average output per 

establishment, other things equal, would result in economies (diseconomies) of 

scale if QE β is less (greater) than one. Likewise, an increase in the establishment 

level diversification within an industry would decrease (increase) total factor 

productivity if β D is greater (less) than zero. 

3. Competitive Market Structure 

An important contribution of this paper is the treatment of changes in 

competitive structure of the market. Therefore, I further decompose ln dtHd

into separate components reflecting changes in the competitive market structure 

due to the deaths of existing firms in an industry, the births of new firms into an 

industry, horizontal mergers, and changes in the market shares of continuing firms 

in the industry. Previous authors have argued that the competitive forces within 

an industry will affect industry cost. The theory that the level of competition 

affects production cost was described by Leibenstein (1966) as x-efficiency. 

Leibenstein wrote that there is “more to output than the obviously observable 

inputs. The nature of management, the environment in which it operates, and the 

incentives employed are significant.”2

 Leibenstein argued that both competition 

and adversity create pressure for changes to improve x-efficiency. Many authors 

have built upon the x-efficiency framework to explain why firms may not operate 

in a cost minimizing fashion and, furthermore, how firms might improve xefficiency. 

Nickell (1996) asked whether competition improves firm performance. His 

analysis of 670 U.K. manufacturing companies supported the view that a more 

 

- 11 -

2

 Leibenstein (1966), p. 401. 
competitive market, measured by both the number of competitors and by 

decreased monopoly rents, was associated with higher total factor productivity 

growth. Stennek (2000) developed a model where both financial constraints and 

the level of competition within an industry act as disciplining powers resulting in 

higher effort and increased x-efficiency. Scherer and Ross (1990) found that xinefficiency was low when competition was strong and that the losses due to xinefficiency were as large as losses from allocative inefficiency. 

As a measure of competition, albeit an imperfect measure, I will utilize the 

Herfindahl-Hirschman (HH) index. The HH index is calculated as the sum of 

squared market shares of each company within an industry. The HH takes a 

maximum value of 10,000 when one company produces the entire industry output 

and a minimum value approaching zero under perfect competition. Changes in 

the HH index are prominent indicators of changes in competition and these 

changes are utilized in the U.S. Department of Justice Merger Guidelines. 

Changes in the HH index of a certain magnitude due to a proposed merger invite 

increased scrutiny of the merger by the Department of Justice or Federal Trade 

Commission. Markets with HH indexes below 1000 are considered 

unconcentrated. Those markets with HH indexes between 1000 and 1800 are 

considered moderately concentrated. Finally, those markets with HH indexes 

above 1800 are highly concentrated. Establishment data are aggregated to the 

company level since an establishment level HH index would be artificially low as 

in the following example. If a monopolist had ten establishments, each producing 

10% of industry output, the HH index should take the maximum value of 10,000 

and not the more competitive appearing value of 1,000. 

The changes in competitive structure due to deaths, births, mergers, and 

changes in market share can be approximated by the changes in the HH index. 

The HH index can change as a result of the death of a company within the 

industry. 3

 A company can close its establishments that produce within the given 

 

- 12 -

3

 I consider deaths to occur separately from other changes in competitive structure. The direct 

change in the HH index as a result of the death of companies is given by 
- 13 -

 

industry or it can sell its establishments and cease production in this industry. If a 

company exits the industry by selling its establishments to a new entrant, I 

consider this action to be the death of the existing firm and the birth of a new firm 

as the establishment's ownership changes. 

The change in the HH index due to deaths will likely be positive reflecting a 

potentially less competitive market with fewer competitors. This increase in the 

HH index due to deaths could impact TFP growth in any or all of three separate 

effects. First, the closing of establishments may remove the least productive and 

highest cost plants from the industry. Therefore, the increase in the HH index due 

to the deaths of companies will increase TFP growth. Second, a company exiting 

the industry can sell its productive establishments to other companies. Matching 

theory of establishment turnover suggests that ownership change of continuing 

plants would reduce average cost and increase TFP growth. The third potential 

effect is that the death of a company reduces the number of competitors within an 

industry. The theory of x-efficiency would lead one to believe that this reduction 

in competition could reduce the cost-cutting incentives of the remaining firms. 

Conversely, one also suspects that a dying firm is likely a high cost and low TFP 

( ) 2 , 2

2 1,

1,

2

2 1,

1,

1,

2

1,

1, ∑ ∑

∑ ∑ ∑ ∑

∑ −

−

−

−

−

− =Δ − + − l

tl

i ti

i ti

l

tl

l i ti

i ti

tl s

s

s

s

s

s

sHH

2

3

2

2

2

11 t− ++= sssHH

 where l indexes firms that 

exist in census year t-1 and do not exist in year census year t, and i indexes companies that exist in 

both census years. The market share of each company is denoted by s. Therefore, the change in 

the HH index due to a death can be described through the following example where one of three 

firms exits between periods. 

and if the continuing firms grow proportionately to their own size in period t-1, then 

.

2

3

21

2

2

2

3

21

1

1 ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

++ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

+= s

ss

s

ss

ss

s t sHH

This is rewritten as 

( ) 2 . 2

21

2

2

2

2 1

3

21

2

2

2

1

3

2

2

2

1

ss

ss

s

ss

ss t sssHH

+

+

+

+

+

++=

Then the change in the HH index between periods due to the death of company 3 is 

( ) 2 ,

2

2 3

21

2

2

2

2 1

3

21

2

2

2

1

31 s

ss

ss

s

ss

ss t t sHHHH − ++

+

+

+ − =−

which can be generalized as in the equation above. 
growth firm. Therefore, the effect of deaths of existing companies upon TFP 

growth is unclear. 

A birth is defined as a company that does not produce any output in industry 

A in census year t-1, but by census year t, the company has at least one 

establishment that produces primarily in industry A.4

 The company can either 

build a new establishment to enter the industry or it can purchase an existing 

establishment and produce in industry A in census year t. 

This change in the HH index will likely be negative,5

 reflecting a potentially 

more competitive market structure with more competitors. Entry into an industry 

can take one of two forms. First, entry can take place when a company builds 

new establishments or purchases unused establishments. One would suspect that 

the latest technology in production would put downward pressure on cost and 

increase TFP growth. Second, entry can occur through a change in ownership of 

an existing establishment. In this case, a firm that does not produce in SIC A 

purchases an existing establishment inside or outside of SIC A and begins 

- 14 -

 

4

 I consider births to occur separately from other changes in competitive structure. The direct 

change in the HH index resulting from a company birth is given by 

( )

2

1,

2

2 1,

,

1,

2

1,

,

2

, 2

∑

∑ ∑ ∑

∑ ∑∑ −

−

−

− −=Δ +

i ti

i ti

m

tm

i ti

i ti

m

tm

m

tm

s

s

s

s

s

ssHH , where m, indexes companies that 

do not exist in census year t-1, but do exist in census year t, and i indexes companies that exist in 

both census years. Therefore, the change in the HH index due to a birth can be described by the 

following example where two incumbents are joined by a new entrant, companies 1, 2, and 3, 

respectively. 

2

2

2

11 t− += ssHH

and if the new firm takes market share proportionately from the two incumbents, then 

.

2

3

2

3

21

2

2

2

3

21

1

1 ss

ss

s

ss

ss

s t sHH + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

−+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ −=

This can be restated as 

( ) 2 . 2

21

2

2

2

1

3

21

2

2

2

1

3

2

3

2

2

2

1

ss

ss

s

ss

ss t ssssHH

+

+

+

+

+

−++=

Then the change in the HH index between periods due to the birth of company 3 is 

( ) 2 , 2

21

2

2

2

1

3

21

2

2

2

1

3

2

31

ss

ss

s

ss

ss t t ssHHHH

+

+

+

+

+ − −=−

which can be generalized as in the equation above. 

5

 An increase in the number of competitors could increase the Herfindahl-Hirschman index if the 

new companies have large enough market shares. 
producing goods in SIC A. The matching theory of plant turnover argues that low 

productivity results from a poor match between the establishment and the parent 

company. This theory would predict lower cost and an improvement in TFP 

growth as a result of the ownership change. 

The HH index can also change as a result of a merger among competitors. 6

 A 

merger among competitors will always increase the HH index. Mergers can have 

one or both of two effects. First, as enforcers of antitrust law assert, mergers 

among competitors can result in a reduction in competition and therefore a 

reduction in x-efficiency as firms lose some cost cutting incentives. This would 

lead to lower TFP growth. Second, nearly every merger among competing 

companies is described by the participants as an opportunity to cut costs and take 

advantage of synergies among the companies involved. This would lead to lower 

cost and higher TFP growth. Therefore, the effect of mergers on TFP growth may 

in theory be either positive or negative. 

 A fourth reason why the competitive structure of the market and the HH index 

will change from one census year to the next is as a result of a simple change in 

market share for continuing firms in the industry. For example, four firms with 

equal market shares, 25% each, would exhibit a HH index calculated as 2,500. If, 

between periods, the market share of one firm grows to 40% while the market 

- 15 -

 

6

 I consider mergers to occur separately from other changes in competitive structure. Only 

horizontal mergers are considered such that the change in the HH index due to a merger is the 

result of a merger among two or more firms within the same 4-digit industry. The direct change in 

the HH index due to the merger of two competitors is given by 

2 , ∑∑ 1,1,

≠

=Δ −−

i i j

tjti HH ss

where firms i and j merge between census years t-1 and t. Three firms merging can be described 

by the following example where three competitors merge to become a single firm between periods 

such that, 

2

4

2

3

2

2

2

11 t− +++= ssssHH and 

( )2

432

2

1 t +++= ssssHH , 

which can be rewritten as 

434232 .222 24

2

3

2

2

2

1 t ++++++= ssssssssssHH

The change in the HH index due to the merger of the three firms is therefore 

t t− +=− + ssssssHHHH 4342321 ,222

which can be generalized as in the equation above. 
shares of the competing firms fall to 20% each, the HH index is calculated as 

2,800. This change in the HH index of over 11% arises from a change in the 

market shares of the continuing firms. The HH index can therefore change, 

possibly by a large amount, even if there are no births or deaths of companies or 

no mergers among competitors. I measure the change in the HH index due to a 

change in company market share as a residual; it is the change in the HH index 

from census year t-1 to census year t that is not due to deaths, births, or mergers. 

A fifth reason why the HH index can change from census year to census year 

is due to a phenomenon I designate as “switching.” Switching is essentially an 

artifact of the definition of a four-digit industry. Consider a single establishment 

company that produces two different products. One product is classified as being 

within industry A, while the other is classified within industry B. In census year 

t-1, fifty-one percent of the establishment's total value of shipments is classified 

within industry A while the remaining forty-nine percent is in industry B. This 

establishment is classified within the LRD as producing in industry A. If, in the 

next census year, forty-nine percent of the establishment's sales are in industry A 

and fifty-one percent are within industry B, then the establishment would be 

classified within industry B. This process is an example of switching. I separate 

it from other types of firm evolution because, for example, there may be no 

change in the production of the above establishment within industry A, but an 

increase in its industry B production. Switching will therefore be considered 

separately from deaths, births, mergers, and changes in market share. 

I substitute the separate changes in the HH index for ln dtHd into equation 

(16) to obtain 

( ) ( )

. ln ln

ln ln ln

ln ln 1 ln 1

dt

Hd

dt

Hd

dt

Hd

dt

Hd

dt

Dd

dt

Td

dt

Ed

dt

Qd PFT

mktshare

H

merger

H

birth

H

death

D H

E T

E

Q

merger mktshare

death birth

E

β β

β β β

β β β

− −

− − −

& −= −+ +

 (17) 

- 16 -
- 17 -

 

A contribution of this paper to the existing literature is its development and 

treatment of the changes in competition, measured as changes in the HH index. 

Section 4 further describes the development of variables that estimate the change 

in the HH index. 

4. Data Set Construction 

To estimate the coefficients of the above theoretical model, I construct a data 

set from two separate resources. The first source of data is the Manufacturing 

Industry Database maintained by Eric J. Bartelsman, Randy A. Becker, and 

Wayne B. Gray. The database is a joint effort between the National Bureau of 

Economic Research (NBER) and the U.S. Census Bureau's Center for Economic 

Studies (CES). The database contains input price indexes and 4-digit industry 

output that are used in the calculation of total factor productivity. Bartelsman and 

Gray (1996) described the calculation of total factor productivity that will be 

utilized in this paper. The database also contains 4-digit industry output price 

deflators. These data are available for download from the NBER website.7

The second source of data is the U.S. Census Bureau and the Longitudinal 

Research Database (LRD). Maintained by the CES, the LRD is an unbalanced 

panel containing cost and output data on all U.S. manufacturing establishments 

collected through the Census of Manufactures. The Census of Manufactures has 

collected this information in the census years: 1963, 1967, 1972, 1977, 1982, 

1987, 1992, and 1997. The LRD contains data on each establishment's inputs of 

labor, materials, and capital, its total value of shipments of goods and services in 

each 7-digit product, its location, and its legal form of organization. Within the 

LRD, each establishment is assigned a permanent identification number allowing 

it to be tracked from census year to census year. The establishment is classified 

by the industry that accounts for the largest percentage of the plant’s output. Each 

establishment ID contains an identifier number that links the establishment to its 

parent company which similarly is assigned an identification number. The LRD 

7

 The NBER – CES website can be found on the world-wide-web at http://www.nber.org/nberces/. 
- 18 -

 

can therefore identify whether the establishment is part of a single establishment 

company or a multiple establishment company. Because of the identifier linking 

an establishment to a parent company, the LRD can determine ownership 

changes. It is also possible to detect the birth of new establishments by the 

appearance of a new establishment ID, and likewise the LRD can detect the death 

of an existing establishment when plant ID numbers disappear from one census 

year to the next. I have obtained 4-digit industry data by rolling up establishment 

level data to both the company level and the industry level.8

The LRD provides three key variables for my analysis. First the total value of 

shipments of each establishment within a 4-digit industry provides industry output 

and the number of establishments in the industry. I compute real industry output 

by utilizing these data and the 4-digit industry price deflators from the NBERCES database. Then, for each 4-digit industry, calculate the average real output 

per establishment and the number of establishments. The product of the average 

real output per establishment, QE, and the number of establishments, E, is equal to 

4-digit industry output. 

Second, the diversification index is developed utilizing the LRD. A complete 

explanation of its construction exists in Gollop and Monahan (1991). Third, the 

data enable the calculation of the Herfindahl-Hirschman index (HH) for each 4-

digit industry. The change in the HH index between census years is decomposed 

into the change in the HH index due to “switching,” deaths, births, mergers, and 

the change in market share. Ideally, the calculations of the changes would occur 

simultaneously, as if all deaths, births, and mergers happened at the same time. 

Since this is computationally impossible, I assume that the different types of firm 

evolution happen sequentially. Therefore, the change in the HH index is 

calculated as the sum of the five changes listed above. 

Begin with the population of companies within an industry and compute the 

HH index for year t-1. Designate this HH index as H1,t-1. Then alter the 

population of firms by adjusting for switching and calculate the HH index, 

8

 Special thanks to James Monahan of the Center for Economic Studies whose assistance was 

invaluable. 
designated as H2,t-1. Next, adjust the population by accounting for all company 

deaths that occur between census years t-1 and t. Designate the HH index 

calculated from this population as H3,t-1. Again adjust the population, this time by 

adding to the population those companies that enter the industry between census 

years t-1 and t. Designate the HH index calculated from this population as H4,t-1. 

Finally, adjust the population of firms by accounting for all the horizontal mergers 

between census years t-1 and t. Designate the HH index calculated from this 

population as H5,t-1. Then calculate the HH index for the census year t population 

of firms and designate it as H1,t. Therefore, the change in the log of the HH index 

is given by 

( ) ( )

( ) (

( ).lnln

lnln lnln

lnln lnln lnln

,1 1,5

1,4 1,3 1,5 1,4

,1 1,1 1,2 1,1 1,3 1,2

−

− − − −

− − − − −

−+

−+−+ )

=− − + −

t t

t t t t

t t t t t t

HH

HH HH

HH HH HH

 (18) 

Switching is calculated initially and this makes sense intuitively. I attempt to 

obtain a more accurate value of the true level of competition within a 4-digit 

industry as measured by the HH index. I therefore want to remove those 

companies that enter or exit the industry simply as a result of the changes in the 

classification of an establishment's output without obvious physical changes. 

Moreover, the change due to mergers should be calculated after births since new 

firms may be involved in mergers with existing firms. The choice of calculating 

first the change due to deaths and then the change due to births is completely 

arbitrary and yet likely has little impact upon the estimation results. 

5. Econometric Model 

I select a functional form for the industry cost function to test the hypothesis 

that changes in the competitive structure of an industry impact TFP growth. 

Consider the Cobb-Douglas cost function as an approximation of industry cost 

, h Q DTEE HDTEQpC H

E

h

h

β β ββββ =α∏ (19) 

where h indexes the four input prices. As with the model described in Section 2, 

take the natural log of each side of equation (19) to obtain 

- 19 -
.lnlnln

ln ln ln ln

HDT

C p Q E

T D H

Q EE

h

h h E

βββ

βα β β

+++

+= ∑ + +

 (20) 

Differentiate equation (20) with respect to time and rearrange to obtain 

( ) ( )

, ln ln

ln 1 ln 1

dt

Hd

dt

Dd

dt

Ed

dt

Qd PFT

DT H

E

E

QE

ββ β

β β

−+ −

& −= −+

 (21) 

which is an expression for TFP growth in continuous time derivatives in terms of 

the parameters from the Cobb-Douglas cost function, equation (19). 

 To estimate the coefficients of equation (21), continuous time derivatives need 

to be converted to discrete differences. The Cobb-Douglas cost function is 

evaluated at two discrete points in time. To obtain the average TFP growth 

between two points in time, restate the left-hand side of equation (21) as a discrete 

change from time t-1 to t, 

( )

( ) lnln ( )].lnln

lnln ln[ln lnln

, 1, 1

1 1 , 1,

− −

− − −

−−−−

−−−=− ∑ −

tQ tE t t

th th

h

t t t t h

QQ EE

TFP TFP CC β pp

 (22) 

Since it is possible that the industry input cost elasticities, β h , change from one 

census year to another, calculate the average elasticity as 

( . 2

1

h += βββ thth −1,, ) (23) 

These expressions allow measurement of TFP growth using discrete data. The 

right-hand side of equation (21) is also converted from continuous to discrete 

time. TFP change is then given by 

( )( ) ( )( )

( ) ( )

( ).lnln

lnln lnln

lnln lnln1lnln1

1

1 1

1 1 1

−

− −

− −

− −

−−+ −

−=− −+− − −

tH t

ttT tD t

t t Q E E tE t

HH

TT DD

TFP TFP QQ EE E t t

β

β β

β β

 (24) 

Again, the average industry cost elasticities are as given in equation (23). The 

resulting final form for the model that can be estimated using discrete data is 

obtained by combining equations (22) and (24) and substituting the components 

of the change in the HH index from equation (18) to obtain 

- 20 -
( )( ) ( )( )

( )( )

( )(

( )( lnln .lnln

lnln lnln

lnln lnln

lnln lnln1lnln1

1,5 1,4 ,1 1,5

1,3 1,2 1,4 1,3

1 1

1 1 1

− − −

− − − −

− −

− −

− −− −

− −− −

−−+ −

)

)

−=− − + − − −

merger t t mktshare t t

death t t birth t t

ttT tD t

t t Q E E tE t

HH HH

HH HH

TT DD

TFP TFP QQ EE E t t

β β

β β

β β

β β

 (25) 

Using equation (25), I estimate the impact of each described category of industry 

evolution upon TFP growth. For example, if βbirth is positive (negative), then 

births, which likely reduce the HH index, will increase (decrease) TFP growth. 

Likewise, if βmerger is positive (negative), then mergers, which will always 

increase the HH index, will decrease (increase) TFP growth. 

 Finally, I append a random error to equation (25) and assume that the error 

structure possesses the characteristics appropriate to the assumptions for ordinary 

least squares estimation. Because the data are first-differenced, I also estimate 

models that account for the possibility of serial correlation. 

6. Econometric Results 

 The data set includes observations of approximately four hundred 4-digit 

industries across six census years. All variables except the diversification index 

are available for seven census years. I have obtained TFP growth, real output, the 

number of establishments, the number of companies, the diversification index, 

and the Herfindahl-Hirschman index for each census year from the sources 

described above. Since T=et

, the change in lnT reflects the time between census 

years. Therefore, the elasticity of cost due to the growth of technology is the 

average annual technological growth across all industries between census years. I 

estimate a series of model specifications using fixed effects estimation methods. 

 Table 1 presents the estimation results of four variations of equation (25). The 

two-sided significance levels (p-values) are given below the estimates in 

parentheses. The fixed effects (within) estimator is used to estimate each 

specification in Table 1. Model (1) is the basic model specification reflecting 

estimation of equation (25). Model (2) includes only the change in the HH index 

due to mergers and drops the changes due to deaths, births, and changes in market 

- 21 -
- 22 -

Table 1: Fixed Effects Estimation Results for All Industry Observations 

Coefficients (1) (2) (3) (4) 

Output per Est. (1-βQE) 0.0672 0.0713 0.0707 

(0.000) (0.000) (0.000) 

Establishments (1-βE) -0.0230 -0.0085 -0.0146 

(0.041) (0.384) (0.150) 

Industry Output (1-βQ) 0.0386 

(0.000) 

Technology βT 0.0001 0.0142 0.0026 0.0177 

(0.991) (0.000) (0.760) (0.000) 

Diversification -βD -0.0244 -0.0243 -0.0091 -0.0244 

(0.001) (0.001) (0.197) (0.001) 

Deaths -βdeath -0.0360 0.0559 

(0.302) (0.092) 

Births -βbirth -0.1260 -0.0365 

(0.001) (0.308) 

Mergers -βmerger 0.1135 0.1146 0.1163 

(0.026) (0.025) (0.024) 

Mkt. Share -βmktshare 0.0409 0.0441 

(0.005) (0.003) 

HH -βHH -0.0124 

 (0.181) 

R2

 Overall 0.0720 0.0781 0.0481 0.0768 

F-Test ui=0 0.0002 0.0011 0.0001 0.0007 

n 2138 2148 2138 2138 

share. Model (3) estimates coefficients for a modified equation (25) where 4-digit 

industry output growth is substituted for average establishment output growth and 

growth in the number of establishments. Model (4) substitutes the change in the 

HH index between census years in place of the separate changes in the HH index 

due to deaths, births, mergers, and changes in market share. In model (1), the 

estimated coefficient on the change in establishment output is 0.0672 and is 

significant at a 1% level. Other things equal, a 10% increase in the average 

output per establishment leads to a 0.62 percentage point increase in TFP growth. 

We therefore observe economies of scale in production since the elasticity of cost 

with respect to average establishment output growth is 0.9328. An increase in the 

average establishment output growth rate of 1% leads to a 0.9328 percentage 

point increase in cost growth. When estimated at the means (provided in Table 3) 

and other things equal, economies of scale contributed 0.68 percentage points to 
- 23 -

TFP growth between census years (calculated as the product of the estimated 

coefficient, 0.0672, and the average growth rate in average establishment output, 

0.1005). 

 The estimated coefficient of the growth in number of establishments is 

-0.0230, significant at a 1% level. We therefore observe diseconomies of multiple 

plant operations. The estimated elasticity of cost with respect to diversification 

growth is -0.0244 and is significant at a 1% level. Therefore, a reduction in 

diversification of 10% leads to a 0.24 percentage point increase in TFP growth. 

When estimated at the means, the reduction in average establishment 

diversification contributed 0.20 percentage points of TFP growth between census 

years (calculated as the product of the estimated coefficient, -0.0244, and the 

average growth rate of diversification, -0.0838). 

 The coefficients of particular interest are those elasticities of cost with respect 

to deaths of existing companies, births of new companies, mergers among 

existing companies, and changes in market share of existing companies. The 

estimated coefficient on the change in the HH index due to deaths is not 

significantly different from zero. The estimated coefficient on the change in TFP 

growth due to the change in the HH index due to births is -0.1260 and is 

significant at a 1% level. Note that a change in the HH index due to births is 

negative such that as new firms enter, the HH index decreases in magnitude. 

Estimated at the means, the births of new firms contributed 2.14 percentage points 

of TFP growth between census years (calculated as the product of the estimated 

coefficient, -0.1260, and the average change in the HH index due to births, 

-0.1701). The estimated coefficient on the change in the HH index due to mergers 

is 0.1135 and is significant at better than a 5% level. Estimated at the means and 

other things equal, mergers contributed 0.36 percentage points to TFP growth 

between census years (calculated as the product of the estimated coefficient, 

0.1135, and the average change in the HH index due to mergers between census 

years, 0.0320). The overall R2

 for the fixed effects model is 0.0720. An F-test of 

the hypothesis that the industry specific effects, ui, are jointly zero can be rejected 
at a 1% confidence level. The hypothesis is rejected at a 1% level for each model 

(1) through (4). 

 Model (2) does not include the changes in the HH index due to deaths, births, 

and changes in market share. The estimated coefficients on changes in output per 

establishment, changes in the number of establishments, changes in 

diversification, and mergers are nearly identical to those estimates from model 

(1). Likewise, the effect of technological growth becomes positive and 

significant. Finally, the overall R2

 for the model is 0.0781. In comparing models 

(1) and (2) it appears that the effect of technological growth may be largely due to 

the entry of new firms with the newest technology and management methods. 

When the births variable is excluded, technological growth is significant and 

positive, but when births are included in the model, technological growth is 

negative and significant. 

 Model (3) substitutes industry output growth for growth of average 

establishment output and growth of the number of establishments. The estimated 

coefficient for TFP growth due to growth in industry output is 0.0386 and is 

significant at a 1% level. The impact of deaths on TFP growth was positive and 

significant at a 10% level. The impact of births on TFP growth was 

insignificantly different from zero. The estimated coefficient on mergers is 

0.1163 and is nearly identical to the estimates from models (1) and (2). The 

overall R2

 is only 0.0481. 

 Model (4) substitutes the change in the HH index between census years for the 

changes in the HH index due to deaths, births, mergers, and changes in market 

share. The estimated coefficient for TFP growth due to the change in the HH 

index is not significantly different from zero. Except for the estimated coefficient 

for technology, which is positive and significant at a 1% level, the other estimated 

coefficients are similar to those in model (1). 

I then estimate the fixed effects model with an AR(1) error term for model (1). 

Therefore, rather than assuming that the error term eit is independently and 

identically distributed, assume that it = ρ −1 + uee itit , where uit is iid normal with 

- 24 -
Table 2: Fixed Effects Estimation Results for Selected Industry Observations 

 (5) (6) (7) (8) (9) (10) 

Coefficients Conc. Unconc. Dur. Nondur. High Tech Low Tech

Output per Est. (1-βQE) 0.0281 0.1442 0.0438 0.1180 -0.0230 0.1593 

(0.237) (0.000) (0.000) (0.000) (0.194) (0.000) 

Establishments (1-βE) -0.0403 0.0660 -0.0603 0.0338 -0.1205 0.0829 

(0.203) (0.000) (0.000) (0.020) (0.000) (0.000) 

Technology βT 0.0203 -0.0173 -0.0008 0.0088 0.0601 -0.0124 

(0.313) (0.027) (0.947) (0.428) (0.000) (0.131) 

Diversification -βD 0.0004 -0.0375 -0.0343 -0.0215 -0.0122 -0.0230 

(0.980) (0.000) (0.004) (0.009) (0.480) (0.001) 

Deaths -βdeath 0.1140 0.0774 -0.0859 0.0045 -0.2663 0.0516 

(0.323) (0.016) (0.096) (0.919) (0.002) (0.100) 

Births -βbirth 0.0484 -0.0299 -0.2068 0.0353 -0.1802 -0.0074 

(0.714) (0.354) (0.000) (0.512) (0.023) (0.842) 

Mergers -βmerger 0.3797 0.0871 0.0539 0.1686 0.1932 0.1013 

(0.070) (0.048) (0.510) (0.003) (0.234) (0.015) 

Mkt. Share -βmktshare -0.0392 0.0218 0.0476 0.0250 0.0436 0.0155 

 (0.420) (0.075) (0.013) (0.260) (0.217) (0.243) 

R2

 Overall 0.0099 0.1168 0.0417 0.1559 0.0104 0.2223 

F-Test ui=0 0.9995 0.0000 0.0000 0.3869 0.0000 0.0257 

n 468 1670 1226 912 588 1550 

 

mean zero. After estimating model (1) using fixed effects and the AR(1) error 

structure, the modified Durbin-Watson statistic, defined by Bhargava, Franzini, 

and Narendranathan (1982), is determined to be 2.29. The null hypothesis that 

ρ = 0 cannot be rejected and serial correlation is no longer considered in this 

paper. 

 I next investigate various data subsets to determine whether the estimated 

relationships differ among different types of industries. Model (5) estimates 

coefficients for equation (25) using only concentrated industry observations. A 4-

digit industry is considered concentrated if the HH index is greater than or equal 

to 1000. Likewise, those industries with HH indexes below 1000 are considered 

unconcentrated. Model (6) estimates coefficients for the basic model using only 

unconcentrated industries. Model (7) estimates the model using only durable 

good industry observations and model (8) is estimated with only nondurable 

goods industry observations. I utilize the Bureau of Economic Analysis definition 

- 25 -
- 26 -

of durable and nondurable goods industries. Durable good 2-digit industries 

include SICs 24, 25, and 32 through 39. Similarly, nondurable goods industries 

include SICs 20 through 23 and 26 through 31. Finally, I consider high 

technology and low technology industries separately. Hadlock et. al (1991) 

classify 3-digit industries as high tech if their proportion of R&D employment is 

greater than or equal to the average proportion for all 3-digit industries (see 

appendix). 

 Table 2 presents the results from these industry specific regressions. Model 

(5) is estimated using only the 468 concentrated industry observations. The 

estimated coefficient for the change in the HH index due to mergers is 0.3797 and 

is significant at a 7% level. Estimated at the means, and other things equal, 

mergers accounted for 0.62 percentage points of TFP growth in concentrated 

industries between census years (calculated as the product of the estimated 

coefficient and the average change in the HH index due to mergers, 0.0162). The 

overall R2

 for this model is equal to 0.0099. 

 Model (6) is estimated with only unconcentrated industry observations. 

Economies of scale are observed in these industries with an estimated coefficient 

on growth of output per establishment of 0.1442. The coefficient on 

establishment growth is 0.0660 and is significant at a 1% level. Surprisingly, 

technological growth is -0.0173 and significant at a 5% level. The estimated 

coefficient on deaths is 0.0774 and is also significant at better than a 5% level 

while the estimated coefficient on births is not significantly different from zero. 

The estimated coefficient for TFP growth due to the change in the HH index due 

to mergers is 0.0871 and is significant at a 5% level. Estimated at the means, and 

other things equal, mergers added 0.32 percentage points to TFP growth between 

census years (calculated as the product of the estimated coefficient and the 

average change in the HH index due to mergers in unconcentrated industries, 

0.0364). The R2

 for this model is 0.1168. 

 Model (7) is estimated using only durable goods industry observations. 

Economies of scale are observed in the coefficient estimate of 0.0438 for growth 
- 27 -

in average establishment output. The elasticity of cost with respect to 

diversification is -0.0343 and is significant at a 1% level. The estimated 

coefficient on the change in the HH index due to births is -0.2068 and is 

significant at a 1% level. Estimated at the means, and other things being equal, 

births accounted for 3.73 percentage points of TFP growth (calculated as the 

product of the estimated coefficient and the average change in the HH index due 

to births, -0.1805). The estimated coefficient on mergers is not significantly 

different from zero. Finally, the overall R2

 for this model estimation is 0.0417. 

 Compare the results of model (7) with those of model (8) which is estimated 

with nondurable goods industry observations. Economies of scale become larger 

with an estimated coefficient of 0.1180. Estimated at the means, other things 

being equal, economies of scale accounted for 1.78 percentage points of TFP 

growth (calculated as the product of the estimated coefficient and the average 

growth of output per establishment, 0.1507). The estimated coefficient on 

establishment growth is significant in both models (7) and (8), but is negative for 

durable goods industries and positive for nondurable goods industries. Also the 

estimated coefficient on births is not significantly different from zero in 

nondurable goods industries, compared to the strong positive effect of births on 

TFP growth in durable goods industries. Another difference between models (7) 

and (8) is the estimated effect of mergers on TFP growth. The estimated 

coefficient on mergers in nondurable industries is 0.1686 and is significant at a 

1% level. Other things equal and estimated at the means, mergers accounted for 

0.61 percentage points of TFP growth (calculated as the product of the estimated 

coefficient and the average change in the HH index due to mergers, 0.0359). 

Finally, the R2

 for model (8) is 0.1559 and the F-test that ui are jointly zero can 

not be rejected as it could be in model (7). 

 Model (9) is estimated using only high tech industry observations and model 

(10) is estimated with low tech (non-high tech) industries. The estimated 

coefficient for growth of output per establishment is not significantly different 

from zero in high tech industries. The same estimated coefficient for low tech 
- 28 -

firms is 0.1593 and is significant at a 1% level. Economies of scale in low tech 

industries accounted for 1.57 percentage points of TFP growth (calculated as the 

product of the estimated coefficient and the average change in output per 

establishment, 0.0983). 

 Comparing models (9) and (10), note the difference between coefficients on 

growth in number of establishments, -0.1205 in the former and 0.0829 in the 

latter. The average growth in the number of establishments was 0.0850 in high 

tech industries and 0.0057 in low tech industries. Therefore, the growth in 

establishments accounted for -1.02 percentage points of TFP growth in high tech 

industries and 0.05 percentage points of TFP growth in low tech industries. The 

estimated coefficient describing technological growth is 0.0601 in high tech 

industries and is insignificantly different from zero in low tech industries. The 

estimated coefficient of technological growth is -0.0124 in low tech industries but 

is only significant at a 13.1% level. The estimated coefficient on diversification is 

not significantly different from zero in high tech industries and is -0.0230 in low 

tech industries. Estimated at the means, reductions in diversification accounted 

for 0.17 percentage points of TFP growth in low tech industries (calculated as the 

product of the estimated coefficient and the average change in diversification in 

low tech industries, -0.0746). 

 The estimated coefficient on births is -0.1802 in high tech industries and is 

significant at better than a 5% level. When estimated at the means, births of new 

firms added 2.74 percentage points to TFP growth (calculated as the product of 

the estimated coefficient and the average change in the HH index due to births, 

-0.1523). The estimated coefficient on births in low tech industries is not 

significantly different from zero. 

 Finally, the estimated coefficient on mergers is not significantly different from 

zero in high tech industries, but is equal to 0.1013 and is significant at a 5% level 

in low tech industries. When estimated at the means, other things equal, mergers 

accounted for 0.36 percentage points of TFP growth in low tech industries 

(calculated as the product of the estimated coefficient and the average change in 
- 29 -

Table 3: Variable Means for Varying Industry Samples 

 All Conc. Unconc. Dur. Nondur. High Tech Low Tech

TFP Growth 0.0264 0.0301 0.0253 0.0249 0.0283 0.0449 0.0193 

Output per Est. 0.1005 0.0501 0.1146 0.0632 0.1507 0.1063 0.0983 

Establishments 0.0275 0.1049 0.0059 0.0632 -0.0204 0.0850 0.0057 

Diversification -0.0838 -0.1231 -0.0727 -0.1008 -0.0608 -0.1081 -0.0746 

Deaths 0.1656 0.0842 0.1884 0.1622 0.1701 0.1279 0.1799 

Births -0.1701 -0.1000 -0.1897 -0.1805 -0.1561 -0.1523 -0.1768 

Mergers 0.0320 0.0162 0.0364 0.0291 0.0359 0.0238 0.0351 

ΔMkt Share -0.0245 -0.0455 -0.0186 -0.0350 -0.0103 -0.0416 -0.0180 

n 2138 468 1670 1226 912 588 1550 

the HH index due to mergers in low tech industries, 0.0351). The overall R2

 for 

high tech industries is 0.0104 and is 0.2223 in low tech industries. 

 Table 3 presents the means for each variable. When the models are estimated 

at the means, one is able to determine which variables contribute most to TFP 

growth. TFP growth has averaged 2.64% in manufacturing industries between 

census years. In model (1) observe that for all industries, births contribute most to 

TFP growth, followed by economies of scale and then mergers. Births may 

increase TFP growth through three separate processes. First, the new firms may 

enter by building new establishments with cutting edge technology. Second the 

new firms may take over existing establishments and manage the establishment 

more successfully than the previous management. Third, the entry of new firms 

may increase the degree of competition in the industry, thereby reducing xinefficiency. Mergers likely increase TFP growth by creating cost cutting 

opportunities for the firms involved. 

 The estimated models for concentrated industries, durable goods industries, 

and high tech industries are relatively poorly estimated so they are not considered 

here. In unconcentrated industries, technological growth had a strongly negative 

impact on TFP growth. Economies of scale and deaths were the largest 

contributors to TFP growth followed by births and mergers. In nondurable goods 

industries, economies of scale were the largest contributor to TFP growth, 

followed by technological growth and mergers. 
- 30 -

 The model estimated with low tech industry observations displays the highest 

R2

 among the regressions presented, equal to 0.2223. Economies of scale were 

the prime contributor to TFP growth, followed by deaths and mergers. 

 An appendix to this paper includes additional regressions not discussed in the 

paper. These regressions include feasible generalized least squares regressions 

where autocorrelation within panels is allowed. 

7. Conclusion 

 This paper attempts to explain some portion of total factor productivity 

growth through changes in the competitive structure of a 4-digit industry. 

Estimations of different specifications lead to a number of conclusions. First, in 

the initial model, the changes in the Herfindahl-Hirschman index due to births, 

mergers, and changes in market share had a statistically significant impact on total 

factor productivity growth. Second, the effect of mergers on TFP growth varied 

across different industry samples. The impact of mergers was greatest in 

concentrated industries, nondurable goods industries, and low tech industries. 

When the model is estimated using only observations from concentrated 

industries, the importance of mergers increased. Conversely, when the model 

specification is estimated using observations from only unconcentrated industries, 

the coefficient on mergers is positive, smaller than for concentrated industries and 

significant at a 5% level, compared to an 8.2% level in concentrated industries. 

Therefore, the argument that mergers lead to greater productivity growth appears 

to be most valid in those industries in which the Department of Justice is 

especially vigilant in regulating mergers. Third, a reduction in the HH index due 

to the births of new companies within an industry also led to an increase in TFP 

growth. Again, this is especially true in durable goods industries and high tech 

industries. 

 Using the Herfindahl-Hirschman index as a measure of competition within an 

industry is imperfect, but it is arguably a more complete measure than others, 

such as the number of competitors or a four-firm concentration ratio. The 
- 31 -

importance that I assign to the HH index as a measure of competition is supported 

by the U.S. Department of Justice Merger Guidelines' dependence upon the index 

as a key component in determining whether a merger will reduce competition 

enough to adversely impact consumers. The results of the model estimation 

suggest a number of potential conclusions. Mergers increased TFP growth by a 

substantial amount, supporting claims by merger participants that mergers allow 

exploitation of economies in production. The births of new companies within an 

industry increased competition and likely introduced the newest technology to the 

industry. This supports the x-inefficiency arguments advanced in Nickell (1996) 

and Stennek (2000). In this instance, increased competition, measured as a 

decrease in the HH index, led to faster TFP growth. A reduction in the 

competitive forces within an industry may reduce cost cutting initiatives and 

increase x-inefficiency, but efficiency gains from mergers often appear to offset 

the reduction in competition. 
- 32 -

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Appendix 

Table 4: Estimation Results for All Industry Observations 

Coefficients (1a) (2a) (3a) (4a) 

Output per Est. (1-βQE) 0.1015 0.1062 0.1090 

(0.000) (0.000) (0.000) 

Establishments (1-βE) 0.0104 0.0229 0.0154 

(0.313) (0.010) (0.100) 

Industry Output (1-βQ) 0.0720 

(0.000) 

Technology βT 0.0061 0.0110 0.0073 0.0130 

(0.264) (0.002) (0.183) (0.000) 

Diversification -βD -0.0310 -0.0312 -0.0146 -0.0311 

(0.000) (0.000) (0.033) (0.000) 

Deaths -βdeath -0.0466 0.0488 

(0.107) (0.068) 

Births -βbirth -0.0794 0.0052 

(0.006) (0.849) 

Mergers -βmerger 0.0773 0.0728 0.0872 

(0.085) (0.105) (0.055) 

Mkt. Share -βmktshare 0.0248 0.0284 

(0.264) (0.035) 

HH -βHH -0.0196 

(0.025) 

Common Corr. Coeff. 0.0321 0.0284 0.0270 0.0235 

n 2130 2143 2130 2130 

Regression Method f.g.l.s. f.g.l.s. f.g.l.s. f.g.l.s. 
- 35 -

Table 5: Estimation Results for Selected Industries 

(5a) (6a) (7a) (8a) (9a) (10a) 

Coefficients Conc. Unconc. Durable Nondurable 

High 

Tech 

Low 

Tech 

Output per Est. (1-βQE) 0.0573 0.1593 0.0892 0.1320 0.0317 0.1681 

(0.002) (0.000) (0.000) (0.000) (0.057) (0.000) 

Establishments (1-βE) 0.0016 0.0727 -0.0165 0.0477 -0.0686 0.0818 

(0.946) (0.000) (0.289) (0.000) (0.002) (0.000) 

Technology βT 0.0100 -0.0088 0.0079 0.0045 0.0381 -0.0057 

(0.477) (0.135) (0.313) (0.513) (0.006) (0.242) 

Diversification -βD -0.0030 -0.0427 -0.0458 -0.0227 -0.0310 -0.0254 

(0.837) (0.000) (0.000) (0.004) (0.071) (0.000) 

Deaths -βdeath 0.0807 0.0517 -0.1115 0.0198 -0.1903 0.0368 

(0.346) (0.058) (0.014) (0.558) (0.014) (0.149) 

Births -βbirth -0.0613 0.0008 -0.1395 0.0112 -0.1890 0.0117 

(0.497) (0.975) (0.001) (0.772) (0.007) (0.657) 

Mergers -βmerger 0.4569 0.0780 0.0596 0.0908 0.1183 0.0754 

(0.009) (0.060) (0.414) (0.066) (0.437) (0.037) 

Mkt. Share -βmktshare 0.0110 0.0151 0.0237 0.0240 0.0169 0.0177 

(0.773) (0.194) (0.187) (0.209) (0.622) (0.133) 

Common Corr. Coeff. 0.1642 0.2110 0.0206 0.0319 0.0732 0.0417 

n 432 1641 1223 907 585 1545 

Regression Method f.g.l.s. f.g.l.s. f.g.l.s. f.g.l.s. f.g.l.s. f.g.l.s. 
- 36 -

High Technology Industries by 1987 3-Digit SIC from Hadlock et al. (1991) 

SIC Code Industry Description 

211 Cigarettes 

229 Msc. Textile goods 

261 Pulp mills 

267 Misc. converted paper products 

281 Industrial inorganic chemicals 

282 Plastics, materials & synthetics 

283 Drugs 

284 Soap, cleaners, & toilet goods 

285 paints & allied products 

286 Industrial organic chemicals 

287 Agricultural chemicals 

289 Misc. chemical products 

291 Petroleum refining 

299 Misc. petroleum & coal products 

335 Nonferrous rolling & drawing 

348 Ordnance & accessories n.e.c. 

351 Engines & turbines 

355 Special industry machinery 

356 General industrial machinery 

357 Computer & office equipment 

359 Industrial machines n.e.c. 

362 Electrical industrial apparatus 

365 Household audio & visual equipment 

366 Communications equipment 

367 Electronic components & accessories 

369 Misc. electrical equipment & supplies 

371 Motor vehicles & equipment 

372 Aircraft & parts 

376 Guided missiles, space vehicles & parts 

379 Misc. transportation equipment 

381 Search & navigation equipment 

382 Measuring & controlling devices 

384 Medical instruments & supplies 

386 Photographic equipment & supplies