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Analyzing the relationships between information technology, inputssubstitution and national characteristics based on CES stochasticfrontier production models

Yueh H. Chen a,, Winston T. Lin b,

a College of Management, National Sun Yat-sen University, Kaohsiung, Taiwanb School of Management, The State University of New York at Buffalo, New York 14260, USA

a r t i c l e i n f o

Article history:

Received 1 September 2006

Accepted 1 July 2008Available online 19 April 2009

Keywords:

Information technology

Constant elasticity of substitution (CES)

One- and two-equation models

Productive (or technical) efficiency

Inputs substitution and complement

The productivity paradox

Two-factor and three-factor CES production

functions

a b s t r a c t

This research examines four interrelated issues at the country level: the value of

information technology (IT), inputs substitution and complement, the complementarity

phenomenon created by IT and national characteristics, and the productivity paradox,

jointly and critically from a global perspective, using the so-called productive efficiency

as the performance measure. To that end, we develop the three-factor constant elasticity

of substitution (CES) stochastic production frontier model and apply it to a set of panel

data from 15 countries over the period 19932003, along with the traditional two-factor

CES models, within the one- and two-equation frameworks. In the two-equation setting,

six national characteristics are selected as the contributing factors of the productive

efficiency. The findings include: (i) the value of IT as measured by the productive

efficiency is duly recognized: (ii) the productivity paradox is found to be absent from the

production process in a majority of developed and developing countries considered,rejecting the existing argument that the paradox exists only in developing economies

but does not exist in developed countries; however, the developed countries have used

IT capital in their production systems more productively efficiently than the developing

nations; (iii) traditional capital (non-IT capital), traditional labor, and IT capital are not

pairwise substitutable, contrary to the notion that they are pairwise substitutable at the

firm level; (iv) constant returns to scale, as commonly assumed, are not supported by

the data; (v) different national characteristics affect a countrys output (represented by

gross domestic product or GDP) and its productive efficiency differently; and (vi) the

complementarity phenomenon is observed in most of the countries (developed and

developing) under study.

& 2009 Published by Elsevier B.V.

1. Introduction

Using the same firm-level panel data set as used in a

number of studies (e.g., Brynjolfsson and Hitt, 1996;

Dewan and Min, 1997; Hitt and Brynjolfsson, 1996; Lin

and Shao, 2000; Lin and Shao, 2006a,b; Shao and Lin,

2000, 2001, 2002), Lin and Shao (2006b) have reached

contradictory conclusions concerning the three issues,

namely, the value of information technology (IT), inputs

substitution among IT capital and ordinary capital and

labor, and the productivity paradox. One source of the

conflicting conclusions is that the three issues must be

investigated simultaneously, yet virtually all previous

research using the same set of firm-level data from the

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/ijpe

Int. J. Production Economics

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0925-5273/$ - see front matter & 2009 Published by Elsevier B.V.doi:10.1016/j.ijpe.2008.07.034

Corresponding authors. Tel.: +886 7 525 2000; fax: +8867 525 4898

(Yueh H. Chen); tel.: +1716645 3257; fax: +1716645 5078

(Winston T. Lin).

E-mail addresses: [email protected] (Y.H. Chen),

[email protected] (W.T. Lin).

Int. J. Production Economics 120 (2009) 552569
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United States private sector treated them separately and

individually.

The study of Lin and Shao (2006b) is the only

exception. Applying the traditional two-factor constant

elasticity of substitution (known as CES) stochastic

production frontier models, (Lin and Shao, 2006b) studied

the above-mentioned issues simultaneously at the firm,

industry, and sector levels, and suggested an immediateextension to it by putting the three issues in a global

perspective (for external validity (Tam, 1998) via globali-

zational generalization Lin, 2009), thereby requiring a

multinational comparison based on country-level panel

data. In particular, we believe that inputs substitutability

or complementarity in production processes is a complex

matter which needs more research taking a global

perspective.

The present study is motivated by the need to study

the country differences associated with the three im-

portant issues stated above as compared with the firm-

level results obtained by Lin and Shao (2006b). The study

is further motivated by the fact that knowledge accumu-lation at the country level is poor (Lin, 2009; Melville et

al., 2004). Therefore, we propose to address the three

issues jointly at the country level and, simultaneously,

examine the possibility of the complementarity phenom-

enon created by IT and national characteristics. The

economic theory and the methodology on which the

present study is based are the theory of production and

the parametric time-varying stochastic frontier produc-

tion approach underlying the theory (Lin, 2009), in

conjunction with the CES production functions, using

the so-called productive efficiency (PE, also called techni-

cal efficiency) as the performance measure that is a

product automatically generated by the parametric sto-chastic frontier production approach (cf. Aigner et al.,

1997; Debreu, 1851; Farrell, 1957; Lin and Shao, 2000,

2006a, b; Lovell, 1993 for the theories of the parametric

frontier production approach and the PE; and Lin and

Shao, 2000, 2006a, b; Lin, 2009; Murillo-Zamorano and

Vega-Cervera, 2001; Park and Lesourd, 2000; Richie and

Rowcroft, 1996 for the justifications of the application of

the frontier production approach and the PE in the

production economics/research and information systems

literatures).

More specifically, the primary objective of this research

is to jointly investigate the four interrelated issues

regarding the value of IT, the possibility of the substitu-tion/complement among IT capital, traditional capital, and

traditional labor, the phenomenon of complementarity

promoted by IT and national characteristics, and the

paradox of productivity, by estimating the IT value in

terms of the effect of IT upon productive efficiencies,

based on the CES stochastic frontier production model. On

the methodological front, we not only consider an one-

equation-two-factor CES model as used in Lin and Shao

(2006b), but also propose to apply the two-equation-two-

factor CES frontier production model; and, in more

importantly, we further develop the one-equation-three-

factor and two-equation-three-factor CES models. Empiri-

cally, the numerous estimated results from differentstochastic frontier models are carefully analyzed. The

whole sample of the 15 countries selected is constituted

by two groups (subsamples). Group 1 consists of eight

developed countries (the G7 countries plus Australia),

while Group 2 is composed of seven emerging economies.

The remainder of the paper is organized as follows.

Section 2 conducts a literature review. Section 3 specifies

the CES stochastic frontier production models. Section 4

explains the data and estimation method used. Then,Section 5 reports empirical estimates, and Section 6

discusses the results collectively and individually, com-

pares them with others for the G7 countries, and offers

additional discussion into the decision-making benefits of

this work for managers and firms. Finally, Section 7

concludes the paper with a summary and some remarks.

2. A literature review

Nobel Laureate economist Robert (Solow, 1987) has

questioned the value of IT investments and observed the

existence of the IT productivity paradox in response to thefact that the massive investment in IT did not seem to

have any positive effects on productivity growth. He has

characterized the research results of the productivity

paradox in this way (Brynjolfsson, 1993; Triplett, 1999):

We can see computers everywhere but in the productiv-

ity statistics. The questions about the business value of IT

and its by-product called the productivity paradox have

perplexed managers and researchers for a number of years

(Hitt and Brynjolfsson, 1996). This is because in recent

years, abundant research has presented conflicting evi-

dence concerning whether vast investments in computers

and related technologies have (e.g., Brynjolfsson and Hitt,

1996; Hitt and Brynjolfsson, 1996; Lin and Shao, 2000,2006a) or have not (Berndt and Morrison, 1995; Bryn-

jolfsson, 1993; Lin and Shao, 2006b; Loveman, 1988,

among others) realized expected benefits.

The empirical results of the studies addressing the

value of IT have indicated that the productivity paradox

did exist in the 1980s but was found to disappear in the

early 1990s (Brynjolfsson and Hitt, 1996; Hitt and

Brynjolfsson, 1996; Lin and Shao, 2000, 2006a, b). A

careful review of more current literature (post-2000) on

IT value (e.g., Lee et al., 2005; Lin and Shao, 2006a;

Melville et al., 2007; Ngwenyama et al., 2007; Peacock and

Tanniru, 2005; Thatcher and Pingry, 2004; Tohidi and

Tarokh, 2006; Zhu, 2004, among others) clearly suggeststhat the paradox has been essentially dispelled at the firm

level.

Most studies, however, have presented evidence at the

firm level (e.g., Berndt and Morrison, 1995; Brynjolfsson

and Hitt, 2000; Harris and Katz, 1991; Hitt and Brynjolfs-

son, 1996; Lin and Shao, 2000, 2006a, b; Loveman, 1988;

Mukhopadhyay et al., 1997; Parsons et al., 1992; Shao and

Lin, 2000, 2001, 2002). As a result, there has been too

much emphasis on US firms and lack of cross-country

studies on the value of IT and the influence of national

characteristics; and, as such, research at the country level

is progressing comparatively slowly. As a second conse-

quence, knowledge accumulation concerning national(macro-) characteristics and IT value at the country level

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has been inhibited and poor (Lin, 2009; Melville et al.,

2004), and this is the source of a good deal of our concern.

The number of country-level studies indeed is coun-

table, consisting of (Dewan and Kraemer, 2000; Jorgenson,

2003; Kraemer and Dedrich, 1994; Lee et al., 2005; Lin and

Chen, 2002; Lin, 2009; Shu and Lee, 2003; Tam, 1998). The

Dewan and Kraemers (2000) work has used a CobbDou-

glas production regression model, while the Lins (2009)study has deployed the stochastic frontier production

models specified by the CobbDouglas, translog produc-

tion functions, and the BoxCox and BoxTidwell trans-

formations. Interestingly enough, the empirical evidence

given by these two studies with respect to the paradox of

productivity is contradictory and inconsistent. The former

has concluded that the productivity paradox is absent

from the developed countries group but does exist in the

developing countries subsample. In contrast, Lin (2009)

has reached a quite different conclusion that the paradox

is a global phenomenon and may exist in a country

regardless of whether it is a developed country or a

developing economy; and the conclusion is fairly robustwith respect to the stochastic production frontier em-

ployed. Nonetheless, unlike the CES production functions,

the widely used CobbDouglas and translog functions and

the BoxCox and BoxTidwell transformation offer no

routes to analyze the phenomenon of complementarity

promoted by IT investments and national characteristics

jointly with the issue of inputs substitution and comple-

ment, under the umbrella of the one-equation parametric

stochastic frontier production approach.

Kraemer and Dedrich (1994) have concluded that the

Asian-Pacific countries show a significantly positive

correlation between the IT investment and the growth in

both GDP and productivity, thereby refuting the produc-tivity paradox. Lin and Chen (2002) have provided an in-

depth comprehensive analysis of the productive efficien-

cies of major industries in Taiwan and China, using a two-

equation stochastic frontier model fitted into a panel

sample covering the 19801988 period. They have con-

cluded that the industries in China perform less produc-

tively efficiently than their counterparts in Taiwan. In

applying the two-equation model, they have identified the

sources of productive (in)efficiency from economic,

financial, political, educational, social, and geographic

differences between Taiwan and China. Shu and Lee

(2003) have done a research on the IT industries of 14

OECD countries and found that their productive efficien-cies are low among these countries in comparison with

their counterparts in Lin (2009). Finally, Lee et al. (2005)

have shown that IT contributes to economic growth in

many developed and newly industrialized economies, but

not in developing countries.

There are different explanations for the lack of positive

returns on IT investments and the existence of the

productivity paradox, which typically include (Lin,

2009): (i) the time lags of the productivity-enhancing

effects of a new technology (David, 1990); (ii) mismea-

surement of outputs (Bessen, 2002; Brynjolfsson, 1993;

Lee and Barua, 1999; Siegel, 1997); (iii) mismeasurement

of inputs (Devaraj and Kohli, 2003); (iv) over investmentsin IT, particularly during the second half of the 1980s

(Morrison, 1997); (v) lack of organizational changes to

accompany IT investments (Brynjolfsson and Hitt, 2000);

(vi) neglect of the substitutability and complementarity

among IT capital, traditional capital, and traditional labor

(Lin and Shao, 2006b), which is an important issue to be

addressed in this research; and (vii) improper use of

econometric methods, which is another issue of special

concern in the present study.Closely related to the issues of the IT value and the

productivity paradox are the substitutability of IT capital

for both traditional capital and labor and the occurrence of

the complementarity phenomenon accounted for by IT

investments and national characteristics. Even though the

literature abounds in research dedicated to address the

value issue and explain or dispel the paradox, the

literature is virtually silent about the possibility of the

substitution/complement among IT capital, non-IT capital,

and labor. In other words, it is scarce of research that

makes the substitutability/complementarity of IT capital

for both ordinary capital and labor a subject for serious

empirical inquiry, with the studies of Dewan and Min(1997), Lin and Shao (2006b), and Menon and Lee (2000)

being the only three exceptions. The first and second

studies represent a firm level analysis using the same set

of panel data, but have provided contradictory evidence.

The third study is an analysis of the healthcare industry,

using a set of panel data.

Similarly, the literature is also totally silent about the

impacts of national (or macro-) characteristics upon

outputs and productive efficiencies in production systems.

In other words, the literature is totally silent about the

potential of the complementarity phenomenon created by

the interaction of IT investments and national character-

istics. Zhu (2004) has sought to assess the complemen-tarity of e-commerce capability and IT infrastructure at

the firm level, but it has nothing to do with the

complementarity between IT spending and national

characteristics that concerns us here.

Various performance measures (Lin and Shao, 2006b)

have been employed in the studies of the business value of

IT and the paradox, including: (i) profitability (Bresnahan,

1986; Cron and Sobol, 1983; Dos Santos et al., 1993; Floyd

and Wooldridge, 1990; Hitt and Brynjolfsson, 1996); (ii)

productivity (Dewan and Min, 1997; Dewan and Kraemer,

2000; Hitt and Brynjolfsson, 1996; Loveman, 1988;

Morrison, 1997; Mukhopadhyay and Cooper, 1993; Mu-

khopadhyay et al., 1997); (iii) quality (Mukhopadhyay etal., 1997); (iv) operative efficiency (Banker et al., 1990); (v)

Tobins q (Bharadwaj et al., 1999; Morrison, 1997); and (vi)

consumer surplus (Bresnahan, 1986; Hitt and Brynjolfs-

son, 1996). As one can observe, the first two measures are

the most popular ones.

The performance measure called productive (or tech-

nical) efficiency (PE) is employed for the first time in the

production economics/research and IS literatures by Lin

and Shao (2000) to investigate the business value of IT and

the paradox of productivity. They have noted several

compelling reasons why PE is used. Several different

specifications of the stochastic frontier production func-

tion have been applied in the literatures of IS andproduction economics/research; and these include: (i)

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the generalized CobbDouglas function (Dewan and

Kraemer, 2000; Lin and Shao, 2000, 2006a; Lin, 2009;

Shao and Lin, 2000, 2001; Shu and Lee, 2003); (ii) the

BoxCox and BoxTidwell transformations (Lin and Shao,

2000; Lin and Shao, 2006a; Lin, 2009); (iii) the translog

function (Lin, 2009; Shao and Lin, 2000; Shao and Lin,

2001); (iv) the data envelopment analysis and Tobit

regression (Shao and Lin, 2002); and (v) the one-equation-two-factor CES function (Lin and Shao, 2006b).

Using the set of firm-level data from the United States

private sector, the positive impact of IT investments on PE

and the disappearance of the productivity paradox have

been recognized in (i)(iv), but conflicting results have

been obtained in (v) and (Lin, 2009).

The present research represents a significant extension

to previous country-level work and is a major effort to

jointly and critically investigate the four interrelated

issues as mentioned earlier. These are the IT value issue,

the productivity paradox, the relevance of national

characteristics, and the potential of the substitution and

complement among IT capital and ordinary capital andlabor. It attempts to estimate the IT value measured by the

impact of IT on PE, within the framework of the CES

stochastic frontier production models. This research is

featured by at least four striking aspects: (i) in addition to

the first of three one-equation-two-factor CES frontier

production models used in Lin and Shao (2006b) that will

be repeatedly considered in this study for purposes of

comparison, the one-equation-three-factor CES model is

developed theoretically and applied empirically; (ii) we

expand the one-equation CES model into a two-equation

model, enabling us to analyze the effect of IT upon PE and

assess the contributions of national characteristics to the

observed output and, hence, the phenomenon of com-plementarity; and (iii) the present study promotes knowl-

edge accumulation concerning IT value and national

characteristics at the country level, which is viewed as

urgently needed by Lin (2009), Melville et al. (2004); and

(iv) this study is engaged in a multinational analysis

which differs significantly from previous research (Dewan

and Min, 1997; Kaynak and Pagan, 2003; Lin and Shao,

2006b; at the firm level; and Dewan and Kraemer, 2000;

Jorgenson, 2003; Lin, 2009; Lin et al., 2009; Shu and Lee,

2003 at the country level) in objectives, research methods

and statistical samples.

3. Methods

3.1. The stochastic production frontier approach: a one-

equation model

The stochastic production frontier model for cross-

sectional data was proposed and applied by Aigner et al.

(1997) and Meeusen and van den Broeck (1977). Subse-

quently, Pitt and Lee (1981), Schmidt and Sickles (1984),

and Ahn and Schmidt (1977) have extended the cross-

sectional stochastic frontier model to accommodate

panel data (cross-sectional and time-series data). The

form of the stochastic production frontier model with atime-varying productive (in)efficiency model can be

described by

Yjt fXjt;b vjt ujt; j 1; . . . ;Nand t 1; . . . ;M

(1)

where Yjt the observed output for the j-th firm (plant),

industry, sector, region, or country, at time t; fXjt;bis the

ideal, desired, or maximum output produced by a setof inputs, Xjt, such as ordinary capital, ordinary labor,

and IT capital, with a vector of unknown coefficients, b, to

be estimated; vjt is the traditional random error repre-

senting the effects of countless uncontrollable factors; and

uit is a one-sided normally distributed random error

representing productive inefficiency that may be influ-

enced by numerous factors controllable by management

at the firm level and a government at the country level.

Thus, in the stochastic production frontier approach, the

observed output is decomposed into three elements: the

theoretical maximum output, the traditional random

shock, and the random indicator of productive inefficiency

influenced by factors under the control of the firm,industry or country, and the ideal (desired) output

requires ujtX0 or ujtp0 (see Lin and Chen, 2002; Lin

and Shao, 2000, 2006a,b; Lin, 2009; Lin et al., 2009;

Lovell, 1993 for more details).

In fact, according to Lin and Chen (2002), Eq. (1), the

stochastic frontier model with a time-varying inefficiency

for panel data (Ahn and Schmidt, 1977; Lin and Chen,

2002; Pitt and Lee, 1981) is evolved from the deterministic

frontier model with a time-invariant inefficiency (ujt uj)

in the absence of vjt appropriate for cross-sectional data

(Aigner and Chu, 1968; Farrell, 1957), the stochastic

frontier model with ujt uj in the presence of vjt vj

for cross-sectional data (Aigner et al., 1997; Chen andTang, 1987; Meeusen and van den Broeck, 1977), and the

stochastic frontier model with a time-invariant ineffi-

ciency (ujt uj) and vjt for panel data (Beeson and Hnsted,

1989; Kumbhakar et al., 1991; Pitt and Lee, 1981; Schmidt

and Sickles, 1984). We strongly feel that to pool a panel

data sample, a time-invariant stochastic frontier model in

which ujt uj is certainly inappropriate.

Several studies (Ahn et al., 2007; Battese and Coelli,

1992; Cornwell et al., 1990; Cuesta, 2000; Kumbhakar,

1990; Lee, 2006; Lee and Schmidt, 1993) have suggested

different specifications to make the one-sided stochastic

component ujt in the one-equation model (1) change

systematically over time and noticeably as time goesby. The notable examples include: (i) Kumbhakar

(1990): ujt 1 expa1t a2t21uj , where ujt is

assumed to be a product of a function of t and a time-

invariant inefficiency; (ii) Cornwell et al. (1990):

ujt b0t b1j b2jt b3jt2, a quadratic t function with a

dynamic intercept; (iii) Battese and Coelli (1992):

ujt expbt muj, where, like (i), ujt is specified to be

a product of a function of t and a time-invariant

inefficiency); (iv) Lee and Schmidt (1993): ujt ytaj, aproduct of a time-varying and a time-invariant

element; (v) Cuesta (2000): ujt expbjt muj , a gen-

eralization of (iii); and (vi) Ahn et al. (2007):

ujt y1ta1j y2ta2j yptapj, a generalization of (ii)and (iv).

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We would expect that different specifications imposed

on ujt lead to quite distinct time-varying stochastic

frontier models. Thus, it is not surprising that empirical

results are very sensitive to different specifications; and if

there are no principles to follow, arbitrary choice of

specifications might bias the results. For instance, the

Battese-Coelli model fitted into our panel data has

produced the productive efficiencies of individual coun-tries that are systematically and noticeably increasing

over time-a kind of results that is neither acceptable nor

justifiable. Fortunately, the LIMDEP program is capable of

estimating productive inefficiencies ujt, for all j and t,

without imposing any specification on it, when the one-

equation model (1) is applied. The specifications on ujtmentioned above are not appropriate for the two-

equation model which we now turn to.

3.2. The generalized stochastic production frontier model: a

two-equation model

The productive inefficiency ujt in the one-equationmodel (1) may be affected by various controllable factors.

To account for this or to identify the sources of the

productive inefficiency, a generalized two-equation sto-

chastic frontier model (cf. Lin and Chen, 2002; Lin and

Shao, 2006b is used):

Yjt fXjt;b vjt ujt (2)

ujt gZjt;a wjt; j 1; . . . N and t 1; . . . ;M (3)

where the stochastic productive inefficiency ujt is con-

stituted by two components, namely, the deterministic

component, gZjt;a, subject to (determined by) the

influence of Zjt and the one-sided distributed randomcomponent, wjt, where Zjt is a vector which represents a

broad set of country-specific characteristics or firm- or

industry-specific factors and macroeconomic factors

common to all firms (or industries) or countries consid-

ered, observable and/or unobservable, that cause or

explain the differences in productive (in)efficiencies

across firms, industries, or countries (Lin and Chen,

2002). The vector may include the time variable (t) to

serve as the proxy of general economic conditions or

technological progresses. Again, a is a vector of unknowncoefficients. The two-equation model constituted by (2)

and (3 is referred to as the generalized stochastic frontier

model with a stochastic and dynamic inefficiency (Lin andChen, 2002) and represents a significant departure from

the frontier models, including model (1), that were

mentioned in the preceding Section 3.1.

In the first Eq. (2) of the two-equation model, just like

in the one-equation model (1), the observed (actual)

output (Yjt) is again decomposed into three components,

namely, the maximum (ideal, desired) output represented

by f, the random inefficiency (ujt), and the traditional

random shock (vjt). The half-normally distributed random

inefficiency ujt is actually equal to the difference between

the maximum output and the observed output (Yjt), i.e.,

ujt f Yjt, which must be non-negative. Therefore,

there are only two ways to changeujt. One is technological,determined by f which in turn is determined by its

functional form and the inputs entering intof. This

means that the determinants of ujt in the technological

aspect are the functional form (e.g., CES) and inputs

substitution and complement. The other way to shift ujt is

to identify the factors that influence observed output Yjt.

To state alternatively or equivalently, an increase (a

decrease) in Yjt means to reduce (increase) ujt. These

two ways represent two major sources of productive(in)efficiency or two main routes to change productive

(in)efficiency.

On the technological side in this study, the functional

form is the CES production function and the inputs are

ordinary (non-IT) capital (K), ordinary labor (L), and IT

capital (I). The other side of the coin lies the factors that

can change Yjt. The factors are called national character-

istics which are largely policy-oriented at the country

level (e.g., the interest rate, foreign reserves, the unem-

ployment rate, the inflation rate, etc.). Therefore, the

elements of the Zjt vector entering into Eq. (3) must be

country-specific national (macroeconomic) characteris-

tics. These are: (i) Tjt the time variable or the indicatorof general economic conditions of country j at time t; (ii)

PCCjt per capita consumer expenditure; (iii)

Rjt government bond yields; (iv) TRIMjt the ratio of

foreign-exchange reserves to imports; (v) UERjt the

unemployment rate; and (vi) FLAjt the inflation rate.

Having understood the two major sources of produc-

tive (in)efficiency, we are in a better position to explain

why these factors are selected. First, Tjt is a time variable

which denotes the trend and is usually treated as the

proxy of general economic conditions (Lin, 1986, 2005; Lin

et al., 1992, 2002; Lin and Chen, 1998; Lin and Lin, 2000).

Good (bad) economic conditions have favorable (unfavor-

able) impacts on Yjt, thereby reducing (worsening) theproductive inefficiency of a country.

In addition to the time variable, the stochastically

varying inefficiency could be attributed to various macro-

economic variables from different sectors of an economy

that affect Yjt represented by GDPjt (Lin, 1999; Lin and Lin,

2000; Lin et al., 2002), including interest rates (proxyed by

government bond yields) from the financial sector (Lin,

1988, 1992, 2005; Lin and Chen, 1998; Lin et al., 2002;

Phelps, 1969), per capita consumer expenditure from the

real sector (Lin, 1992), and TRIM from the external sector

(Kaminsky and Reinhart, 1999; Lin, 1999; Lin and Chen,

1998; Lin and Lin, 2000; Lin et al., 2002; Miller, 1998). For

example, normally, consumer expenditure generates ef-fective demand, according to the Keynesian theory, and

effective demand stimulates more production that will be

accompanied by the increase in actual (observed) output,

leading to the decrease in productive inefficiency (ujt).

Furthermore, there are two policy objectives (Fisher

and Tanner, 1978; Lin, 2005; Lin and Chen, 1998; Phelps,

1969; Zarnowitz, 1985) to be fulfilled at the national level:

internal equilibrium to be achieved by UER and FLA and

external equilibrium to be achieved by the exercise of

TRIM. Whether or not the two policy objectives is

achieved would directly or indirectly affect the level

(e.g., boom or recession) of the economic activity of a

country as measured by GDP in the country and GDP is thedependent variable representing the observed output Yjt

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in the stochastically varying frontier models (one-equa-

tion or two-equation). For these reasons, we consider that

the instruments (UER, FLA, and TRIM) used to reach

internal and external equilibria should have impacts on

GDP and, hence, on ujt. In particular, TRIM is regarded as

one of the causes of the balance of payments disequili-

brium (referred to as a currency crisis Kaminsky and

Reinhart, 1999; Miller, 1998).To sum up, the choice of the six national characteristics

is based on a number of criteria: their importance,

significance, and influence; suggestions from many pre-

vious studies in the literature; and more importantly, data

availability. The two-equation model composed of Eqs. (2)

and (3) enables us to analyze the effects of the chosen

national characteristics on the value of IT, GDPs (i.e., Y0jts)

and productive (in)efficiencies.

Thus, the presence of Eq. (3) indicates that the

productive inefficiency concerned is both dynamic and

stochastic and provides a channel to identify the sources

of productive (in)efficiency. Moreover, the two-equation

model also represents a two-stage analysis of productiveinefficiency; and it not only measures the productive

inefficiency but also examines the causes that explain the

differences in productive inefficiencies across different

firms, industries, or countries and over time. Therefore, as

stated earlier, from the methodological point of view, the

proposed application of the two-equation model (2)(3)

departs substantially from all previous research based on

the one-equation model (1) (e.g., Ahn and Schmidt,

1977; Ahn et al., 2007; Aigner and Chu, 1968; Aigner et

al., 1997; Battese and Coelli, 1992; Beeson and Hnsted,

1989; Cornwell et al., 1990; Cuesta, 2000; Farrell, 1957;

Kaynak and Pagan, 2003; Kumbhakar, 1990; Kumbhakar

et al., 1991; Lee, 2006; Lee and Schmidt, 1993; Lin andShao, 2000, 2006a, b; Meeusen and van den Broeck, 1977;

Murillo-Zamorano and Vega-Cervera, 2001; Pitt and Lee,

1981; Schmidt and Sickles, 1984; Shao and Lin, 2000; Shao

and Lin, 2001, 2002 among others).

3.3. Treating IT in two ways: choice between one- and two-

equation models

As stated above, the time-varying stochastic frontier

production approach indicates that there are two major

sources of productive (technical) (in)efficiency and, there-

fore, there are two ways to treat IT in the production

system (Lin et al., 2009). One way is to treat IT as anobserved output-influencing factor. In this way, the two-

equation-two-factor model is required; and IT enters into

the second equation as one of the factors, without or with

national characteristics. The other way is to treat IT as a

production factor, i.e., a desired (ideal or maximum)

output-impacting factor. In this way, IT appears in the

production function, f; and the one-equation-three-

factor model is needed if the Zjt vector is absent.1 The

empirical evidence provided by both (Lin et al., 2009) and

the present study suggests that these two ways lead to

virtually the same conclusions. Nevertheless, to avoid or

at least alleviate the omitted variable problem which may

arise from the estimation without IT while analyzing the

effects of IT on productive efficiency, we adopt the first

way by applying the two equations model with IT as one

of the factors (with or without the selected six nationalcharacteristics) in the second equation; and the results are

reported in Tables 68.2

3.4. Specifications of the production function

Both the one- and two-equation efficiency frontier

models require the specification of the functional forms of

the production functionfXjt;b. This research is built on

the specification of the two-factor CES production func-

tion (as used in Lin and Shao, 2006b) and the develop-

ment of the three-factor CES production function.

First, in the two-factor case, we simply follow the

footstep of Lin and Shao (2006b) by using the threestochastic frontier production models proposed by them

as follows:

Model I:

ln Yjt b0 b1 ln Kjt b2 ln Ljt

b3ln Kjt ln Ljt2 vjt ujt

Model II:

ln Yjt b0 b1 ln Kjt b2 ln Ijt b3ln Kjt ln Ijt2 vjt ujt

Model III:

ln Yjt b0 b1 ln Ljt b2 ln Ijt b3ln Ljt ln Ijt2 vjt ujt

where Yjt is the observed output as defined above, Kjt is

the traditional (non-IT) capital, Ijt is the IT capital, Ljt is the

traditional labor, and vjt and ujt are the traditional random

error and the random productive inefficiency , distributed

according to N0;s2v and jN0;s2uj, respectively (see, e.g.,

ARTICLE IN PRESS

1 The presence and absence of IT is related to the classical issues of

the omission of relevant variables from, and the inclusion of irrelevant

variables in, a regression model (Pindyck and Rubinfeld, 1998). If IT is a

relevant variable (which is the case in this study), then the one-equation-three-factor model is the correct regression model and the

( footnote continued)

one-equation-two-factor model is the incorrect one. Under this situation,

the OLS estimators of the incorrect model are biased and inconsistent,

unless CovKit; Iit CovLit; Iit 0 (i.e., only when the omitted variable

Iit is uncorrelated with all the included regressors do the bias and

inconsistency disappear; but, in general, the incorrect model has some

merit of more efficiency. On the other hand, if IT is an irrelevant variable

(which is not the case for this study), then the one-equation-three-factorregression is the incorrect model and the one-equation-two-factor

model is the correct model. Under this situation, the inclusion of the

irrelevant variable does not bias the OLS estimators of the coefficients of

the relevant variables, the expected value of the estimator of the

coefficient of the irrelevant variable is zero, and the inclusion of

irrelevant variables does affect the efficiency of the OLS estimators

(Pindyck and Rubinfeld, 1998). Nevertheless, the OLS method is not valid

for the time-varying stochastic frontier models of one equation and two

equations, regardless of whether IT is relevant or irrelevant. Instead, a

two-step nonlinear maximum-likelihood (NML) method is used (Lin and

Shao, 2000) (see Section 4.2), in which the OLS estimates are used as

initial values in the second step. The two-step NML estimates of the

unknown coefficients involved are biased but consistent.2 Another way to analyze the effects of IT on productive efficiency is

to compare the efficiency estimates of a country (firm) with different

sizes (large, medium, and small) of IT stocks. This method of analysis hasbeen considered in, e.g., Lin and Shao (2000, 2006b).



7/18

Lovell, 1993). Here, input vector Xjt is equal to (Kjt; Ljt),

(Kjt; Ijt), (Ljt; Ijt) in Model I, Model II, and Model III,

respectively. Model I is the CES stochastic frontier

production model when ordinary capital (Kjt) and ordin-

ary labor (Ljt) are employed; Model II is obtained from

Model I when IT capital Ijt is used to substitute for Ljt; and

Model III follows from Model I when Kjt is substituted by

Ijt. Model I uses no IT capital (Ijt) but traditional capitalKjt and labor Ljt in the production process and is

frequently seen in the literature.

These three models are based on the two-factor CES

production function proposed by Arrow et al. (1961) to

allow for the observed variation in the degree of

substitutability (or complementarity) between Kjt and

Ljt, which can be described as (also cf. Kmenta, 1986;

Usawa, 1962): Yjt gdKpjt 1 dL

pjt

a=pevjtujt;

g40; 14d40; a40; pX 1, where g is called the effi-ciency parameter, d and 1d are the distribution para-

meters for traditional capital and labor, respectively, a isthe returns-to-scale parameter, and p is the substitution

parameter. The nonlinear CES function corresponds to thefollowing stochastic production efficiency frontier approx-

imation given by (cf. Kmenta, 1986; Lin and Shao, 2006b):

ln Yjt ln g ad ln Kjt a1 d ln Ljt 1=2pad1 d

ln Kjt ln Ljt2 vjt ujt

which is the same as the following unrestricted version

with nonlinear restrictions under exact identification:

ln Yjt b0 b1 ln Kjt b2 ln Ljt

b3ln Kjt ln Ljt2 vjt ujt

Thus, the parameters of the restricted approximation

correspond to the coefficients of the unrestricted model asfollows:

g anti ln b0 expb0; d b1=b1 b2

1 d b2=b1 b2; a b1 b2 (4)

and

p 2b3b1 b2=b1b2 (5)

Relation (5), coupled with Models IIII, is particularly

relative to the inputs substitution issue which in turn

relates to the IT value (measured by productive efficiency)

and the paradox of productivity, that is, it measures the

possibilities of the substitution or complement betweenKjt and Ljt based on Model I, between Kjt and Ijt based on

Model II, and between Ljt and Ijt when Model III is used

(see Lin and Shao, 2006b for more details). However, to

facilitate a meaningful comparison between the two-

factor (K, L) and the three-factor (K, L, I) results and to

avoid potential bias and inconsistency arising from the

two-factor models when there are three input variables

available, we consider Model I only and ignore Model II

and Model III even though these two two-factor models

are highly relevant to the issues of IT value, inputs

substitution or complement, and the productivity paradox

(Lin and Shao, 2006b).

Next, we develop the model for the three-factor case.The three-factor CES counterpart of the two-factor CES

function can be written as

Yjt gd1Kpit d2L

pjt 1 d1 d2I

pjt

a=pevjtujt

g40; 14d1; d240; a40; pX 1

j 1; . . . ;Nand t 1; . . . ;M (6)

where d1, d2, and 1dd2 are the distribution parameters

for capital, labor and IT capital, respectively, and the

definitions of other parameters in the nonlinear CES

function (6) remain the same as given above. By means

of the Taylors series expansion, we obtain the stochastic

approximation given by

lnYjt ln g ad1 lnKjt ad2 ln Ljt a1 d1 d2 ln Ijt

12pad1d2lnKjt ln Ljt2

12pad2l d1 d2ln Ljt ln Ijt2

12pad11 d1 d2lnKjt ln Ijt2 vjt ujt (7)

As in the two-factor CES case, the right-hand side of

Eq. (7) is constituted by two parts: one part corresponding

to the CobbDouglas production function (represented by

the first four terms on the right-hand side of Eq. (7)) and

the other part being a correction (or an adjustment) factor

(represented by the 5th, 6th, and 7th terms on the right-

hand side of Eq. (7)) due to the departure of p from zero so

that, as p tends to 0, the adjustment factor would

disappear and the CES function would approach to the

three-factor CobbDouglas function.

The estimation of the restricted Eq. (7) corresponds to

that of the following unrestricted model with nonlinear

restrictions under exact identification:

lnYjt b0 b1 lnKjt b2 ln Ljt b3 ln Ijt

b4

lnKjt ln Ljt2 b

5

ln Ljt ln Ijt2

b6lnKjt ln Ijt2 vjt ujt (8)

and, as a result, the coefficients of the restricted Eq. (7)

relate to those of the unrestricted version (8) as follows:

g anti lnb0 expb0; d1 b1=b1 b2 b3

d2 b2=b1 b2 b3; 1 d1 d2 b3=b1 b2 b3

a b1 b2 b3 (9)

ARTICLE IN PRESS

Table 1

Some general and limiting cases of correspondences between p or pi and

s in the CES production models.

Parameter ofsubstitution: p and

pii 1; 2; 3

Elasticity ofsubstitution:

s

Economic meaning

Range: 1; 1 Range:

1; 1

0 1 The CES reduces to the

CobbDouglas function with

constant returns to scale

N N The CES reduces to fixed

proportions (a straight line)

40 40 I nputs substitutability

1pp; pio0 (i 1, 2,

3)

o0 I nputs complementarity

Note: p is the substitution parameter in the one-equation two-factormodel considered in Lin and Shao (2006b).



8/18

and

p1 2b4b1 b2 b3=b1b2

p2 2b5b1 b2 b3=b2b3

p3 2b6b1 b2 b3=b1b3 (10)

where p1 can be used to measure (estimate) thesubstitutability (or complementarity) between ordinary

capital and labor when IT capital is held constant, p2between labor and IT capital when ordinary capital is held

constant, and p3 between ordinary capital and IT capital

when labor is held constant.

Lin and Shao (2006b) have set up a table to summarize

some general and limiting cases of the correspondence

between the substitution parameter (p in the two-factor

case) and the elasticity of substitution (s, Allen, 1962). Weregard this table useful and expand it to include the

substitution parameters pi; i 1; 2; 3, for the new (three-

factor) model. The expanded table is designated as Table 1.

Lin and Shao (2006b) have provided a detailed discussionin relation to Table 1, which is not repeated here to save

space.

In sum, methodologically, the new model (7) or its

unrestricted form (8) is an important addition. Besides the

one-equation-two-factor CES stochastic production effi-

ciency frontier model ( Models I), we now have developed

the one-equation-three-factor CES stochastic production

efficiency frontier model. Incorporating the single equa-

tion model into the two-equation framework of Eqs. (2)

and (3), we then have a two-equation-two-factor model

and a two-equation-three-factor model.

Finally, the measure of productive (or technical)

efficiency is defined as (Lovell, 1993 and Lin and Shao,2000, 2006a,b) PEjt expujt for country j at time t

which must lie between 0 and 1, and the higher the value,

the higher the productive efficiency is. The average

productive efficiency of country j is denoted by APEj Ptexpujt=M and the overall average productive effi-

ciency by APEP

j;texpujt=MN. Like (Lin and Shao,

2006b), we emphasize the importance of inputs substitu-

tion or complement because the substitution (or comple-

ment) between a pair of inputs influences the maximum

(desired or ideal) output f and, hence, ujt (i.e., the

difference between the maximum output and the actual

output or the so-called productive inefficiency) and

expujt (i.e., the so-called productive efficiency). Thus,

the stochastic production efficiency frontier approach in

cooperation with the CES production function provides an

appropriate methodology to analyze the four contem-

plated issues of IT value, inputs substitution and comple-

ment, productivity paradox, and complementarity

phenomenon jointly and critically.

4. Country-level data and estimation method

4.1. Data

A set of country-level panel data covering the period

from 1993 to 2003 was collected from a number of

sources for each of the 15 countries included in our

sample. The countries selected consist of eight developed

countries (Group 1) and seven emerging (developing)

economies (Group 2). The countries in Group 1 are

Australia (AU), Canada (CN), France (FR), Germany (GM),

Italy (IL), Japan (JP), the United Kingdom (UK), and the

United States (US), while the seven economies in Group 2

are China (CH), Hong Kong (HK), Malaysia (MA), Singapore(SG), South Korea (SK), Taiwan (TW), and Thailand (TL).

Yjt is set equal to GDPjt, Kjt is defined as non-IT

(ordinary) capital, and Ljt as non-IS (ordinary) labor.

Sources of the data on these variables and the six national

characteristics include the Yearbook of each country, the

United Nation Common Database, the Statistics Department

of each country, OECD Database, International Financial

Statistics, International Marketing Data and Statistics, and

European Marketing Data and Statistics. The data on IT

capital (Ijt) were collected from Digital Planet 2004The

Global Information Economy. All data are transformed into

millions of the 1995 constant US dollars.

4.2. Estimation

The task of estimation was accomplished by using the

Limit Dependent (LIMDEP) statistical package applied to

the one-equation-two-factor model (Model I), the one-

equation-three-factor model, the two-equation-two-fac-

tor model, and the two-equation-three-factor model. The

estimation of these models was carried out in a two-step

nonlinear maximum-likelihood (NML) procedure as ex-

plained in Lin and Shao (2000). If the exception condition,

i.e., wrong skewness (w.s.) exists, the estimation process

would stop and no results are available (Waldman, 1982).

If the estimation process succeeds, LIMDEP can provide

ARTICLE IN PRESS

Table 2

Estimated results of the one-equation-two-factor model (Model I).

Model b0 b1 b2 b3 APE R2 g d 1d a p

Model I Group 1 (w/o GM)

1.2263 0.1165 0.8901 00.3247 0.8677 0.9696 3.4086 0.1157 0.8843 1.0066 4.9944

Group 2

2.7253 0.6612 0.2023 0.3327 0.8260 0.9690 15.261 0.7657 0.2343 0.8635 0.1758

Combination

0.6356 0.6866 0.3784 0.0740 0.7866 0.9815 1.8882 0.6447 0.3553 1.0650 0.0869

Note: GM stands for Germany, IL for Italy, and CH for China; and w/o means without.

Significant at the 1% or 5% level. Significant at the 10% level.



9/18

the estimates of the productive inefficiencies ujtfor all j

and t; and then productive efficiencies expujt, APEj, and

APE are obtained. Then, using the estimated coefficients,

the five parameters in (4) and (5 for the two-factor model

(Model I) and the eight parameters in (9) and (10) for the

three-factor model are calculated.

In estimating each of the proposed models, we

consider two groups and the whole sample. Group 1

(N 8) and Group 2 (N 7) are subsamples, while the

whole sample deals with the combination (N 15) of

Groups 1 and 2. Due to the presence of the so-called

exception condition (wrong skewness), we are forced to

drop GM in order to get empirical results when IT istreated as a production factor. The failure to obtain

estimates is caused by wrong skewness which is related

to the distribution and pattern of the data involved as well

as by the fact that the stepwise NML estimation procedure

used in LIMDEP is sensitive to the choice of the initial

values.

Moreover, separating the sample countries into twogroups and comparing empirical results from each group

sample are reasonable. However, comparing average

efficiency estimates from Groups 1 and 2 does not include

valuable information For this reason, we base the

comparisons of average efficiency measures on the results

estimated from the whole sample (see Tables 68).

5. Results

Tables 25 report estimated results of the one-

equation-two-factor model (Model I), the one-equation-

three-factor model (the new model), the two-equation-two-factor model (the expanded model based on Model I),

and the two-equation-three-factor model (the expanded

model based on the new model), respectively. Included in

these tables are the coefficient of determination (R2), the

overall average technical efficiency (APE), the estimates of

the coefficients and five parameters associated with the

one-equation-two-factor model, the estimates of the

coefficients and eight parameters in the one-equation-

three-factor model, and the estimates of the coefficients of

the six national characteristics appearing in the second

equation of the two-equation models.

Note that the estimates of the one-equation-two-factor

(K, L) model presented in Table 2 are needed to comparethem with those of the one-equation-three factor (K, L, I)

ARTICLE IN PRESS

Table 3

Estimated results of the one-equation-three-factor model (the new

model).

Parameter Group 1 (w/o GM) Group 2 Combination (w/o GM)

b0 2.6553 1.8200 1.9112

b1 0.9276 0.5225 0.7567

b2 1.0460 1.3238 0.2029

b3 1.1153 1.0103 0.4532

b4 0.2601 0.4020 0.1316

b5 0.6732 0.0194 0.0079

b6 0.5634 0.2340 0.0756

APE 0.9508 0.8596 0.8519

R2 0.9978 0.9736 0.9909

g 14.2290 6.1719 6.7609d1 0.9305 0.6251 0.7514

d2 1.0494 1.5838 0.2015

1d1d2 1.1188 1.2089 0.4501

a 0.9968 0.8359 1.0070p1 0.5345 0.9716 1.7263

p2 1.0000 0.0243 0.1730

p3 1.0000 0.7410 0.4440

Note: GM stands for Germany and w/o for without. Significant at the 1% or 5% level. Significant at the 10% level.

Table 4

Estimated results of the two-equation-two-factor model (based on

Model I).

Parameter Group 1 (w/o GM) Group 2 Combination

b0 1.2341* 1.2387* 1.5317*

b1 0.7680* 0.8713* 0.7503*

b2 0.2710 0.0453 0.2789*

b3 0.0281 0.5933* 0.0410

a1 0.0280 0.0588* 0.0181

a2 0.0501 0.1530* 0.0097a3 0.0724 0.0916

* 0.0144

a4 0.2163* 0.0494* 0.0777*

a5 0.1891* 0.0057 0.0494

a6 0.0095 0.0037 0.0070APE 0.9441 0.8909 0.8317

R2 0.9973 0.9822 0.9873

g 3.4354 3.4512 4.6262d 0.7392 1.0549 0.7290

1d 0.2608 0.0549 0.2710

a 1.0390 0.8260 1.0292p 0.2806 24.8324 0.4033

Note: The note given just below Table 3 applies.

Table 5

Estimated results of the two-equation-three-factor model (based on the

new model).

Parameter Group 1 (w/o GM) Group 2 Combination w/o GM

b0 0.1552 1.4388* 1.7510*

b1 0.1969 0.3057** 0.8850*

b2 0.4999** 0.4776** 1.0496*

b3 0.7285* 0.0 06 8 1.1523*

b4 0.3677* 0.5651* 0.2461*

b5 0.0530 0.1086* 0.0020

b6 0.1617* 0.0933** 0.2321*

a1 0.0295* 0.0691* 0.0452*

a2 0.0954 0.1589* 0.0696*

a3 0.0359** 0.0980* 0.0464**

a4 0.0298** 0.0612** 0.0236

a5 0.1356*

0.0604 0.0940*

a6 0.0112* 0.0 004 0.0031

APE 0.9823 0.9125 0.9095

R2 0.9996 0.9865 0.9929

g 1.1679 4.2156 5.7601

d1 0.1909 0.3869 0.8961

d2 0.4846 0.6045 1.0628

1d1

d2

0.7063 0.0086 1.1667

a 1.0315 0.7901 0.9877p1 1.0006 0.9395 0.5767

p2 0.3002 0.0038 0.0033

p3 2.3256 70.9254 0.4496

Note: The Note given just below Table 3 applies.



10/18

model given in Table 3. For a similar reason, the estimates

of the two-equation-two-factor model shown in Table 4

are required in order to compare them with those of the

two-equation-three-factor model as reported in Table 5.

As mentioned above, there are several cases in which

GM was dropped out of a group in order to correct w.s..

Such cases include Group 1 w/o GM in Model I (Table 2)

and Group 1 w/o GM and Combination w/o GM in the

two-equation-three-factor model (Table 5), where w/o

stands for without.

Moreover, to analyze the effects of IT on productive

efficiency, we have used the estimates obtained from thetwo equations model with IT as one of the factors in the

second equation. Tables 68 present estimates of the APEjfor countries j 1; . . . ; 15 and their rankings. The esti-

mates and rankings provide the important information

needed for a comprehensive comparison of the IT value of

individual countries and, for determining whether the

productivity paradox still exists or actually disappears in

an individual country (developed or developing).

Finally, Table 9 shows a summary comparison of the

CES-based IT-efficiency (from the one-equation-three-

factor model) and IT/characteristics-efficiency (from the

two-equation-three-factor model) with Lins (2009) IT-

efficiency, Shu and Lees (2003) IT-efficiency, and Jorgen-sons (2003) IT-productivity for the G7 countries.

ARTICLE IN PRESS

Table 6

Comparison of average technical efficiencies APEjs from the two-equation-two-factor with IT as one of the factors in Eq. (2) (obtained from the whole

sample).

Country Two-equation-two-factor model w/o six characteristics Two-equation-two-factor model with six characteristics

Group 1 (Developed) Group 2 (Developing) Group 1 (Developed) Group 2 (Developing)

With IT RK w/o IT RK With IT RK w/o IT RK With IT RK w/o IT RK With IT RK w/o IT RK

CN 0.9408 3 0.9613 1 0.9278 3 0.9463 3

FR 0.9011 4 0.9588 2 0.9100 5 0.9485 2

GM 0.8710 5 0.5979 8 0.9133 4. 0.6709 8

IL 0.9789 2 0.8055 4 0.9441 2 0.8660 5

JP 0.7314 8 0.6152 7 0.8829 7 0.7275 7

UK 0.8522 6 0.7803 6 0.8974 6 0.8873 4

US 0.9875 1 0.9159 3 0.9563 1 0.9803 1

AU 0.8307 7 0.7926 5 0.8814 8 0.8002 6

CH 0.9178 3 0.9169 1 0.9295 3 0.9516 2

HK 0.9203 2 0.8904 2 0.9413 2 0.8955 3

SK 0.6951 7 0.5510 7 0.8165 7 0.6090 7

MA 0.7510 5 0.7180 5 0.9163 4 0.7106 6

SG 0.7242 6 0.7674 4 0.8834 6 0.7475 5

TL 0.8007 4 0.7115 6 0.8972 5 0.7792 4

TW 0.9483 1 0.8158 3 0.9640 1 0.9557 1

AVG 0..8867 0.8034 0.8225 0.7673 0.9142 0.8534 0.9069 0.8070

Note: AVG stands for the average, w/o for without, and RK for ranking.

Table 7

Comparison of average technical efficiencies APEjs with/without IT from the whole sample.


With IT Ranking w/o IT Ranking With IT Ranking w/o IT Ranking

CN 0.9408 4 0.9613 1 0.9278 6 0.9463 5

FR 0.9011 7 0.9588 2 0.9100 9 0.9485 4

GM 0.8710 8 0.5979 14 0.9133 8 0.6709 14

IL 0.9789 2 0.8055 7 0.9441 3 0.8660 8 JP 0.7314 13 0.6152 13 0.8829 13 0.7275 12

UK 0.8522 9 0.7803 9 0.8974 10 0.8873 7

US 0.9875 1 0.9159 4 0.9563 2 0.9803 1

AU 0.8307 10 0.7926 8 0.8814 14 0.8002 9

CH 0.9178 6 0.9169 3 0.9295 5 0.9516 3

HK 0.9203 5 0.8904 5 0.9413 4 0.8955 6

SK 0.6951 15 0.5510 15 0.8165 15 0.6090 15

MA 0.7510 12 0.7180 11 0.9163 7 0.7106 13

SG 0.7242 14 0.7674 10 0.8834 12 0.7475 11

TL 0.8007 11 0.7115 12 0.8972 11 0.7792 10

TW 0.9483 3 0.8158 6 0.9640 1 0.9557 2

AVG 0.8627 0.7866 0.9108 0.8317

Note: AVG stands for the average and w/o for without.



11/18

6. Discussions

The strategy taken to analyze the empirical results

consists of two methods. One is collective in nature,

meaning to analyze the results collectively based on the

expected signs of the coefficient estimates and theirstatistical significance provided by the whole sample or

subsamples (groups). This is the commonly practiced

method which essentially fails to compare countries

individually. To correct such a weakness associated with

the collective analytical method, a second method is taken

to analyze the value of IT, the paradox of productivity, and

the impacts of the six national characteristics by compar-ing the APE j of individual nations. The applications of the

ARTICLE IN PRESS

Table 8

Does the IT investment alone enhance (E) or reduce (R).


E or R %() E or R %()

CN R (2.13) R (1.96)

FR R (6.02) R (4.06)

GM E 45.68 E 36.13

IL E 21.53 E 9.02

JP E 18.89 E 21.36

UK E 9.21 E 1.14

US E 7.81 R (2.45)

AU E 4.81 E 10.15

CH E 0.10 R (2.32)

HK E 3.36 E 5.11

SK E 26.15 E 34.07

MA E 4.60 E 28.95

SG R (5.63) E 18.18

TL E 12.54 E 15.14

TW E 16.24 E 0.87

Table 9

Comparison of this study with others for the G7 countries.

Study, measure, period, etc. G7 Countries

CN FR GM IL JP UK US

This study

IT-APEja 0.9408 0.9011 0.8710 0.9789 0.7314 0.8522 0.9875

Ranking 3 4 5 2 7 6 1

IT/Characteristics-APEja 0.9278 0.9100 0.9133 0.9441 0.8829 0.8974 0.9563

Ranking 3 5 4 2 7 6 1

Model: CES

Period: 19932003

Lin (2009)

IT-APEjb 0.9466 0.9468 0.7440 0.9477 0.6658 0.9180 0.9856

Ranking 4 3 6 2 7 5 1

Model: CD

Period: 19931999

Shu and Lee (2003)

IT-APEjc 0.5410 0.5774 0.5958 0.5105 0.6229 0.5870 0.6268

Ranking 7 5 3 6 2 4 1

Model: CD

Periods: starting years vary, with the same ending year of 1997

Jorgenson (2003)

IT-productivityd 0.1550 0.4250 0.5400 0.5300 0.3150 0.5700 0.3550

Ranking 7 4 2 3 6 1 5

Model: None

Period: 19892001

A countrys APEj and do national characteristics strengthen IT value?a The average technical efficiency of country j (APEj) was based on the whole sample.b The APEjs were obtained based on the CobbDouglas (CD) production efficiency frontier.c The estimates were obtained by means of the full information maximum likelihood method applied to the CD function.d The values of productivity are the average of the results of the two subperiods, 19891995 and 19952001 from Jorgensons (2003) Table 14.



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time-varying stochastic production frontier approach and

the so-called productive efficiency as the performance

measure make it wholly possible to undertake individual

comparisons. The second method is a considerable

departure from previous country- or firm-level studies

as far as analytical methods are concerned. The collective

analysis is based on Tables 25, whereas the individual

analytical method is relative to Tables 69.

6.1. Analyzing the estimated results collectively

First, we consider the estimated results of the one-

equation-two-factor model (Model I) as reported in Table

2. The results of Model I indicate: (i) that all the coefficient

estimates are statistically significant; (ii) that the coeffi-

cients of determination are high (ranging from 0.97 to

0.98); (iii) that the APE for from the entire sample is

acceptably high (0.7866); (iv) that the estimates of the

substitution parameter (p) for the group of developed

countries and for the group of developing economies are4.9944 (positive) and 0.1758 (negative), respectively,

implying that K and L are substitutable in the first group

but are complementary in the second group and that the

notion of unity elasticity (as observed by, e.g., Devaraj and

Kohli, 2003 corresponding to p 0 is rejected; (v) that the

one-equation-two-factor CES frontier model does not

show constant returns to scale as observed by conven-

tional wisdom (e.g., Berndt, 1991; Dewan and Min, 1997)

and , actually, it shows increasing returns to scale

(a 1.006) and decreasing returns to scale (a 0.8635)for Groups 1 and 2, respectively; and (vi) that the

distribution parameters from the CES frontier model tell

different tales for the developed nations (the outputshares distributed to K and L are 11.57% and 88.43%,

respectively) and the developing economies (76.57% and

23.43%, respectively).

Second, we discuss the results (Table 3) of the new

one-equation-three-factor CES frontier model. Certainly, it

would become more meaningful if this model compares

with Model I in Table 2. We notice that the estimate of the

coefficient of IT stock (I) is positively significant (1.1153)

for Group 1, negatively (wrongly) significant (1.0103) for

Group 2, and positively significant (0.4532) for Combina-

tion, all at the 1% level of significance, and that the APE for

Combination has increased considerably from 0.7866 to

0.8519 (8.30%), so does R2

(from 0.9696 to 0.9978 forGroup 1, from 0.9690 to 0.9736 for Group 2, and from

0.9815 to 0.9909 for Combination). Thus, there is no doubt

that IT capital is a source of productive efficiencies,

suggesting the absence of the productivity paradox

provided that technological changes are constant or

increasing (Lin and Shao, 2000; Lin, 2009; Shao and Lin,

2001). Furthermore, based on the estimates of the

substitution parameters (p1, p2, and p3), (K, L, and I) are

pairwise complementary for the developed countries

subsample because p1 0.5345, p2 1.0000, and

p3 1.0000 are all negative; but for the developing

economies subsample, (L and I) are substitutable since

p2 0.0243 is positive, while (K and L) with p1 0.9716and (K and I) having p3 0.7410 are complimentary.

Accordingly, the empirical evidence does reject the notion

that (K, L, and I) are pairwise substitutable (Dewan and

Min, 1997). Also, both the group of developed countries

and the group of developing economies face decreasing

(rather than constant Dewan and Min, 1997) returns to

scale, although for the group of developed countries the

returns-to-scale parameter a 0.9968 is very close to

one. These findings at the country level are consistentwith those of Lin and Shao (2006b) at the firm level.

Third, we now turn to an analysis of the results of the

two-equation-two-factor model (incorporating Model I)

as shown in Table 4. Recall that in the second equation of

the two-equation-two-factor setting, the Zjt vector con-

tains six national characteristics (i.e., Tjt, PCCjt, Rjt, TRIMjt,

UERjt, and FLAjt). The second equation serves to identify

the sources of the productive (in)efficiency and their

impacts on the actual output (GDP), the value of IT, and

inputs substitution or complement.

A careful review of Table 4 in comparison with Table 2

reveals some points of particular interest: (i) In Model I

without IT, the APE gains led by the six characteristics forCombination is considerable, increasing from 0.7866

without the six characteristics to 0.8317 in the presence

of the six characteristics. (ii) The impacts of the national

characteristics upon inputs substitution and complement

are mixed: for example, the pair (K, L) is complementary

for Group 1 since p 0.2806 (negative) and is

substitutable for Group 2 since p 24.8324 (positive), in

the presence of the six characteristics. (iii) Not all the six

characteristic variables are uniformly significant across

different groups; there is only one characteristic, namely,

TRIM (the ratio of reserves to imports), which is uniformly

significant across three different groups (Group 1, Group 2,

and Combination) and there is also only one character-istic, that is, FLA (the inflation rate), which is uniformly

insignificant across three different groups. (iv) T (the

indicator of general economic conditions), PCC (per capita

consumption expenditure) and R (the interest rate) appear

to be significant for Group 2. (v) TRIM and UER (the

unemployment rate) are significant for Group 1. (vi)

Consequently, the effects of the six characteristic variables

on observed outputs and, hence, on productive (in)effi-

ciencies differ from Group 1 to 2 and to Combination, and

are a complex matter.

Finally, our attention is directed to the estimates of the

two-equation-three-factor model as reported in Table 5.

Again, it is instructive to compare the results with theircounterparts as presented in Table 4. We highlight the

findings as follows. (i) All R2 s are very high, as high as

0.9996 for Group 1, 0.9865 for Group 2, and 0.9929 for

Combination. (ii) The estimated coefficients (0.7285 and

1.1523) of the IT capital are positive and significant for

both Group 1 and Combination, but that (0.0068) of the IT

capital is insignificant for Group 2, implying that the

productivity paradox is absent from the developed

countries group but is present in the developing countries

subsample, supporting the argument of Dewan and

Kraemer (2000). (iii) The impacts of the six national

characteristics on the productive (in)efficiencies differ

from Group 1 to Group 2; for example, UER and FLA areimportant for Group 1 (because a5 0.1356 and

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a6 0.112 are significant) but are not for Group 2(because a5 0.0604 and a6 0.004 are both insignif-icant) and, in contrast, PCC is significant for Group 2 but

insignificant for Group 1. (iv) In the presence of the six

national characteristics variables, (K and L) are comple-

mentary for both Groups 1 and 2. (v) Comparing Table 5

with Table 4, we find that the APE gain led by the IT

investment and the six national characteristics aresubstantial for the whole set of countries (Combination):

0.8317 without IT vs. 0.9095 with IT, which means a 9.35%

increase in the APE that is contributed by IT in the

presence of the six national characteristics, implying that

national characteristics can be used to strengthen the

value of IT in the developed and developing countries.

It is of special interest to point out that finding (v)

clearly indicates the existence of the phenomenon of

complementarity (Zhu, 2004). Here, the complementarity

(substitutability) phenomenon means that an enhance-

ment (a reduction) of IT value arises when IT investment

produces greater (smaller) gains in the presence of

national characteristics than by itself. In other words,the presence of national characteristics strengthens

(weakens) the IT value and, therefore, IT and national

characteristics are complementary (substitutable) in the

value-creation process of production or transformation

from inputs into outputs. These phenomena have im-

portant bearings on government policies concerning the

investment of IT and the execution of national policies via

national characteristics.

The phenomenon of complementarity is also observed

from the APE estimates given in Tables 68, based on the

two-equation-two-factor models in which IT is treated as

an observed output-generating factor rather than a

production input, thereby IT appears in the secondequation rather than in the f function in the first

equation. For example, in the presence of the six national

characteristics, the APE is 0.8317 without IT vs. 0.9108

with IT (see Table 7), meaning a 9.51% gain in the APE

because of the presence of the national characteristics

along with IT. The empirical evidence again indicates that

the joint appearance of IT and national characteristics has

strengthened IT valuethe phenomenon of complemen-

tarity.

6.2. Analyzing the empirical results individually

The collective analytical method, though commonly

and popularly practiced, cannot be used to address the

issues of the value of IT and the productivity paradox for

individual countries. Equipped with the CES stochastic

frontier production models and the productive efficiencies

derived from them, we are able to do this. Tables 6 and 7

provide comparisons of the average productive efficien-

cies (APEjs) of individual countries, based on the two-

equation-two-factor model (with or without IT appearing

in the second equation in the absence of the six national

characteristics) and the two-equation-two-factor model

(with or without IT appearing in the second equation in

the presence of the six national characteristics) fitted intothe whole sample. Then, Table 8 is designed to answer the

question: Do IT investments enhance (E) or reduce (R) the

APEj of country j?

First, looking at Tables 68, we immediately find that

there are efficiency gains led by IT even without national

characteristics in most of the developed countries and

developing economies under study, based on the two-

equation models. Consider JP (Japan) as an example. Its

APEj is 0.6152 without IT, but increases to 0.7314 with IT,suggesting that Japan becomes more technically efficient

with than without IT investments. Consider TW (Taiwan)

from the group of developing economies as another

example. Its APEjs are 0.8158 and 0.9483 without and

with IT, respectively, implying that Taiwan encounters the

same situation as Japan. However, there are three

countries (two from the group of developed countries

and one from the group of developing economies) where

IT spending has resulted in the decline in their productive

efficiencies; these are CN, FR, and SG. But US and TW rank

first with IT, followed by IL and HK; and CN and CH rank

first without IT, followed by FR and HK. In the cases of CN

and FR from the developed countries group and SG fromthe developing economies group, their IT investments

failed to improve their rankings. In the case of SK from the

developing countries group, it ranks last with and without

IT although its IT spending has led to a 26.15% gain in

itsAPEj. Like CN and FR, the engagement of IT investments

in SG did not improve its ranking but, actually, has

worsened its productive efficiency during the time period

19932003.

Therefore, the empirical evidence suggests that IT

capital alone may not be a good prescription to change a

countrys efficiency status but that IT, if supplemented by

some national characteristics in the production process,

could lead to improvements on productive efficiencies.The APEjs and their corresponding rankings from the

two-equation models in the presence of the six national

characteristics (see Tables 68) tell us exactly this point

which is of critical relevance and importance to national

policies implied by the phenomenon of complementarity,

as explained in the preceding section.

From Tables 68, we immediately find that the six

national characteristics have indeed contributed to effi-

ciency improvements in nine countries if we compare the

two percentage-change columns in Table 8. These coun-

tries are CN, FR, JP, AU, HK, SK, MA, SG, and TL. For

instance, in the cases of CN and FR, the national

characteristics have helped reduce their negative percen-tage changes in efficiency from 2.13 to 1.96% fro CN

and from 6.02% to 4.06% for FR; and the other seven

countries, JP, AU, HK, SK, MA, SG, and TL, have also

evidently shown higher APEjs with IT than those without

IT (0.8829 vs. 0.7275, 0.8814 vs. 0.8002, 0.9413 vs., 0.8995,

0.8165 vs. 0.6090, 0.9163 vs. 0.7106, 0.8834 vs. 0.7475, and

0.8972 vs. 0.7792, respectively), under the national

policies of implementing the national characteristics in

their production systems, resulting in higher positive

percentage changes in efficiency with than without the six

national characteristics. There are six countries (GM, IL,

UK, and US from the group of developed countries and CH

and TW from the group of developing economies) that donot benefit from the incorporation of the national

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characteristics with IT investments in their production

processes because the six national characteristics have

lowered their percentage increases in efficiency (see Table

8). Consequently, the complementarity phenomenon is

confirmed in nine countries (four of them are developed

and five are developing). Stated alternatively, the sub-

stitutability phenomenon, which means the situation

where the presence of national characteristics weakensIT value, is observed in six countries (four are developed

and two are developing) in the sample.

Second, consider Tables 7 and 8 again. In the two-

equation model without the six characteristics, two

developed countries (i.e., CN and FR) and one developing

nation (i.e., SG) have actually suffered from the deploy-

ment of IT investments (0.9408 with IT vs. 0.9613 without

IT in the CN case, 0.9011 with IT vs. 0.9588 without IT in

the FR case, and 0.7242 with IT vs. 0.7674 without IT in the

case of SG). In the absence of IT, CN ranks first but drops to

the fourth place with IT spending. In contrast, US ranks

the fourth place without IT but raises its ranking to the

first place in the presence of IT capital. The last place waswon by SK with and without IT.

In the two-equation models incorporating the six

selected national characteristics, eleven out of 15 coun-

tries under consideration have slightly or greatly in-

creased their productive efficiencies during the

19932003 period. The notorious ones include GM

(+36.13%), JP (+21.36%), AU (+10.15), SK (+34.07%), MA

(+28.95%), SG (+18.18), and TL (+15.14%). On the contrary,

there are four countries that have not benefited from the

practice of national characteristics at all; these are CN, FR,

US, and CH. For example, in the case of CN, APEj 0.9463

in the absence of IT but in the presence of the six

characteristics in comparison with APEj 0.9613 whenboth IT and the six characteristics are absent; while its

APEj is 0.9278 when both IT and the six characteristics are

present in comparison with APEj 0.9408 in the presence

of IT but in the absence of the six national characteristics.

FR is the other country that faces the same fate as CN.

TW is a developing economy that seems to have

actually benefited from the application of the national

characteristics, having APEj with IT slightly larger than

that without IT. Its records are: APEj 0.9557 without IT

in the presence of the six national characteristics,

APEj 0.8158 without IT in the absence of the six

characteristics, APEj 0.9640 with IT in the presence of

the six characteristics, which is larger than APEj 0.9483with IT in the absence of the six characteristics consid-

ered. However, the net consequence from these records is

that its efficiency percentage change declines from 16.24%

without, to 0.87% with, the implementation of the six

national characteristics. Furthermore, we also can observe

from Tables 7 and 8 that CH is the only developing country

that has not been benefited by the introduction of the six

national characteristics into its production process along

with IT. When the six national variables appear in its

production process, its APEj is 0.9295 with IT vs. 0.9516

without IT.

To sum up, we ask two questions of critical importance.

Question 1 is: Does the IT investment alone enhance acountrysAPEj? The answer is positive because there are 13

out of 15 countries have experienced efficiency gains led

by IT. Question 2: Do the IT spending and the six national

characteristics combined strengthen a countrys perfor-

mance as measured by productive efficiency? The answer

is again positive. There are eleven countries whose

efficiencies have been strengthened by the introduction

of the national characteristics; but there are four nations

who suffered from efficiency decreases as a result of thepresence of the national characteristics along with ITthe

substitutability phenomenon.

The empirical findings have the following implications.

(i) The empirical evidence disagrees very strongly to the

notion that the productivity paradox exists only in

developing economies and does not appear in developed

countries (Dewan and Kraemer, 2000); as a matter of fact,

it may or may not exist in a country irrespective of

whether it is a developing or a developed country. (ii) The

value of IT as measured by productive efficiency is

recognized in most of the countries considered (developed

and developing), but is questionable for some countries

(developed and developing). (iii) The issues of IT value andthe paradox of productivity (efficiency) are highly relevant

to the relationships of substitution and complement

among IT capital, non-IT capital, and ordinary labor;

conventional wisdom suggesting that these three produc-

tion inputs are pairwise substitutable has been rejected at

the firm level (Lin and Shao, 2006b) and is now shown

empirically unacceptable at the country level. (iv) Na-

tional policies in the form of prudently incorporating

certain national characteristics into production processes

may be used to improve productive efficiencies; more

importantly, such national policies and IT use may be

combined together in order to enhance productive

efficiencies

hence, the complementarity phenomenonthat has been surfaced in both the collective and the

individual analysis; however, the phenomenon does not

take place uniformly across different nations, though it

happens in a majority of the countries considered.

6.3. A comparison with others for the G7 countries

It is both interesting and instructive to compare the

CES-based IT-efficiency and IT/national characteristics-

efficiency with Lins (2009) IT-efficiency, Shu and

Lees (2003) IT-efficiency, and Jorgensons (2003) IT-

productivity for the G7 countries. A summary of theinformation needed to undertake such a comparison is

presented in Table 9. The information contained in Table 9

reveals some points of interest which are stated as

follows.

In the first place, the APEjs without and with national

characteristics from this study differ, as discussed in the

preceding subsection. The six national characteristics

selected have increased the APEjs of all G7 economies

and changed the rankings except for CN and IL, and US has

won the first place and JP the last place in both the

absence and presence of the national characteristics. In

the case of CN, its APEj has decreased from 0.9408 in the

absence of the national characteristics to 0.9278 in theirpresence, an equivalent of a 1.38% decrease.

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Next, both the studies of Lins (2009) and Shu and Lee

(2003) have deployed the same stochastic production

efficiency frontier model specified by the CobbDouglas

production function. But their empirical results differ

considerably. In general, the APEjs reported by Shu and Lee

are much smaller than their counterparts given by Lin

and, accordingly, the rankings are also quite different. For

example, the APEj of CN obtained by Lin is 0.9466 whichmeans to be the fourth place in comparison with 0.5410

estimated by Shu and Lee which ranks last among the G7

economies. Nevertheless, both studies have awarded the

first place to the US The significant difference between

these two works may be caused by the data irregularities

in time periods for different countries in the sample used

by Shu and Lee. Another good explanation is the different

methods of estimation used. Shu and Lee applied the full

information maximum-likelihood procedure, while Lin

relied on the two-step nonlinear maximum-likelohood

procedure.

In the third (final) place, Jorgensons (2003) study

represents another distinguished view. He has analyzedthe productivity of IT in the G7 countries. His results and

ranking do not convey a similar tale. In his ranking on the

basis of productivity, UK is the biggest winner and the

last place goes to CN; and US wins the fifth place, followed

by JP.

Nevertheless, it should be cautioned that although the

same measure, APEj, is applied to different studies, the

comparison of the results to previous studies is unconvin-

cing because of the differences in data (from different

time periods), econometric methods, and other factors. As

such, the comparison of inter-study results may not be

over-emphasized unless such a comparison is based on

some standardization process that would make the inter-study results at least more comparable. Accordingly, the

inter-study comparison may not provide useful informa-

tion until a standardization process is found available.

6.4. The decision-making benefits of this work for managers

and firms

Although this work examines the country as the level

of analysis, there are obviously some decision-making

benefits of this work for managers and firms. These

benefits include, but are not limited to, the following:

First, the stochastically dynamic frontier approach andthe performance metric called productive (or technical)

efficiency which is built in and generated by the approach

are well applicable at the fir

it n characteristis country

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