1

Firm Size and Information Technology Investment:

Beyond Simple Averages

Tianyi JiangLeonard N. Stern School of BusinessNew York UniversityDecember 16, 2003

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MotivationEffectiveness of information technology (IT) investments…

Specifically: How does IT impact firm sizes and firm boundaries

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IT’s Theoretical Impact on Firm

IT…

decreases decision cost, agency cost, & coordination costs between & across firms

- Gurbaxani et al. 1991could make firms smaller

- Malone et al. 1987

lead to outsourcing from fewer suppliers - Bakos et al. 1993

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Empirical Evidence on the impact of ITIT investment…

is negatively correlated with firm size across all industries. – Brynjolfsson, et al. 1994

is negatively correlated with vertical integrationis weakly positively correlated with diversification

– Hitt, 1999

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Research Questions:1. In the context of new NAICS classifications, are IT

investments negatively correlated with firm size across all industries?

2. In measuring impact of IT investments at the industry level, is average employees per firm a good measure?

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NAICS Industries IT investment ratio in 1992

0%

5%

10%

15%

20%

25%

30%

Rat

io o

f IT/

Oth

er in

vest

men

ts

7

Regression on 1992 COMPUSTAT Data  All Industry Regression for 1992 COMPUSTAT Data

Dependent Variable

Log(Employees)

Constant -1.16***IT Investment Ratio -0.10***

Log(Net Sales) 0.85***Industry Dummies 

   

R-Squared 0.87Durbin-Watson 1.92F Statistic 2637.40Observations 6577

 

Key: *= Significant at 90% level; **= Significant at 95% level; ***= Significant at 99% level;

13/16 industries significant at 99% level

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Problems with simple firm averages

Observations: • Large numbers of small firms can bring down average firm sizes even if the bigger firms got bigger

example: firms sizes = {1,1,1,1,100,100}

average size = 34

• Most entry & exit has relatively little effect on the largest firms in the industry - Sutton 1997

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1992 Employee Sizes - Professional Services

-4

-3

-2

-1

0

1

2

3

Companies Sorted by Employees

Log(

Em

ploy

ees)

1992 Annual Sales - Professional Services

-3

-2

-1

0

1

2

3

4

5

6

Companies Sorted by EmployeesLo

g(An

nual

Sal

es)

Problems with median firm sizes

1992 Professional Services Employee Histogram

MedianMedian

.8%.8% total Salestotal Sales 99.2%99.2% total Salestotal Sales1%1% total Emptotal Emp 99%99% total Emptotal Emp

1992 Professional Services Sales Histogram

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Employee weighted firm sizes

• Emphasize the size of larger firms to minimize the effects of entry & exit - Kumar et al. 2001 *

Weighted Average Number of Employees =

= total number of employees in a bin

= total number of employees in the sector

= total number of firms in a bin

n

Firmsbin

Empbin

EmpSector

Empbin

NN

NN

1

EmpbinNEmpSectorNFirmsbinN

* Kumar, K., Rajan, R., & Zingales, L. “What Determines Firm Size?” Working Paper, The University of Chicago Graduate School of Business, 2001.

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Employee size calculation example

Example: firms sizes = {1,1,1,1,100,100} average size = 34

Employee weighted average: 2 bins: {1,1,1,1} and {100, 100}

weighted average = (4/204)*(4/4) +(200/204)*(200/2)

=98.05882

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0

0.25

0.5

0.75

1

0 0.25 0.5 0.75 1

% of firms with i employees

Entro

py

Automated bin partitionRecursive Minimum Entropy Partitioning – Fayyad et al. 1993

Entropy: A measure of homogeneity of values – Mitchell 1997

Example: 2 distinct values, i,j, ij S be a bin of firms with i

or j employeesthen

jjii ppppSEntropy 22 loglog)(

Pi = percentage of firms with i employees

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Recursive Minimum Entropy Partitioning

Let S = original bin A = set of newly split bins Gain (S,A) = Entropy(S)-E[Entropy(A)]

Idea: Recursively split data into smaller bins with nearly homogenous values until gain < threshold

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Recursive Minimum Entropy Partitioning (cont.)

RecursiveSplits

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Sales weighted firm sizes• Alternatively, we could emphasize firms with higher proportion of sales to minimize the effects of entry & exit

Sales Weighted Employees Sizes =

= total number of employees in a bin

= total number of firms in a bin

= total amount of sales in a bin

= total amount of sales in a sector

n

Firmsbin

Empbin

SalesSector

Salesbin

NN

NN

1EmpbinNFirmsbinN

SalesbinNSalesSectorN

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Firm size measures across NAICS industries with low IT investment ratio

Real Estate & Rental & Leasing (Employees per firm)

0

0.5

1

1.5

2

2.5

3

3.5

1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Year

Aver

age

Empl

oyee

s (th

ousa

nds)

0

10

20

30

40

50

60

70

80

Wei

ghte

d Av

erag

e Em

ploy

ees

(thou

sand

s)

AverageEmployees WeightedAverageEmpolyees SalesWeightedAvgEmployee

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Firm size measures across NAICS industries with low IT investment ratio (cont.)

Utilies (employees per firm)

0

1

2

3

4

5

6

7

8

1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Year

Aver

age

Empl

oyee

s (th

ousa

nds)

0

10

20

30

40

50

60

70

80

90

100

Wei

ghte

d Av

erag

e Em

ploy

ees

(thou

sand

s)

AverageEmployees WeightedAverageEmpolyees SalesWeightedAvgEmployee

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Firm size measures across NAICS industries with medium IT investment ratio

Information Industry (Employees per firm)

0

2

4

6

8

10

12

1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Year

Aver

age

Empl

oyee

s (th

ousa

nds)

0

50

100

150

200

250

Wei

ghte

d Av

erag

e Em

ploy

ees

(thou

sand

s)

AverageEmployees WeightedAverageEmpolyees SalesWeightedAvgEmployee

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Firm size measures across NAICS industries with high IT investment ratio (cont.)

Professional Services (Employees per firm)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Year

Aver

age

Empl

oyee

s (th

ousa

nds)

0

50

100

150

200

250

300

Wei

ghte

d Av

erag

e Em

ploy

ees

(thou

sand

s)

AverageEmployees WeightedAverageEmpolyees SalesWeightedAvgEmployee

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Regression Model

= natural log of 3 different employee measures in year t = natural log of IT investment ratio per industry

in year t = natural log of net sales per industry per year

= 17 industry dummy variables

= i.i.d. error term with zero meanitINDUSTRY

t

ttiti

tttttt

NetSalesINDUSTRY

ITITITITITSIZE

76

4534231210

tNetSalestIT

tSIZE

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Data & Methodology• Computed industry level employee measure & net sales

via COMPUSTAT data from 1982 to 2001 (443,507 records)

• Extracted IT investment ratio from BEA (Bureau ofEconomic Analysis) Input-Output use tables for the benchmark years of 1982, 1987, 1992, & 1997(Required many to many mappings of NAICS to SIC

and SIC to IO codes)

• Interpolated IT investment ratios for other years

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Regression Results – Across 6 NAICS Industries

  All Industry Regression TableVariable SIZE1 (Simple Average) SIZE2 (Employee Weighted

Average)SIZE3 (Sales Weighted Average)Constant 1.15 9.20*** 5.25

IT Investment Ratio by year      

ITINVRATIO(0) -0.04* 0.02 -0.05ITINVRATIO(-1) 0.05* 0.01 -0.03ITINVRATIO(-2) -0.01 0.04 -0.01ITINVRATIO(-3) 0.01 -0.04 -0.06ITINVRATIO(-4) -0.04*** -0.04* -0.05NetSales 0.11** -0.33*** -0.13

Industry Dummies     Professional Services -1.32*** -0.58** 0.60Manufacturing -0.98*** -1.80*** -1.62***Finance & Insurance -1.25*** -1.25*** -2.09***Education -1.81*** -5.85*** -4.54***WholeSale Trade -1.85*** -2.25*** -2.01***R-Squared 0.99 0.99 0.96Durbin-Watson 1.26 0.73 0.60F Statistic 709.90 539.00 136.76Number of observations 72 72 72

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Regression Result: Professional Services  Professional Services Regression Table

Variable SIZE1 (Simple Average)

SIZE2 (Employee Weighted Average)

SIZE3 (Sales Weighted Average)

Constant -2.45** 1.18 2.06

IT Investment Ratio by year      

ITINVRATIO(0) 0.22* 0.56* 0.52*ITINVRATIO(-1) 0.04 -0.06 -0.10ITINVRATIO(-2) -0.01 -0.0346 0.1065ITINVRATIO(-3) -0.20 -0.82** -0.87**ITINVRATIO(-4) -0.02 0.16 0.17*NetSales 0.31*** 0.22 0.18

       

R-Squared 0.87 0.98 0.98Durbin-Watson 2.59 2.30 2.72F Statistic 5.66 52.23 52.32Number of Observations 12 12 12

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Research Limitations• Need yearly IT investment data across all industries

• Tried Brookings panel data, replicated previous results across industries, but lacked the data for Professional Services

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SummaryTechnical Research Contributions:

• Apply recursive minimum entropy methods to the empirical economics domain

Economic Research Contributions:

• Utilize weighted average employee sizes to replicate previous studies on IT investments and firm sizes

• Found varying patterns of evolving firm sizes across industries with different IT investment ratios

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Thank You!Special thanks to Ramesh Sankaranarayan & Shinkyu Yang