The impact of defense expenditure on economic productivity in OECD countries

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The impact of defense expenditure on economic productivity in OECD countries

Tung-Pao Wang

a,1

, Stacy Huey-Pyng Shyu

b,

, Han-Chung Chou

c,2

a

Institute of Business and Management, National Chiao Tung University, 4F, No. 114, Section 1, Chung-Hsiao West Road, Taipei 100, Taiwan b

Graduate Institute of Business Management, National Kaohsiung First University of Science and Technology, 2 Jhuoyue Rd, Nanzih, Kaohsiung City, 811, Taiwan cDepartment of Financial Management, National Defense University, No. 70, Sec. 2, Zhongyang North Road, Beitou, Taipei 112, Taiwan

a b s t r a c t

a r t i c l e i n f o

Article history: Accepted 28 June 2012 Keywords:

Defense expenditure strategy Economic productivity Productivity index Bootstrap OECD

Evaluating the effects of defense spending on macroeconomic performance and, in particular, on economic productivity is a critical issue. This study integrates Malmquist productivity index (MPI) with bootstrapping to establish statistical inferences that provide a complete, effective analysis of the impact of defense expen-diture on economic productivity between 1993 and 2009 for Economic Co-operation and Development mem-ber countries. The findings indicate that the average MPI with defense expenditure is higher than that without defense expenditure. Additionally, region based productivity analysis indicates that the appropriate allocation of defense expenditure can increase regional economic productivity effectively across Asia, Oceania and Europe. Moreover, the results further prove that the effective defense expenditure strategies undertaken by government are important for improving economic productivity of countries. The integrated methodology approach applied in this study can be used for further similar studies.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

Defense expenditure is part of government'sfiscal strategy to

en-sure the strength of the economy and national security. Defense

ex-penditure comes from national finance that receives revenue

through the redistribution of household incomes. Therefore, the

scale of defense expenditure is limited by nationalfinance conditions.

Generally, if nationalfinance is in good condition, the scale of defense

expenditure is potentially larger. The status or condition of national finance is ultimately limited by the level of economic development. Faster economic development produces a higher growth rate and re-sults in the availability of more resources for defense expenditure.

DeGrasse (1993) showed that defense expenditure provides and creates job opportunities, increases workers' buying power,

intro-duces greater demand, and boosts economic growth.Benoit (1978)

argued that increasing military expenditure can promote economic growth and improve the quality of human capital through education. Particularly in underdeveloped countries, military industry fosters technological intensity in other industries such as aerospace industry.

Military industry has a positive impact on a country's develop-ment through network infrastructure developdevelop-ment, such as the development of infrastructure (highways, airports, harbors, and

telecommunication technologies), and ultimately boosts economic growth. Therefore, defense expenditure provides internal and exter-nal security and safety for a country's citizens, and creates a worldwide environment for trade and investment opportunities. Furthermore, the defense economics literature argued that the eval-uation of military spending as necessary to manage changing mar-kets and encourage investments and innovations is eventually to ensure the safety of people and property from internal and external

threats (Dunne et al., 2005). That is, in the long term, defense

expen-diture provides national security and boosts economic growth (Ram,

1996).

However,Deger and Smith (1983)argued that increasing defense

expenditure may hinder economic growth. Sivard (1996) also

showed that defense expenditure excludes other economic activities,

such as public education and healthcare.Safdari et al. (2011)showed

an insignificant effect of military expenditure on economic growth in

developing countries (Iran and Saudi Arabia), but in industrialized countries (South Korea and Malaysia), military expense and econom-ic growth have a one-way or two-way correlation effect. To extend

the scope of research,Chang et al. (2011)incorporated economic

de-velopment perspective across countries to analyze the possible rela-tionships between military expenditure and economic growth. The

result identified that the crowding-out effect of military spending in

turn would lead to ensuing economic slowdown. Using the Feder–

Ram and military Keynesian Models to examine the link between

de-fense expenditure and economic growth, Wijeweera and Webb

(2012)further indicated that the national economic growth is depen-dent upon the political decision of the government for recognition.

Pieroni (2009) also highlighted a weak substitution of defense ⁎ Corresponding author. Tel.: +886 7 601 1000x3806; fax: +886 7 601 1070.

E-mail addresses:tungpao.wang@gmail.com(T.-P. Wang),stacyshyu@gmail.com,

stacy@nkfust.edu.tw(S.H.-P. Shyu),hanchung@pie.com.tw(H.-C. Chou). 1

Tel.: +886 2 2349 4924; fax: +886 2 2349 4926. 2Tel.: +886 2 2898 6600x604981; fax: +886 2 2898 5927.

0264-9993/$– see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.econmod.2012.06.041

Contents lists available atSciVerse ScienceDirect

Economic Modelling

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expenditure on aggregate consumption. Regardless of the nega-tive or posinega-tive impact of defense expenditure on economic growth, the core value of defense expenditure is to ensure na-tional security and protect a nation from external threats (Feridun et al., 2011).

The spatiotemporal background and characteristics (resources and geographical location) of a country, level of external threats, and level of internal political stability affect defense expenditure and economic growth. Countries with high defense expenditure do not necessarily experience economic recession. A country with low defense expenditure may not experience high economic growth.

However, economic growth is a key factor influencing the supply of

defense expenditure. Therefore, the impact of defense expenditure on economic productivity and the strategic issues behind it is a signif-icant issue for further discussions. Maintaining the optimal size of government spending by including practical decompositions of mili-tary spending into private sector expenditure such as consumption and investment is the best way to achieve economic growth (d'Agostino et al., 2011).

The Organization for Economic Co-operation and Development

(OECD)3was founded to assist member countries to maintain

advan-tages in economy, education, and society. The organization provides advice and numerous reports for creating farsighted national poli-cies. The OECD promotes the development of developed and devel-oping countries, emphasizes the establishment of robust economic systems, improves free trade mechanisms in the market, and pro-vides member countries with a think tank for policy-making, as well as a platform for information exchange (e.g., Ministers' confer-ences and professional forums). In the upcoming era of the global

village,“internalization” and “involvement in international affairs”

are crucial factors for all governments to increase competitive capability.

Therefore, this study investigates the impact of national defense on economy by taking OECD member countries as research subject units. A majority of previous studies have mainly conducted

longitu-dinal analyses of defense, economy, and other factors for“a single

country” or “across countries” (e.g., unemployment rate, political

fac-tors, or budget deficits) without exploring the impact of defense

ex-penditure on economic productivity. This study uses the Malmquist productivity index (MPI) of data envelopment analysis (DEA) to mea-sure the economic productivity changes of numerous countries across several periods. However, the disadvantage of traditional MPI is that it cannot provide statistical inferences. Therefore, we integrate MPI with bootstrapping to establish statistical inferences that provide a complete, effective analysis of the impact of defense expenditure on economic productivity between 1993 and 2009 for OECD member countries.

This paper measures the macroeconomic performance of OECD countries by moderating unwanted externalities of economic growth

using panel data between 1993 and 2009, and comparing efficiency

changes in productivity. In this study, performance is defined by a

country's capability to provide citizens with wealth and less defense expenditure. Based on the economic theory of production,

productivity is generally defined as the efficiency of inputs (e.g.,

cap-ital and labor) being transformed into outputs (e.g., gross domestic product, GDP) through production. Defense expenditure is added and the analysis is repeated to determine changes in productivity performance.

MPI measures productivity changes by considering panel data (Caves et al., 1982a,b; Lo and Lu, 2009).Malmquist (1953)first pro-posed a quantity index that can be used to construct the productivity indexes, as ratios of input or output distance functions. This method

was applied byFäre et al. (1994a,b)to analyze productivity growth

of OECD countries by considering labor and capital as inputs and GDP as an output. Numerous reasons for the popularity of MPI exist. First, the index demands less data because it does not require

information on cost or revenue shares to aggregate inputs and outputs. Second, MPI has the advantage of simpler computation compared with other productivity indices. Finally, the bootstrap

estimation procedure allows the construction of confidence

inter-vals for DEA-based Malmquist indices of productivity and their

de-compositions of efficiency changes. The bootstrap estimation

procedure can determine whether differences between two or

more estimates are statistically significant. Simar and Wilson

(1999)have also discussed the bootstrap approach which has the advantage of allowing for the inclusion of random errors while

making it possible to obtain statistical properties of the efficiency

estimates.

The remainder of this paper is organized as follows:Section 2

in-troduces an estimation methodology, including techniques that

ad-dress the MPI and bootstrapping.Section 3introduces the sample

and data collection.Section 4presents the empirical results and

anal-ysis. Finally, the conclusion is discussed.

2. Methodology

2.1. Measuring productivity change: the Malmquist productivity index (MPI)

MPI wasfirst introduced byMalmquist (1953), and has been

studied and further developed by several authors in the

nonpara-metric framework, such as examples illustrated in Caves et al.

(1982a,b)andFäre et al. (1994a,b). It is an index that represents the total factor productivity (TFP) growth of a decision-making

unit (DMU), and reflects progress in efficiency, and progress or

re-gress of the frontier technology between two periods in the

multi-ple inputs and multimulti-ple outputs framework.Fig. 1shows the MPI

measures using a single output (Y) and two inputs (X1 and X2) for country A. MPI under constant returns to scale (CRS) for tech-nology indicates a rise in potential productivity as the techtech-nology

frontier shifts from period 1 t to 2 t. Efficiency change (EC) and

technological change (TC) shown inFig. 1are represented by the

distance functions. Y/X1 Y/X2 O Period t1 Period t2 a b c d e f g h i At1 At2 Bt1 Bt2 Ct2 Ct1 Dt2 Dt1 Et2 Et1 Period t1 Period t2

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The country's productivity level is less than what is feasible under each period. Furthermore, it does not require input and output prices and it is likely to compute productivity only with information on quantity. MPI measures the changes in TFP and is calculated as a

product of EC (efficiency change) and TC (technical efficiency change)

in Eq.(1). An MPI value is greater than one which indicates

pro-ductivity growth, whereas an MPI value is less than one which in-dicates a decline in productivity. Additionally, increases in either of the two MPI components are also associated with values great-er than one, and any declines are associated with values less than one. MPI¼ " Dt2jt2 Dt1jt1 #  " Dt1jt2 Dt2jt2 D t1jt1 Dt2jt1 #1 2 ¼ EC  TC: ð1Þ

MPI distance functions are calculated using linear programs

simi-lar to DEA. Benefits of using a DEA-type efficient frontier technique

include non-reliance on price information; organizations must be as-sumed to be efficient. The linear programs,Dt1|t1,Dt2|t2,Dt2|t1and Dt1|t2,

are as follows.

As an example, assume that there are j = 1,…,n countries that

pro-duce r = 1,…,q outputs Ykt1= (y1kt1, y2kt1,…,yqkt1) using i = 1,…,p inputs

Xkt1= (x1kt1, x2kt1,…,xpkt1) at each period t = t1, t2. Input-orientated

DEA-type linear programs with constant returns to scale (CRS) are

summarized in Eqs.(2)(5). Eqs(2)(3)represent the cases where

a datum point observed in a period is compared to the production technology (frontier) for that period. Similarly, data points are

com-pared to the technology of the previous period in Eqs.(4)–(5). Eqs.

(2)–(5)must be solved once for each country in each pair of adjacent

time periods. Dt1jt1¼ Min θ;λ θ st−yt1 rkþ ∑ n j¼1λtkj1y t1 rj≥0; r ¼ 1; …; q; θxt1 ik−∑ n j¼1λtkj1x t1 ij≥0; i ¼ 1; …; p; θ; λt1 kj≥0: ð2Þ Dt2jt2¼ Min θ;λ θ st−yt2 rkþ ∑ n j¼1λtkj2y t2 rj≥0; r ¼ 1; …; q; θxt2 ik−∑ n j¼1λtkj2x t2 ij≥0; i ¼ 1; …; p; θ; λt2 kj≥0: ð3Þ Dt2jt1¼ Min θ;λ θ st−yt1 rkþ ∑ n j¼1λtkj2y t2 rj≥0; r ¼ 1; …; q; θxt1 ik−∑ n j¼1λtkj2x t2 ij≥0; i ¼ 1; …; p; θ; λt2 kj≥0: ð4Þ Dt1jt2¼ Min θ;λ θ st−yt2 rkþ ∑ n j¼1λtkj1y t1 rj≥0; r ¼ 1; …; q; θxt2 ik−∑ n j¼1λtkj1x t1 ij≥0; i ¼ 1; …; p; θ; λt1 kj≥0: ð5Þ

2.2. Bootstrap in Malmquist productivity index

The bootstrap method introduced byEfron and Tibshirani (1993)

is a general resampling procedure f for estimating the distributions of statistics based on independent observations, and has been stud-ied and further developed by several authors in the nonparametric

framework, such asCaves et al. (1982a,b)andFäre et al. (1992,

1994).

As a deterministic model, MPI does not explicitly model random error terms, and the overall deviation from the frontier is interpreted

as inefficiency. However, MPI accuracy may be affected by sampling

variation. In the input-oriented model, efficiency estimates might be

biased toward higher scores (i.e., approaching one), whereas ef

ficien-cy estimates in the output model might be biased downward if the countries that determine the frontier are not contained in the sample.

Attention to sampling noise in the efficiency estimates is increasing in

relevant literature, although previous studies about country efficiency

typically ignore this problem.

Bootstrap methodology is the only approach that can be employed to investigate the sampling variability of MPI point esti-mates by correcting the bias inherent in the MPI procedure and

providing confidence intervals (Simar and Wilson, 2000a) in

multi-output or multi-input cases. The bootstrapping procedure relies on repeating the parameter estimation with data resampled by mimicking the data generation process, which in this case is

the process generating the efficiency scores. The observed

distribu-tion is taken to be an estimate of the true distribudistribu-tion (Brümmer,

2001).

The smoothed homogeneous bootstrap method and the

proce-dure proposed bySimar and Wilson (1998, 2000b)were applied.

The bandwidth parameters were selected according to the normal

reference rule (Simar and Wilson, 2000b), and 3000

boot-strapping iterations were performed. Ninety-five percent

confi-dence intervals were constructed using bootstrapping.Simar and

Wilson (2007)have discussed these issues. For the MPI approach, the complete bootstrap algorithm is summarized by the following steps:

Step 1 From the original data setχn, compute ^θtkusing Eq.(6)for each

observation (xijt, yrjt), r = 1,…,q; i=1,…,p; j=1,…,n;t=t1, t2. ^θt k¼ Minfθkjy t k≤∑ n j¼1λtkjy t rj; θkx t ij≥∑ n j¼1λtkjx t ij; θk> 0; λ t j≥0; k ¼ 1; …; ng: ð6Þ

Step 2 Using the smooth bootstrap method, generate a random

sam-ple of size n from ^θt

k(k = 1,…,n,t=t1, t2) to obtainθ1t *,…,θnt *.

The smoothed bootstrap steps are summarized as follows:

♦ Generate τ1t *,…,τnt *by selecting replacements from the set

D2nt , t = t1, t2. Dt2n¼ ^θ t 1; …; ^θ t n; 2−^θ t 1   ; …; 2−^θtn   n o ð7Þ

♦ Select a value for h.Silverman (1986)shows an optimal

value for bivariate data by setting h = (4/5n)−1/6because

this study uses a bivariate normal kernel scaled to possess an identical shape as the data.

♦ For k=1,…,n,t=t1, t2, computeθkt * θtk ¼ γ t k ifγ t k≤1 2−γt k otherwise ;  ð8Þ

whereεkt *is a random deviant drawn from the standard

normal and γkt= (1 + h2)−1/2(τt *k+ hεkt *−∑k = 1n τkt */n) +

∑k = 1n τkt */n.

Step 3 Repeat step 2 B times to provide for k=1,…,n a set of bootstrap

samples χb*={(xikbt*,yrkt*)| k=1,…,n, b=1,…,B}, where

xtikb¼ ^θtk=θtkb

 

xikb; ytikb¼ yikb

 

, k=1,…,n, t=t1,t2, b=1,…,B.

Step 4 The distance functions, f ^Dt1jt2

kb ; ^D t2jt2 kb ; ^D t1jt2 kb ; ^D t2jt1 kb g B b¼1,

be-tween t1and t2are measured to obtain bootstrap estimates

for each country k = 1,…,n. These estimates can then be

used to construct bootstrap estimates ^ MPIkbðt1; t2Þ

 B

b¼1

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EC

^

kbðt1; t2Þ, and TC ^

kbðt1; t2Þ, where (k=1,…,n and b=

1,…,B) corresponds to Eqs.(2)–(5), respectively, by replacing

the true distance function values in Eqs.(2)–(5)with their

corresponding bootstrap estimates. Hall (1986) suggested

setting B = 1000 to ensure adequate coverage of the con

fi-dence intervals.

Step 5 Estimate the confidence intervals for each observed country.

From this procedure, the construction of confidence intervals

can be based on bootstrap percentiles (Simar and Wilson,

1998). However, the MPI, EC, and TC estimators must be

corrected for bias, and this introduces additional noise (Simar and Wilson, 2000a).Simar and Wilson (2000b) pro-posed a procedure that automatically corrects bias. As an ex-ample, consider a set of bootstrap estimates for the MPI of country k: ^ MPIkbðt1; t2Þ

 B

b¼1

. The EC and TC indices can be analyzed similarly by changing MPI to EC or TC, as noted

below. For a (1−α) percent confidence interval, it starts

from the following probability:

Pr −aα≤ MPI

^

kðt1; t2Þ−MPIkðt1; t2Þ ≤ −bα

 

¼ 1−α; ð9Þ

where MPIkðt1; t2Þ denotes the real productivity score of the kth

country. Because the distribution (MPI^kðt1; t2Þ−MPIkðt1; t2Þ) can

be approximated by the distribution (MPI^ kðt1; t2Þ−MPI ^

kðt1; t2Þ),

aαand bαcan be estimated using the following probability:

Pr −^aα≤ MPI ^  kðt1; t2Þ−MPI ^ kðt1; t2Þ ≤ −^bα   ¼ 1−α: ð10Þ

Finding ^aα and ^bα involves sorting the values ( MPI

^

kbðt1; t2Þ−

MPI

^

kðt1; t2Þ) for b=1,…,B in ascending order, and then deleting

((α/2)×100) percent of elements at both ends of the sorted list.

The variables -aαand -bαare equal to the end points of the

trun-cated array, with aα≤bα. Thus, the estimated (1−α) percent

con-fidence interval for MPIkðt1; t2Þ of the kth country is:

MPI

^

kðt1; t2Þ þ ^aα≤ MPIkðt1; t2Þ ≤ MPI

^

kðt1; t2Þ þ ^bα ð11Þ

3. Data selection and description

This study primarily examines the impact of defense expenditure on economic productivity in OECD countries. MPI is used to measure

economic productivity and investigate four data items,“defense

ex-penditure,” “GDP,” “capital,” and “labor force” (the definitions of input

and output items and descriptive statistics are shown inTable 1), for

32 countries. These items are used as variables and the correlations be-tween them are examined.

This study extracts a total of 512 annual data from the 32 coun-tries between 1993 and 2009. A world frontier is constructed from

the data from a specific country. In the analysis without defense

ex-penditure impacts, there are two inputs and one output. Capital

and labor forces comprise the inputs, and GDP is the output for a specific

country. The data of our multiple comparisons are obtained from the World Bank. Transformed defense expenditure is also added to the model. The defense expenditure data were obtained from the Stockholm International Peace Research Institute.

Macroeconomic performance is evaluated according to a country's ability to maximize desirable GDP output and minimize defense expen-diture. Summary statistics of these inputs and outputs are shown in

Table 2.Fig. 2shows that the average value for overall defense

expendi-ture increased significantly between 1994 and 1998, and that variation

among countries increased after 2000. Therefore, investigating the im-pact of defense expenditure on economic productivity has become an essential topic.

4. Empirical results and discussion

4.1. Productivity change with/without defense expenditure

Using MPI, the average cumulative changes of 32 OECD countries'

productivity with/without defense expenditure are shown in Fig. 3,

with 1993 as the base year. The overall productivity growth with/without defense expenditure increased steadily from 2000 to the end of the sam-ple period. The productivity growth without defense expenditure is less than the productivity growth with defense expenditure for every year. The gap between these two trends seems to be widening each year. In 2009, the difference was approximately 7.45%.

Further comparisons considering defense expenditure among

coun-tries are displayed inTable 3. On the left side, MPI without defense

ex-penditure of the total sample is 1.010, with 25 OECD countries' indices exceeding unity, implying that these had positive production growth. Ireland had the highest productivity growth, followed by Norway,

Turkey, Israel and USA.Table 3also indicates an increase in MPI (on

average, 1.0% per year) driven more by technological progress than tech-nical efficiency.

The computation was repeated after adding the transformed defense

expenditure data. The average MPI is shown on the right side ofTable 3,

with a defense expenditure total sample mean of 1.015. Among the 32 OECD countries, Ireland, Norway and Turkey rank higher regardless of

Table 1

Descriptions of input and output variables in MPI model.

Variables Unit Description

GDP (output) US$ millions GDP at purchaser's prices is the sum of gross value added by all resident producers in the economy plus any product taxes and minus any subsidies not included in the value of the products.

Capital (input) US$ millions Gross capital formation (formerly gross domestic investment) consists of outlays on additions to thefixed assets of the economy plus net changes in the level of inventories. Fixed assets include land improvements (fences, ditches, drains, and so on); plant, machinery, and equipment purchases; and the construction of roads, railways, and the like, including schools, offices, hospitals, private residential dwellings, and commercial and industrial buildings.

Labor (input) Million population

Total labor force comprises people ages 15 and older who meet the International Labor Organization definition of the economically active population.

Defense expenditure (input)

US$ millions A military budget (or military expenditure), also known as a defense budget, is the amount offinancial resources dedicated by an entity (most often a nation or a state), to raising and maintaining an armed forces.

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defense expenditure. The average MPI with defense expenditure (MPI-D) is higher than that without defense expenditure, and so is the TC index.

The relationship coefficient between MPI and MPI-D is 0.908. Therefore

the appropriate allocation of defense expenditure can increase national economic productivity effectively.

In summary, overall productivity for MPI-D is greater than that for MPI without defense expenditure, indicating that defense expenditure had an impact on increasing economic productivity during the study period. For example, through collaboration with the defense industry, a country can provide and create job opportunities, increase workers' purchasing power, and boost economic growth by increasing demand. Furthermore, through education, a country can improve the quality of human capital, infrastructure (highways, airports, harbors, and information technologies) can be developed, military and private enterprises can complement each other and achieve a combined effect, and civilian industry can be upgraded through the development

of defense industry. For example, defense technology can be privatized,

converting investments into products and creating economic benefits.

Civilian industry can be assisted to upgrade technologies through tech-nology transfer, and private sectors can be encouraged to participate in defense construction. This enhances the progress of technology, moves

the efficiency frontier (efficient frontier) forward, and ultimately boosts

the growth of national economic productivity. 4.2. Regional productivity changes

The results in the previous section show that defense expenditure as included in the MPI-D can boost economic productivity. Next, OECD countries are divided into three regions for examination. Because threats faced by countries are primarily from intra-regional competition or resource preemption, we used the concept of region as a basis for

analysis. First, we analyze the productivity change presented inFig. 4.

Table 2

Descriptive Statistics for Inputs and Outputs.

Pearson Correlations GDP Capital Labor Defense Expenditure

GDP 1.000

Capital 0.969 1.000

Labor 0.955 0.903 1.000

Defense expenditure 0.924 0.939 0.850 1.000

Year Output data Input data

GDP Capital Labor Defense expenditure

Mean SD Mean SD Mean SD Mean SD

1993 647,708.6 1,371,542.5 137,202.4 293,789.5 16.0 25.8 26,794.2 77,864.5 1994 692,070.2 1,471,784.2 149,335.0 319,886.1 16.2 26.2 25,715.6 73,185.1 1995 760,584.9 1,572,415.2 166,418.0 346,025.5 16.3 26.5 24,669.9 69,218.6 1996 766,006.7 1,574,878.3 166,241.4 338,554.9 16.5 26.8 24,123.0 65,532.8 1997 754,548.8 1,610,349.0 164,971.8 343,431.7 16.7 27.3 24,034.9 65,164.2 1998 761,363.2 1,657,088.7 164,161.9 345,618.6 16.9 27.6 23,833.6 63,695.5 1999 800,588.1 1,773,973.2 173,012.1 373,686.0 17.1 27.9 24,099.2 63,855.2 2000 817,183.6 1,878,776.9 180,106.2 402,224.8 17.2 28.2 24,636.5 66,240.6 2001 809,365.0 1,897,204.7 167,643.6 374,529.3 17.3 28.3 24,761.0 66,757.7 2002 845,890.8 1,946,966.9 168,117.1 366,806.7 17.5 28.5 26,544.8 74,785.2 2003 950,223.9 2,052,586.7 189,614.9 385,988.1 17.6 28.6 28,454.6 84,987.7 2004 1,057,804.3 2,196,226.6 217,759.9 431,471.6 17.8 28.7 29,856.6 92,528.4 2005 1,116,454.3 2,313,774.0 234,536.8 465,878.1 18.0 29.0 30,648.5 96,851.0 2006 1,178,266.2 2,429,591.2 253,964.0 493,615.9 18.2 29.4 31,090.1 98,289.5 2007 1,291,666.3 2,560,505.7 277,205.8 495,644.9 18.4 29.7 31,657.5 100,827.8 2008 1,370,891.3 2,634,570.8 285,286.6 475,938.8 18.6 30.0 33,227.6 108,261.7 2009 1,285,930.7 2,592,037.9 226,701.9 387,900.1 18.7 30.0 35,190.1 116,972.6

Note: SD stands for“standard deviation.”

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The results show that productivity changes in Europe (MPI-E) are

sig-nificantly less than those in the Americas (MPI-A), as well as Asia and

Oceania (MPI-A&O). MPI-A was lower than MPI-A&O prior to 2000 and greater than MPI-A&O after 2000. This increase in productivity may have resulted from an increase in arms sales in the United States.

Fig. 5shows consistency in TC among continents despite small var-iations in some years. This indicates that each continent combines

defense industry into industrial development effectively and improves production technology. The modernization of defense technology af-fects the defense industry and improves production technology for the whole economy.

Finally,Fig. 6shows that EC in Europe (EC-E) is significantly less

than in the Americas (EC-A), as well as Asia and Oceania (EC-A&O). Because the ratios of defense expenditure to GDP in European coun-tries are lower than the Americas, Asia, and Oceania, utilization Fig. 3. Cumulative change in the MPI.

Table 3

Decomposition of MPI without/with defense expenditure by country.

Country Average annual change without defense expenditure Average annual change with defense expenditure

Malmquist index (MPI) Technical change (TC) Efficiency change (EC) Malmquist index (MPI-D) Technical change (TC-D) Efficiency change (EC-D) Americas Canada 0.994 1.009 0.985 1.007 1.025 0.982 Chile 1.021 1.005 1.016 1.021 1.005 1.016 Mexico 0.996 1.006 0.990 1.007 1.007 1.000 USA 1.025 1.027 0.998 1.025 1.027 0.998 Mean 1.009 1.012 0.997 1.015 1.016 0.999

Asia and Oceania

Australia 1.000 1.010 0.990 1.001 1.013 0.989 Israel 1.028 1.014 1.014 1.028 1.014 1.014 Japan 1.003 1.024 0.980 1.009 1.028 0.981 Korea, South 1.023 1.010 1.013 1.018 1.014 1.004 New Zealand 1.011 1.009 1.002 1.033 1.037 0.996 Mean 1.013 1.013 1.000 1.018 1.021 0.997 Europe Austria 1.014 1.022 0.992 1.021 1.030 0.991 Belgium 1.011 1.021 0.991 1.018 1.027 0.992 Czech Rep. 1.014 1.006 1.008 1.020 1.011 1.009 Denmark 1.014 1.019 0.995 1.019 1.024 0.995 Estonia 1.020 1.007 1.013 1.009 1.009 1.000 Finland 1.004 1.012 0.993 1.012 1.019 0.993 France 1.007 1.019 0.988 1.008 1.020 0.988 Germany 1.013 1.018 0.995 1.015 1.021 0.994 Greece 1.013 1.006 1.007 1.013 1.006 1.007 Hungary 0.994 1.006 0.988 1.000 1.011 0.989 Ireland 1.040 1.040 1.000 1.043 1.043 1.000 Italy 1.009 1.017 0.992 1.012 1.020 0.991 Netherlands 1.016 1.021 0.995 1.018 1.023 0.995 Norway 1.037 1.036 1.002 1.037 1.036 1.002 Poland 0.983 1.005 0.978 0.985 1.006 0.979 Portugal 1.007 1.006 1.001 1.008 1.007 1.001 Slovak Rep. 0.974 1.006 0.968 0.986 1.006 0.980 Slovenia 0.985 1.002 0.983 0.996 1.014 0.983 Spain 0.997 1.009 0.988 1.014 1.030 0.984 Switzerland 1.000 1.012 0.988 1.011 1.023 0.988 Sweden 1.020 1.027 0.993 1.026 1.027 0.999 Turkey 1.036 1.005 1.031 1.034 1.003 1.031 UK 1.014 1.010 1.004 1.014 1.010 1.004 Mean 1.010 1.014 0.995 1.014 1.019 0.995 Total mean 1.010 1.014 0.996 1.015 1.019 0.996

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efficiency in Europe is relatively lower than other continents. The

Americas had lower efficiency in defense expenditure utilization

than Asia and Oceania, except for the years 1999, 2006, and 2009. However, the Americas experienced greater EC and overall stability in 2009, indicating that defense expenditure could assist overall in-dustrial development and boost economic growth. Additionally, the greatest reduction of EC from 2008 to 2009 resulted from the global financial crisis, as well as the subprime lending crisis in the United States that negatively affected economies worldwide.

Although the overall performance of Europe is worse than other continents, changes in various European indices are lower than other continents. Because Europe was the origin of the industrial

revolution and has experienced significant financial loss from two

world wars, Europe began to combine politics and economics to de-fend against the powerful United States and avoid a third tragedy. Additionally, the economic unity of the European Union is strong

be-cause no natural boundary exists between European countries (Life

Science, 2010). Because Europe's social welfare expenditure ratio is higher than other continents, the defense expenditure in Europe is more stable than other continents. In the Americas, Asia, and Ocea-nia, the consistency of development levels among countries is lower. The overall performance of the Americas is boosted by the United States' role as a primary supplier of arms and its deployment

of soldiers in several countries. Various economic indicesfluctuate

significantly in Asian countries because of a greater potential for

conflict, and a significant difference in political environments,

reli-gious backgrounds, and wealth gaps.

4.3. Statistical inferences in the Malmquist productivity index

Maintaining the assumption of constant returns to scale, this study applied the discussed bootstrap methods to obtain bias and variance

estimates, and to test for significant differences from unity, with the

B value set at 2000. Additionally, an asterisk (*) is used to indicate

cases where the indices are significantly different from unity (0.05).

Results for the original and bootstrap estimates are presented in

AppendicesA–C.

Examining changes in efficiency shows that “Mexico” is efficient in

all time periods, as indicated by unity values for EC between all

suc-cessive pairs of years (seeAppendix A). Three countries had

statisti-cally insignificant changes in all but one pair of years (Austria,

Norway and Sweden). Only 174 (40.5%) of the 430 EC estimates

shown inAppendix Adiffer significantly from unity. The TC index in

Appendix Bshows that the bootstrap results support the MPI state-ments regarding TC. This study shows that between 2000 and 2001, as well as 2008 and 2009, most countries experienced technical prog-ress. The results show that the TC estimates are statistically

non-significant at the 0.05 level between 1998 and 2000 in all. TC

es-timates between 2006 and 2007 are statistically non-significant at the

0.05 level, except for 2 instances.

The productivity change results (seeAppendix C) generally support

MPI statements. This study found productivity gains in 312 cases and

productivity losses in 192 cases, whereas this research identified

signif-icant (at 0.05) gains in 279 cases, and significant (at 0.05) losses in 175

cases; 90.1[(279+175)/(312+192)] percent of the estimates shown in

Table 4differ significantly from unity at the 0.05 level.

In summary, the bootstrap method corrects inherent MPI bias, and is a suitable method for checking whether bias-correction increases

mean-square errors. Confidence intervals are essential for

inter-preting MPI estimates. As with any estimator, it is insufficient to

de-termine if the MPI estimator indicates an increase or decrease in productivity; the goal is to determine if the indicated changes are

sta-tistically significant. The bootstrap procedure allows researchers to

make these distinctions. Fig. 4. Cumulative change in the MPI for three regions.

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5. Conclusion

This study applied MPI and the bootstrap methods to explore the im-pact of defense expenditure on economic productivity of OECD countries. The results show that the productivity measured in terms of MPI-D was higher than that is measured in terms of MIP for OECD countries during

the period examined (1993–2009). From a regional economic

develop-ment view, the overall productivity in the Americas is superior to other continents such as Asia, Oceania and Europe. This means that the United States' arms sales boosts its own defense industry and strongly foster Americas' overall productivity. Conversely, European countries have adopted defense-cutting budget annually since the end of World War II and even after the establishment of the European Union (EU). That is, this study also indicates the weak link between defense expenditure and economic productivity examined in the EU members. The effective defense expenditure strategies employed to improve economic produc-tivity can be concluded as follows.

Firstly, by implementing“defense resources privatization” policy

aimed at improving defense industrial base technology and

self-reinforcing cycle of economic prosperity, the whole society benefits

from which the defense resources can be directly or indirectly under-taken by domestic arms weapon manufacturers. Organizing resources of private and public sectors, government can achieve defense autono-my, improve national defense technology, boost the econoautono-my, and cre-ate jobs. Furthermore, privcre-ate sectors are encouraged to serve and

invest in the national securityfield for exploiting the synergies that

can result from integration of the research and development (R&D), production, and maintenance elements of the weapons and equipment and general military based supply activities. To reallocate defense resources from short-term military capabilities to long-term military potential, expand domestic privatization, and enhance economic devel-opment in private sectors, government should consider three principles for future defense production: 1) reduce self-sponsored programs and

business in the military industry; 2) reduce foreign procurement; and 3) increase the budget for privatization.

Secondly, by undertaking“industrial cooperation” projects,

gov-ernment can impose an obligation on a foreign contractor under a government procurement project to execute certain industrial or commercial activities such as local investment, local procurement, technology transfer, etc. Such obligation is particularly stipulated in procurement project concerning national defense, transportation and power generation. This approach aimed at fostering domestic industrial improvements and revitalizing long-term economic prosperity through economical procurement or purchase con-tracts, promoting industrial competitiveness in global markets, and ensuring independent and autonomous equipment and

facil-ity maintenance (Dowdy, 1999). Six action plans are undertaken

for the strategy of private investment promotion as follows: 1) technology transfer; 2) research and development collaboration; 3) domestic investment; 4) personnel training; 5) assistance to expand international trade and marketing; and 6) domestic procurement.

Thirdly, recent trends and intense international competition require countries to reform industrial structure quickly, conduct industrial collab-oration, complement each other's technology and production advantages, and relax or revise technology protection, export, and R&D investment policies. Countries should also collaborate with numerous countries that

have strong defense industries base in thefields of tactical missiles,

gro-und weapons, aircraft, shipbuilding, and satellites, to reduce the produc-tion cost, improve quality, and reinforce negotiaproduc-tion posiproduc-tions in

international competition (Dowdy, 1999; Neal and Taylor, 2001).

Finally, successful defense management will require better coordi-nation and cooperation between government and industry and be-tween the executive units. Finding a winning strategy acts on the role of economic security for most households and national security

is needed (Pieroni, 2009).

Fig. 6. Cumulative change in the efficiency change for three regions.

Table 4

Original MPI and bootstrapping MPI.

Malmquist productivity index (MPI) Efficiency change (EC) Technological change (TC)

>1 =1 b1 >1 =1 b1 >1 =1 b1

Original MPI 312 8 192 211 82 219 311 3 198

Bootstrapping MPI 279 8 175 77 4 97 162 2 88

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Appendix A. Changes in efficiency, 32 OECD countries. Numbers greater than one indicate improvements (constant returns to scale) Country Year 1993– 1994 1994– 1995 1995– 1996 1996– 1997 1997– 1998 1998– 1999 1999– 2000 2000– 2001 2001– 2002 2002– 2003 2003– 2004 2004– 2005 2005– 2006 2006– 2007 2007– 2008 2008– 2009 Australia 0.979 0.978 1.014 1.084⁎ 0.937 0.970 1.051 1.066 0.940 0.906⁎ 1.012⁎ 1.043 1.007 1.028⁎ 0.977⁎ 0.858⁎ Austria 0.970 1.015 1.024 0.957 1.029 0.922 0.974 1.046 0.998 0.955 1.012 1.044 1.018 0.962 1.003 0.937⁎ Belgium 1.004 1.020 0.961 0.990 1.017 0.976 0.928 1.058 1.036⁎ 0.981 0.987 0.984 0.990 1.020 0.944⁎ 0.977⁎ Canada 0.962 1.059⁎ 0.995 1.010 0.991 0.978 1.089 1.021⁎ 0.926 0.938 0.952 1.017 1.003 1.021⁎ 0.994 0.797⁎ Chile 1.157⁎ 1.024⁎ 0.923 0.970⁎ 1.102⁎ 1.312⁎ 0.953⁎ 0.955⁎ 1.022⁎ 1.005 1.070 0.897⁎ 1.128 1.041⁎ 0.745⁎ 1.076 Czech Rep. 0.963⁎ 0.985⁎ 0.934⁎ 1.085 1.148 1.068⁎ 0.916⁎ 1.003⁎ 1.005⁎ 1.030 0.993 1.064⁎ 1.006⁎ 1.050 1.129 0.812⁎ Denmark 1.000 1.000 0.987 0.970⁎ 1.013 1.022 0.927 0.999 0.998 1.015 1.005 1.002 0.960 1.031 1.014 0.991⁎ Estonia 0.967 0.988⁎ 1.091⁎ 0.904⁎ 1.001 1.056⁎ 0.924⁎ 0.995⁎ 0.829⁎ 0.957⁎ 0.995 1.000⁎ 0.923⁎ 1.009⁎ 1.298⁎ 1.135⁎ Finland 1.012 1.077 0.931 0.936⁎ 1.024 1.030 0.968 1.040⁎ 0.988 0.968 0.987 0.979 1.040⁎ 1.013 1.003 0.902⁎ France 0.968 1.033 0.980 0.992 1.003 0.975 0.953 0.991⁎ 1.027⁎ 0.995⁎ 0.985 0.998 0.991 0.999 0.979⁎ 0.945⁎ Germany 1.004 1.027 0.976 0.978 1.008 0.975 0.960 1.085 1.077⁎ 0.977 1.015 1.009 1.000 1.000 1.000 0.831⁎ Greece 1.133⁎ 1.093 0.923 0.968⁎ 1.005 0.966 0.939 0.983⁎ 1.028 0.896⁎ 1.103⁎ 1.132 0.986 0.988 0.973 1.038 Hungary 0.960 1.114⁎ 0.886 0.934⁎ 0.967 1.094⁎ 0.960⁎ 1.081⁎ 0.984⁎ 0.980⁎ 0.936⁎ 1.048 1.071⁎ 1.166⁎ 1.050 0.692⁎ Ireland 1.000 1.000 1.000 1.000⁎ 1.000 0.975 0.990 1.036⁎ 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Israel 1.057 1.052⁎ 0.998 1.073⁎ 1.030 0.984 1.102 0.981⁎ 1.039⁎ 1.036⁎ 1.009⁎ 0.930⁎ 1.062 1.001 0.965⁎ 0.923⁎ Italy 1.010 0.969 1.016 1.011 1.015 0.981 0.980 0.988⁎ 0.968 1.003⁎ 1.007 1.029 0.988 1.029⁎ 1.010 0.870⁎ Japan 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.925 0.957 0.983 0.993 0.939 1.031⁎ 1.022 0.860⁎ Korea, South 1.048 1.029 1.014 1.009 1.283⁎ 0.875⁎ 1.009⁎ 1.015 0.957⁎ 0.958⁎ 0.993 1.026⁎ 1.045 1.031⁎ 0.923⁎ 0.910⁎ Mexico 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Netherlands 0.987 1.045 0.943 0.982 1.019 0.997 0.993 1.015⁎ 1.042⁎ 0.999 1.012 1.034 0.988 1.019 0.996 0.868⁎ New Zealand 1.063 1.008 1.071 1.022 0.971⁎ 0.927⁎ 1.028⁎ 0.967⁎ 1.019⁎ 0.997⁎ 0.992 1.031 0.974 1.049 1.002⁎ 0.843⁎ Norway 0.969 1.003 1.037 1.017⁎ 0.921 1.078 1.008 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Poland 0.937⁎ 1.021⁎ 0.866⁎ 0.875⁎ 1.000 1.012 1.043 1.171⁎ 1.074⁎ 0.973 0.944 1.035⁎ 0.955⁎ 0.896⁎ 1.074 0.842⁎ Portugal 1.030 1.023 0.957 0.905⁎ 1.015 0.981 1.043⁎ 1.008⁎ 1.033 1.076⁎ 0.979 1.011 1.066⁎ 1.051 0.982 0.880⁎ Slovak Rep. 1.255⁎ 0.909⁎ 0.693⁎ 0.976⁎ 1.093 1.230⁎ 1.087⁎ 0.874⁎ 0.983⁎ 1.157⁎ 0.934⁎ 0.936⁎ 1.119 1.026 0.992⁎ 0.647⁎ Slovenia 1.004 0.976⁎ 0.984 0.992 1.016 0.958 1.022⁎ 1.016⁎ 0.983 0.929⁎ 0.910⁎ 1.046 0.975 0.988⁎ 1.000⁎ 0.937⁎ Spain 1.002 1.034 1.026 0.968 1.021 0.929 0.959 1.020⁎ 0.953 0.997 0.988 1.022 0.916⁎ 1.020 1.048 0.863⁎ Sweden 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.828⁎ Switzerland 1.000 1.000 1.000 1.000 1.000 1.000 0.917 1.028 1.020 0.984 1.013⁎ 0.969 0.987 1.043⁎ 1.032 0.994⁎ Turkey 1.333⁎ 0.902 1.002 0.960⁎ 1.214⁎ 1.179⁎ 0.917⁎ 1.176⁎ 0.970 0.980⁎ 0.922⁎ 0.963 0.943⁎ 1.069 0.946⁎ 1.133 UK 1.022 1.046 0.981 0.963⁎ 1.002 1.035 1.020 1.000 1.000 1.000 0.996 1.004 1.000 1.000 1.000⁎ 1.000 USA 0.968 0.993 0.953 1.064⁎ 1.029 1.002 0.983 1.014 1.003⁎ 0.958 0.968⁎ 1.010 1.008 1.034⁎ 1.022 0.970⁎

Note: Single asterisks (⁎) denote significant differences from unity at 0.05.

Appendix B. Changes in technology, 32 OECD countries. Numbers greater than one indicate improvements (constant returns to scale)

Country Year 1993– 1994 1994– 1995 1995– 1996 1996– 1997 1997– 1998 1998– 1999 1999– 2000 2000– 2001 2001– 2002 2002– 2003 2003– 2004 2004– 2005 2005– 2006 2006– 2007 2007– 2008 2008– 2009 Australia 1.015 1.023⁎ 1.051 0.957 0.989 0.993 0.965 1.007⁎ 1.031⁎ 1.045⁎ 1.027⁎ 0.992⁎ 0.995⁎ 1.004⁎ 1.050 1.064⁎ Austria 1.042 1.050 0.974 0.974 0.985 1.073 0.982 0.993⁎ 1.084 1.102⁎ 1.066 0.988 1.039 1.043⁎ 1.041 1.059⁎ Belgium 1.040 1.070⁎ 1.028 0.938 0.991 1.001 0.995 0.989 1.060⁎ 1.100⁎ 1.058⁎ 1.015 1.032⁎ 1.022⁎ 1.050 1.051⁎ Canada 1.007 0.968⁎ 1.045 0.982 0.983 1.038 0.965 0.995⁎ 1.083 1.073⁎ 1.045⁎ 0.982 1.014 1.000⁎ 1.013 1.228⁎ Chile 0.937⁎ 0.927 1.036 1.019⁎ 0.935⁎ 0.981 1.004 1.031⁎ 0.993⁎ 1.021⁎ 0.985⁎ 1.007 0.961⁎ 0.960⁎ 1.097 1.222 Czech Rep. 0.937⁎ 0.927 1.041 1.015⁎ 0.935⁎ 0.981 1.004 1.009⁎ 1.034⁎ 1.023⁎ 0.998⁎ 1.007 0.965⁎ 0.971⁎ 1.004⁎ 1.401⁎ Denmark 1.016⁎ 1.037⁎ 1.029 0.945 0.987 1.005 1.006 1.018⁎ 1.038⁎ 1.099⁎ 1.043⁎ 1.014⁎ 1.003⁎ 1.005⁎ 1.057 1.094⁎ Estonia 0.956⁎ 1.002⁎ 0.942⁎ 0.966 1.009 1.027 0.956 1.015⁎ 1.054 1.037⁎ 1.021⁎ 0.976 0.967⁎ 0.968⁎ 1.005⁎ 1.289⁎ Finland 0.973⁎ 1.010⁎ 1.041 0.986 0.978 1.021 0.958 0.989⁎ 1.084 1.072⁎ 1.039⁎ 0.993⁎ 0.994⁎ 1.011⁎ 1.037⁎ 1.139⁎ France 1.033 1.032 1.041 0.964 0.981 1.001 0.973 1.025⁎ 1.034⁎ 1.051⁎ 1.012⁎ 0.989⁎ 0.999⁎ 1.011⁎ 1.056 1.121⁎ Germany 1.041 1.070 1.028 0.941 0.994 1.007 0.973 1.000⁎ 1.042⁎ 1.038⁎ 1.005⁎ 1.004 0.967⁎ 0.981⁎ 1.010⁎ 1.274⁎ Greece 0.937⁎ 0.928 1.035 1.019⁎ 0.935 0.981 1.004 1.023⁎ 1.013⁎ 1.025⁎ 0.988⁎ 1.007 0.961⁎ 0.960⁎ 1.097 1.218 Hungary 0.937⁎ 0.927 1.036 1.019⁎ 0.952 0.982 0.980 1.010⁎ 1.038⁎ 1.023⁎ 1.017⁎ 0.970 0.968⁎ 0.966⁎ 1.003⁎ 1.435⁎ Ireland 0.974⁎ 0.984⁎ 0.987⁎ 0.981 0.994 1.047 0.992 0.998⁎ 1.098 1.194 1.086 1.019 1.061 1.115 1.068 1.112 Israel 1.005⁎ 1.017 1.037 0.947 0.989 0.996 0.967 1.024⁎ 1.027⁎ 1.021⁎ 0.985⁎ 1.007 0.961⁎ 0.960⁎ 1.097 1.219⁎ Italy 1.014⁎ 1.023⁎ 1.054 0.951 0.989 0.998 0.971 1.020⁎ 1.031⁎ 1.066⁎ 1.019⁎ 0.987⁎ 0.999⁎ 1.012⁎ 1.036 1.176⁎ Japan 1.076 1.061 0.903 0.941 0.947 1.110 1.035 0.921 1.090 1.085 1.056⁎ 0.991 1.042 0.978⁎ 1.002 1.268⁎ Korea, South 1.013 1.043⁎ 0.985⁎ 0.979 0.959⁎ 0.981 0.961 1.014⁎ 1.053 1.032⁎ 1.007⁎ 0.987 0.969⁎ 0.983⁎ 1.008⁎ 1.282⁎ Mexico 0.891 0.943⁎ 0.977 1.071 1.037 1.073 1.087 1.103 1.046 1.000 1.039 1.053 0.989 0.981 1.024 0.844 Netherlands 1.041 1.044⁎ 1.036 0.947 0.988 1.002 0.985 1.009⁎ 1.045⁎ 1.075⁎ 1.029⁎ 0.981 0.994⁎ 1.007⁎ 1.031⁎ 1.177⁎ New Zealand 1.008 1.035⁎ 0.986 0.978 0.986 1.033 0.960 1.015⁎ 1.066 1.073⁎ 1.050⁎ 0.997 1.031 1.012⁎ 1.012 1.420⁎ Norway 1.040 1.060 1.017 0.928⁎ 1.014 0.989 1.048 1.033 1.064 1.124 1.057⁎ 1.080 1.048 1.046⁎ 1.114 0.928 Poland 0.937⁎ 0.928⁎ 1.036 1.019⁎ 0.935⁎ 0.981 0.975 1.012⁎ 1.033⁎ 1.024⁎ 0.993⁎ 1.007 0.959⁎ 0.969⁎ 1.008⁎ 1.342⁎ Portugal 0.937⁎ 0.927⁎ 1.036 1.019⁎ 0.954 0.997 0.963 1.014⁎ 1.041⁎ 1.023⁎ 1.001⁎ 1.007 0.959⁎ 0.964⁎ 1.016⁎ 1.294⁎ Slovak Rep. 0.937⁎ 0.928⁎ 1.035 1.019⁎ 0.939⁎ 0.981 0.977 1.011⁎ 1.041⁎ 1.023⁎ 1.003⁎ 0.982 0.968⁎ 0.974⁎ 1.003⁎ 1.339⁎

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Färe, R., Grosskopf, S., Lovell, C.A.K., 1994b. Production Frontiers. Cambridge University Press, London. (continued) Country Year 1993– 1994 1994– 1995 1995– 1996 1996– 1997 1997– 1998 1998– 1999 1999– 2000 2000– 2001 2001– 2002 2002– 2003 2003– 2004 2004– 2005 2005– 2006 2006– 2007 2007– 2008 2008– 2009 Slovenia 0.937⁎ 0.951 1.024 0.980 0.987 1.038 0.980 1.022⁎ 1.057 1.048⁎ 1.035⁎ 0.969 0.966⁎ 0.973⁎ 1.002 1.289⁎ Spain 1.017 0.990⁎ 1.001⁎ 0.977 0.983 1.041 0.972 0.995⁎ 1.083 1.095⁎ 1.059⁎ 0.991 1.037 1.041⁎ 1.027 1.187⁎ Sweden 0.987⁎ 1.018⁎ 1.059 0.982⁎ 0.966 1.010 0.957 0.990⁎ 1.068 1.077⁎ 1.050⁎ 0.983 1.004⁎ 1.005⁎ 1.010 1.225⁎ Switzerland 1.056 1.105 0.985 0.903 1.003 0.990 1.032 0.992 1.070 1.143⁎ 1.057⁎ 1.033 1.021⁎ 1.001⁎ 1.048 1.022⁎ Turkey 0.937⁎ 0.928⁎ 1.035 1.019⁎ 0.935⁎ 0.981 1.004 1.122⁎ 0.904⁎ 1.021⁎ 0.985⁎ 1.007 0.961⁎ 0.962⁎ 1.046 1.252 UK 0.945⁎ 0.938⁎ 1.035 1.019⁎ 0.943 0.981 0.995 1.008 1.029⁎ 1.036⁎ 1.003⁎ 0.997 0.987⁎ 0.991⁎ 1.063 1.213 USA 1.018 ⁎ 1.016 1.051 0.949 0.988 1.016 1.035 1.043 1.028⁎ 1.054 1.010⁎ 0.990⁎ 0.999⁎ 1.018⁎ 1.046 1.194⁎

Note: Single asterisks (⁎) denote significant differences from unity at 0.05.

Appendix C. Changes in productivity, 32 OECD countries. Numbers greater than one indicate improvements (constant returns to scale)

Country Year 1993– 1994 1994– 1995 1995– 1996 1996– 1997 1997– 1998 1998– 1999 1999– 2000 2000– 2001 2001– 2002 2002– 2003 2003– 2004 2004– 2005 2005– 2006 2006– 2007 2007– 2008 2008– 2009 Australia 0.994⁎ 1.000⁎ 1.066⁎ 1.038⁎ 0.926 0.964⁎ 1.015⁎ 1.073⁎ 0.969⁎ 0.947⁎ 1.039⁎ 1.035⁎ 1.002⁎ 1.032⁎ 1.025⁎ 0.913⁎ Austria 1.010⁎ 1.066⁎ 0.997⁎ 0.932⁎ 1.014⁎ 0.989 0.957⁎ 1.039⁎ 1.082 1.052⁎ 1.080⁎ 1.032 1.057 1.004⁎ 1.044⁎ 0.993⁎ Belgium 1.044⁎ 1.091⁎ 0.988⁎ 0.929⁎ 1.008⁎ 0.977⁎ 0.924 1.047⁎ 1.097⁎ 1.079⁎ 1.045⁎ 1.000⁎ 1.022⁎ 1.043⁎ 0.991⁎ 1.027⁎ Canada 0.968⁎ 1.025⁎ 1.040 0.992 0.974 1.015⁎ 1.051⁎ 1.015 1.003⁎ 1.007⁎ 0.995⁎ 0.999⁎ 1.018⁎ 1.022⁎ 1.007⁎ 0.978⁎ Chile 1.084⁎ 0.949⁎ 0.956⁎ 0.988⁎ 1.031⁎ 1.287⁎ 0.956⁎ 0.984⁎ 1.015⁎ 1.026⁎ 1.053⁎ 0.903⁎ 1.084⁎ 1.000⁎ 0.817⁎ 1.314⁎ Czech Rep. 0.902⁎ 0.914⁎ 0.972⁎ 1.101⁎ 1.073⁎ 1.048⁎ 0.919⁎ 1.012⁎ 1.039⁎ 1.054⁎ 0.992⁎ 1.071⁎ 0.971⁎ 1.020⁎ 1.134⁎ 1.138⁎ Denmark 1.016⁎ 1.037⁎ 1.015 0.916⁎ 1.000⁎ 1.027⁎ 0.932⁎ 1.016⁎ 1.035⁎ 1.115⁎ 1.048⁎ 1.017⁎ 0.963⁎ 1.036⁎ 1.072⁎ 1.084⁎ Estonia 0.925⁎ 0.990⁎ 1.028⁎ 0.874⁎ 1.010⁎ 1.085⁎ 0.884⁎ 1.010⁎ 0.873⁎ 0.992⁎ 1.016⁎ 0.976⁎ 0.893⁎ 0.977⁎ 1.305⁎ 1.464⁎ Finland 0.984⁎ 1.088⁎ 0.970 0.923⁎ 1.002⁎ 1.052⁎ 0.927 1.029 1.071⁎ 1.038⁎ 1.026⁎ 0.972⁎ 1.034⁎ 1.024⁎ 1.040⁎ 1.028⁎ France 1.000⁎ 1.066⁎ 1.021 0.957⁎ 0.984⁎ 0.976⁎ 0.927 1.016⁎ 1.062⁎ 1.046⁎ 0.997⁎ 0.987⁎ 0.990⁎ 1.011⁎ 1.034⁎ 1.060⁎ Germany 1.045 1.099⁎ 1.003⁎ 0.920⁎ 1.002⁎ 0.981 0.934⁎ 1.085⁎ 1.122⁎ 1.015⁎ 1.019⁎ 1.014 0.967⁎ 0.981⁎ 1.010⁎ 1.059⁎ Greece 1.061⁎ 1.014⁎ 0.955⁎ 0.986⁎ 0.940⁎ 0.948⁎ 0.943⁎ 1.006⁎ 1.041⁎ 0.919⁎ 1.090⁎ 1.140⁎ 0.948⁎ 0.949⁎ 1.067⁎ 1.264⁎ Hungary 0.899⁎ 1.033⁎ 0.918⁎ 0.951⁎ 0.921⁎ 1.074⁎ 0.941⁎ 1.092⁎ 1.021⁎ 1.002⁎ 0.952⁎ 1.017⁎ 1.037 1.127⁎ 1.054⁎ 0.994⁎ Ireland 0.974⁎ 0.984⁎ 0.987⁎ 0.981⁎ 0.994⁎ 1.021⁎ 0.982⁎ 1.034⁎ 1.098 1.194 1.086⁎ 1.019⁎ 1.061⁎ 1.115⁎ 1.068⁎ 1.112⁎ Israel 1.062⁎ 1.069⁎ 1.035⁎ 1.017 1.018 0.980⁎ 1.065⁎ 1.004 1.067⁎ 1.058 0.993⁎ 0.936⁎ 1.021⁎ 0.961⁎ 1.059⁎ 1.125⁎ Italy 1.024⁎ 0.991⁎ 1.071⁎ 0.961 1.003⁎ 0.979⁎ 0.951⁎ 1.008⁎ 0.998⁎ 1.069⁎ 1.026⁎ 1.015⁎ 0.987⁎ 1.042⁎ 1.046⁎ 1.023⁎ Japan 1.076⁎ 1.061⁎ 0.903 0.941⁎ 0.947⁎ 1.110⁎ 1.035⁎ 0.921⁎ 1.008 1.038⁎ 1.039⁎ 0.985 0.979⁎ 1.009⁎ 1.024⁎ 1.090⁎ Korea, South 1.062⁎ 1.074⁎ 1.000⁎ 0.988⁎ 1.231⁎ 0.858⁎ 0.969⁎ 1.030⁎ 1.008⁎ 0.989⁎ 0.999⁎ 1.013⁎ 1.012⁎ 1.014⁎ 0.930⁎ 1.166⁎ Mexico 0.891⁎ 0.943⁎ 0.977⁎ 1.071⁎ 1.037⁎ 1.073⁎ 1.087⁎ 1.103⁎ 1.046⁎ 1.000⁎ 1.039⁎ 1.053⁎ 0.989⁎ 0.981⁎ 1.024⁎ 0.844 Netherlands 1.028⁎ 1.091⁎ 0.977⁎ 0.929 1.007⁎ 0.999⁎ 0.978 1.024⁎ 1.088⁎ 1.074⁎ 1.041⁎ 1.015⁎ 0.983⁎ 1.026⁎ 1.027⁎ 1.021⁎ New Zealand 1.071⁎ 1.043⁎ 1.056⁎ 0.999⁎ 0.957⁎ 0.958⁎ 0.987⁎ 0.981⁎ 1.086⁎ 1.069⁎ 1.042⁎ 1.027⁎ 1.004 1.062⁎ 1.014⁎ 1.197⁎ Norway 1.007⁎ 1.063⁎ 1.054⁎ 0.944⁎ 0.933⁎ 1.066 1.056 1.033 1.064⁎ 1.124 1.057⁎ 1.080⁎ 1.048⁎ 1.046⁎ 1.114⁎ 0.928⁎ Poland 0.878⁎ 0.947⁎ 0.897⁎ 0.891⁎ 0.935⁎ 0.993⁎ 1.017 1.185⁎ 1.109⁎ 0.996⁎ 0.937⁎ 1.042⁎ 0.916⁎ 0.868⁎ 1.083⁎ 1.130⁎ Portugal 0.965⁎ 0.949⁎ 0.991⁎ 0.922⁎ 0.968⁎ 0.979⁎ 1.005⁎ 1.022⁎ 1.076⁎ 1.101⁎ 0.981⁎ 1.018⁎ 1.022⁎ 1.013⁎ 0.998⁎ 1.139⁎ Slovak Rep. 1.176⁎ 0.844⁎ 0.718⁎ 0.994⁎ 1.026⁎ 1.207⁎ 1.062⁎ 0.884⁎ 1.023⁎ 1.184⁎ 0.937⁎ 0.919⁎ 1.083⁎ 1.000⁎ 0.996⁎ 0.866⁎ Slovenia 0.940⁎ 0.929⁎ 1.008 0.973⁎ 1.003⁎ 0.994⁎ 1.001⁎ 1.038 1.039⁎ 0.974⁎ 0.942⁎ 1.014⁎ 0.942⁎ 0.961⁎ 1.002⁎ 1.209⁎ Spain 1.019 1.023⁎ 1.027 0.946⁎ 1.004⁎ 0.968⁎ 0.933⁎ 1.015⁎ 1.033⁎ 1.092⁎ 1.046⁎ 1.013⁎ 0.950⁎ 1.062⁎ 1.076⁎ 1.025⁎ Sweden 0.987⁎ 1.018⁎ 1.059⁎ 0.982⁎ 0.966⁎ 1.010 0.957 0.990⁎ 1.068⁎ 1.077⁎ 1.050⁎ 0.983⁎ 1.004⁎ 1.005⁎ 1.010⁎ 1.014⁎ Switzerland 1.056⁎ 1.105⁎ 0.985⁎ 0.903⁎ 1.003⁎ 0.990 0.946⁎ 1.020 1.091 1.124⁎ 1.071⁎ 1.001⁎ 1.008⁎ 1.044⁎ 1.082⁎ 1.016⁎ Turkey 1.248⁎ 0.837⁎ 1.038⁎ 0.978⁎ 1.136⁎ 1.156⁎ 0.921⁎ 1.319⁎ 0.876⁎ 1.001⁎ 0.908⁎ 0.970⁎ 0.906⁎ 1.028⁎ 0.990⁎ 1.419⁎ UK 0.966⁎ 0.981⁎ 1.016⁎ 0.981⁎ 0.945⁎ 1.015⁎ 1.016⁎ 1.008⁎ 1.029⁎ 1.036⁎ 0.998⁎ 1.001⁎ 0.987⁎ 0.991⁎ 1.063⁎ 1.213⁎ USA 0.986⁎ 1.008⁎ 1.001⁎ 1.010⁎ 1.017⁎ 1.018⁎ 1.017⁎ 1.058⁎ 1.032⁎ 1.009⁎ 0.977⁎ 0.999⁎ 1.007⁎ 1.053 1.069⁎ 1.158

Note: Single asterisks (⁎) denote significant differences from unity at 0.05. Appendix B(continued)

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數據

Fig. 1. A two-input, one-output MPI model showing the efficient frontier.
Fig. 1. A two-input, one-output MPI model showing the efficient frontier. p.2
Table 2 . Fig. 2 shows that the average value for overall defense expendi-

Table 2 .

Fig. 2 shows that the average value for overall defense expendi- p.4
Fig. 2. Mean and standard deviation (defense expenditure).
Fig. 2. Mean and standard deviation (defense expenditure). p.5
Fig. 5 shows consistency in TC among continents despite small var- var-iations in some years
Fig. 5 shows consistency in TC among continents despite small var- var-iations in some years p.6
Fig. 5. Cumulative change in the technical change for three regions.
Fig. 5. Cumulative change in the technical change for three regions. p.7
Table 4 differ signi ficantly from unity at the 0.05 level.

Table 4

differ signi ficantly from unity at the 0.05 level. p.7
Fig. 6. Cumulative change in the efficiency change for three regions.
Fig. 6. Cumulative change in the efficiency change for three regions. p.8

參考文獻