# Abstract

The main objective of this article is the evaluation of the efficiency and its evolution over time of 27 member countries of the North Atlantic Treaty Organization (NATO). We analyse the relationship between defense expenditure and the spending on military personnel as well as how security is perceived by citizens. To this end, a data panel for the years 2010 to 2017 has been used, consisting of various inputs at the macroeconomic level and one output, associated with the performance of the defense sector of NATO countries. For this, a production function has been estimated based on Data Envelopment Analysis methodology. According to the results obtained, the countries show high efficiency rates, around 80% with an increasing trend of 2.5% in the period studied. Thus, the estimated average technical efficiency was approximately 85.3%, that is, the NATO countries analyzed could increase their citizen security index by around 14.7% without modifying the resources used in their defense.

Data Envelopment Analysis, Economics of defense, Efficiency, Effectiveness,NATO.

MSC Subject classifications: 90C08.

# Introduction

The provision of public services that are as efficient as possible has become a universal target of central importance in economic policy, especially in times of economic crisis. A main concern is to measure the relative efficiency of different public entities providing the same public service. The traditional productivity literature defines measures of organizational efficiency as the distance of the unit under scrutiny from a frontier function, which is estimated using the best observed practice of the set of other similar units, Briec (1998), Briec and Lemaire (1999).

The essence of our research stems from the worldwide importance of optimizing available resources and increasing the outputs obtained, linked to public spending in the field of national defense. Our objective in particular is to evaluate the relative efficiency and effectiveness and their evolution over time for the 27 countries belonging to the North Atlantic Treaty Organization (NATO), studying the relationship between defense spending minus spending on military personnel and the perception of citizen security and safety. To this end, we used a panel data for the years 2010-2017. Generally speaking, two countries can be identical in terms of effectiveness if they achieve exactly the same results, while they can differ in terms of efficiency, if a different amount of resources are used to produce the same results, Farrell (1957).

Most research focuses its analysis on GDP(Gross Domestic Product), either to measure the country’s economic growth, or to analyze the importance of investment in defense and its effect on the national economy, Dunne and Tian (2015), Lee et al. (2016). Thus, defense spending can slow economic growth by crowding out historically more productive private investment. [Lebovic and Ishaq (1987), Mintz and Huang (1990), Scheetz (1991), Ward and Davis (1992)]. Authors like Lowell et al. (1995), analyze the effect of economic growth on the inflation rate, unemployment rate and on the trade balance, but it is not yet clear that defense investment produces a significant effect on the GDP growth rate, while its effect on a country’s economy is recognized. In particular, Asseery (1996), Dunne and Vougas (1999), Dunne et al. (2002) and Kollias et al. (2004) provide evidence supporting this hypothesis in several countries.

Some European studies point out that there is a causal relationship between GDP, and defense spending, Dunne and Nikolaidou (2005).Thus, there are variables that affect military spending that differ between countries, as in the case of NATO. Therefore, it is recognized that it is possible to conveniently group them into three groups: economic/political factors, income inequality and different traditions in defense and security among the Alliance members, Neira and González (2007).

The existing need for economic analysis to determine efficiency of a military organization (NATO), is based on the foundations of economic theory. This deals with comparing the performances completed over a period of time looking for the maximum optimization of resources. There is a marked difference between effectiveness and efficiency, based on how these goals have been accomplished. It must be taken into account that they are essential for better planning, an optimal distribution of resources and an accurate evaluation of the performance of NATO countries. Effectiveness is defined as the ability to obtain the outputs in the shortest possible time. Efficiency, on the other hand, is the ability to achieve a desirable end with respect to factors and productive results, maximizing production or minimizing the necessary resources. Remembering that the production function includes multiple inputs and one output security. Hildebrandt (2007), analyzes three methods of estimating the military production function that relate military inputs to a measure of military effectiveness: econometric, production and production function analysis. Other authors such as Martí and Fonfria (2020), analyze a behavior model of government agents, companies, product innovation and imitation in production processes, among others.

The measurement of efficiency is a problem associated with the aggregation of indicators in a single compound variable. When selecting the variables involved, each country faces the opportunity cost problem when redistributing the available resources to make the most of the resources invested in the public sector of national defense.

Adapting to the current conceptualization of relative efficiency and the estimation of its production function, we will use the econometric frontier technique called Data Envelopment Analysis –DEA-, so that the distance calculation of each unit –country- will be performed, to this frontier, focusing our attention on the 27 NATO countries.

The most relevant questions that will be answered in our research are the following: Which NATO countries can serve as a reference to others, in order to be more efficient? What is the relative level of efficiency of NATO countries? How does the degree of relative efficiency of NATO countries evolve over time?

In order to answer these questions, and solving the objective of this work, we consider the following structure of variables in our analysis. We are going to consider four inputs: personnel spending, equipment spending, infrastructure spending and other expenses (operations, maintenance, R&D) at the macroeconomic level. As output, associated with the performance of the defense sector of NATO countries, we will consider the Global Peace Index, which develops metrics to analyze peace, quantify its economic benefits, measure the level of negative peace in a country using indicators that determine the safety and protection of society. In addition, we will consider several uncontrollable variables (exogenous variables): the population, the surface area and the kilometers of coastline of the country. We will adapt our methodology to measure a country’s efficiency using this type of exogenous variables.

The rest of the article is structured as follows. First, a review of the existing literature is presented; pointing out the concepts necessary to carry out the analysis before establishing a general model for the production function.

Secondly, the efficiency calculations and certain benchmarking analyzes of the group of NATO countries are carried out, assuming variable returns to scale (VRS), with output orientation, by years, for the period 2010-2017.

Finally, research lines are proposed that, together with the efficiency evaluation, can improve the military administration and enable military means to offer better and more efficient services to citizens.

# Review of the Literature

Current defense studies focus largely on the interaction of military spending in various aspects. In the literature, we highlight the following authors, who analyze these items: Smith (1980), studies military expenditures and investments in the OECD 1954–1973. Ward and Davis (1992), focus on the peace dividend, in relation to economic growth and military spending. Dunne et al. (2018), review growth and defense in NATO countries. MacNair et al. (1995), analyze the demand of military expenditure in Turkey 1960–1992. Chletsos and Kollias (1995), study the distributions of the net burden contributed to NATO. Chen and Sherman (2004), study formulas to improve efficiency through DEA. Ebrahimnejad and Tavana (2014), analyze defense ministry spending and economic growth in Turkey.

Regarding productivity in the industrial and technological security sectors, we highlight the work of Martínez and Rueda (2005, 2013), which gives rise to assumptions, that are supported by a wide variety of statistical methodologies. Thus, they break down the productivity growth of 5 productive and technological subsectors, in defense and security in Spain. Neira and González (2007), analyze the determinants of military spending and demand in developing countries, NATO and the Asia-Pacific region. Grautoff and Miranda (2009), study military spending in Colombia. Haerpfer and Wallace (1997), analyze internal and external security in postcommunist Eastern Europe. Hartley (2011), studies defense outputs from an economic perspective, evaluating 12 nations. Scalco et al. (2012), calculate an efficiency index in the fight against crime in Minas Gerais (Brazil). Duch-Brown, et al. (2014), study the relationship between structure and productivity of the Spanish Defense markets. Diez Nicolás (2015), analyzes the perception of citizen security and safety at an international level. Hanson (2016) focuses on efficiency and productivity in 11 districts of the Norwegian National Guard operating units.

# Methodology and Data Desacription

Given the pressure of demand and the search for efficiency in a challenging environment, it is essential to count on studies that evaluate the performance of technical efficiency, facing analysis such as: the homogeneity of the sample, conceptualization and measurement of inputs/outputs, as well as the secrecy affecting classified documentation. DEA1 was used in this study to estimate the efficiency of the different NATO countries and their evolution throughout the 2010-2017 period. DEA is a non-parametric methodology based on Mathematical Programming, which allows the efficiency analysis of a sample of homogeneous units that consume the same set of inputs, to produce the same set of products, Cooper et al. (2000). Faced with other possibilities, such as stochastic frontiers, DEA does not require the functional specification of a production frontier, as well as being able to deal with a context of multiple products easily. In DEA, there are multiple efficiency measures that use different methods for calculating the distance of the unit evaluated to the frontier of the estimated technology.

## Data Envelopment Analysis (DEA)

To capture the underlying performance involved in the defense systems of NATO countries, we start by measuring the efficiency of each country on a yearly basis ($$t$$) as regards its combination of inputs and outputs. Efficiency is calculated based on a standard Data Envelopment Analysis (DEA) model (see Charnes et al. 1978 and Banker et al. 1984). For a period t, let us define an input vector as $$X^t=(x_{1}^{t},…,x_{m}^{t})\in R_{+}^{m}$$ and an output vector as $$Y^t=(y_{1}^{t},…,y_{s}^{t})\in R_{+}^{s}$$. We assume that for each period $$t$$ we have Decision Making Units (DMUs) that use $$m$$ inputs to produce $$s$$ outputs, denoted as $$(X_{j}^t,Y_{j}^t)$$ $$j=1,…,n$$ which come from a reference technology $$T^t=\lbrace ( X^{t},Y^{t} ) \in R_{+}^{m} \times R_{+}^{s}: X^t$$ $$produces\ Y^t\rbrace$$ he relative efficiency of every DMU (country, in our context) may be determined by calculating the distance of that unit to the frontier of the reference technologies $$T^t$$.

This distance can be calculated following the seminal contributions by Charnes et al. (1978) and Banker et al. (1984). The mathematical formulation of the first DEA measure of technical efficiency published in the literature exploits the notion of productivity, defined as a ratio of outputs and inputs: $\label{ec1} \mbox{Max } v^t,\mu^t \frac{\sum_{r=1}^{s} \\ \mu_{rk}^t \ y_{sk}^t }{\sum_{i=1}^{m} \ v_{ik}^t \ x_{mk}^t }\qquad(1)$
s.t.: \begin{aligned} && \frac{\sum_{r=1}^{s} \mu_{rk}^t \ y_{sk}^t }{\sum_{i=1}^{m} v_{ik}^t x_{mj}^t } \leq 1, \ j=1,…,n \\ && v_{ik}^t \geq 0, \ i=1,…,r\\ && \mu_{rk}^t \geq 0, \ r=1,…,s.\end{aligned}\qquad(2)

Where $$(v_{1k}^{t*},…,v_{mk}^{t*})$$ and $$(\mu_{1k}^{t*},…,\mu_{sk}^{t*})$$ denote the optimal input and output weights when the relative efficiency of unit $$(X_{k}^t,Y_{k}^t)$$ is evaluated with respect to all $$j=1,…,n$$ units, including itself. Model [ec1] identifies the most favorable input and output weights that result in the maximum feasible productivity level of $$(X_{k}^t,Y_{k}^t)$$ relative to that of the remaining observations. Note that since the weights constitute aggregator functions, both the objective function and the set of $$j=1,…,n$$ constraints in [ec1] represent proper definitions of productivity a ratio of aggregate output to aggregate input, normalizing maximum productivity through the constraints of model [ec1].

In DEA, there are two possible orientations for efficiency models. The first one is associated with input orientation, where the objective is to minimize the consumption of resources given a certain level of production; whereas under output orientation, the DEA models aim to maximize the outputs for a fixed level of inputs. Additionally, the models can be executed under the assumption of Constant Returns to Scale (CRS) and Variable Returns to Scale (VRS). Model [ec1] above corresponds to a DEA model under CRS and assuming input-orientation. In this paper, we will apply a VRS model under output-orientation. The VRS assumption is due to the existence of different ‘sizes’ among the analyzed NATO countries, while the assumption of output-orientation is because we understand that the resources (personnel, equipment, infrastructure and other defense expenditures) are fixed and the objective is the maximization of the perception of citizen security and safety (our selected output). In this sense, model [ec1] can be converted as follows:

$\label{ec2} \mbox{Min } v^t,\mu^t,\pi \ \frac{\sum_{i=1}^{m} v_{ik}^t x_{mk}^t + \pi }{\sum_{r=1}^{s} \mu_{rk}^t y_{sk}^t }\qquad(3)$
s.t.: \begin{aligned} && \frac{\sum_{i=1}^{m} \ v_{ik}^t \ x_{mk}^t + \pi }{\sum_{r=1}^{s} \ \mu_{rk}^t \ y_{sk}^t } \geq 1, \ j=1,…,n\\ && v_{ik}^t \geq 0, \ i=1,…,r\\ && \mu_{rk}^t \geq 0, \ r=1,…,s.\end{aligned}\qquad(4)

Model [ec2] is not linear, but can be easily linearized through model [ec3]:

$\label{ec3} \mbox{Min } v^t,\mu^t,\pi \ \sum_{i=1}^{m} \: v_{ik}^t \: x_{mk}^t + \pi\qquad(5)$
s.t.: \begin{aligned} && \sum_{r=1}^{s} \mu_{rk}^t \ y_{sk}^t =1 \\ &&\sum_{r=1}^{s} \mu_{rk}^t y_{rj}^t -\sum_{i=1}^{m} v_{ik}^t x_{ij}^t – \pi \leq 0, \ j=1,…,n\\ &&v_{ik}^t \geq 0, \ i=1,…,r\\ &&\mu_{rk}^t \geq 0, \ r=1,…,s.\end{aligned}\qquad(6)

Usually, in the literature, instead of solving model [ec3], researchers and practitioners solve its dual linear program [ec4]:

$\label{ec4} \mbox{Max }\lambda^t_k,\phi_k \phi_{k}\qquad(7)$
s.t.: \begin{aligned} && \sum_{j=1}^{n} \ \lambda_{jk}^t x_{ij}^t \leq x_{ik}^t, \ i=1,…,m\\ &&\sum_{j=1}^{n} \ \lambda_{jk}^t y_{rj}^t \geq \phi_k y_{rk}^t, \ r=1,…,s\\ &&\sum_{j=1}^{n} \lambda_{jk}^t=1\\ &&\lambda_{jk}^t\geq 0, \ j=1,…,n.\end{aligned}\qquad(8)

Model [ec4] is known as the output-oriented BBC model in the DEA literature (Banker et al., 1984). It can be shown that $$\phi_k^*$$ at optimum, is always greater or equal to one and, additionally, it can be interpreted as the efficiency score for DMU $$k$$ . Moreover, it is wellknown that the inverse of $$\phi_k^*$$ is the estimation of the famous Shephard output distance function (Shephard, 1953) under the assumption of piecewise linear production frontiers. In particular, when a country k presents a Shephard output distance function value that equals one, then the distance from the evaluated unit to the reference frontier will be zero (see, for example, unit B in Figure 1 with respect to the production frontier). This type of unit would be evaluated as technically efficient. On the contrary, if the assessed unit performs inefficiently and presents a Shephard output distance function value strictly less than one, then the distance from this point to the reference frontier will be strictly greater than zero (see, for example, unit D in Figure 1 with respect to the production frontier). In the graphical example, the piecewise linear function corresponds to the production function estimated by DEA, which upper envelops all the observations.

Using model [ec4] has several additional advantages. For example, the value, at optimum, of the decision variables $$\lambda_{jk}^t$$ , also called ‘intensity variables’, gives information on the efficient DMUs that are key in the evaluation of the technical efficiency of the assessed unit $$k$$ . Strictly positive values for $$\lambda_{jk}^{t*}$$ indicate that DMU $$j$$ is a peer (a reference unit) for the evaluated unit $$k$$. Indeed, the projection point in the production frontier associated with unit can be expressed as a convex combination of peer units. In Figure 1, D’ denotes the projection point linked to the inefficient unit D, while efficient DMUs B and C are the peers of D. Notice that point D’ is the midpoint between B and C.

On the other hand, in most empirical studies using data about public services, the results of the efficiency measurement depend on variables that are beyond the control of the considered DMUs, commonly known as contextual, exogenous or environmental variables. These factors do not take part in the production process, but they have an impact on the production level as well as on the use of inputs. Therefore, they must be considered in the efficiency estimation and must be specifically treated according to their features. This is the only way to properly reflect whether producers are performing efficiently or there are factors not allowing them to achieve the production objectives that are feasible for others even when doing their best. Incorporating the effects of exogeneous variables in the estimation of efficiency measures has been one of the topics that has generated more controversial discussions in the literature, since there are multiple approaches that can be used to deal with them, Badin et al. 2014.

In the DEA framework, the most well-known model to incorporate the effect of exogeneous variables is probably the Banker and Morey (1986) approach, which adapts the original DEA formulation to explicitly consider the exogenous character of this type of variables. In this paper, we adopt this formulation due to its simplicity and the existence of a high number of articles that have proven their reliability in practice.

Let us assume that, for a period of time $$t$$, we have additionally observed $$h$$ exogenous variables for each DMU $$j, j=1,…,n: Z_{j}^t=(z_{1j}^t,…,z_{hj}^t) \in R_{+}^m$$. Then, under the Banker and Morey (1986) approach, unit should be evaluated by solving the following linear optimization program:

$\label{ec5} \mbox{Max }\lambda^t_k,\phi_k \phi_{k}\qquad(9)$
s.t.: \begin{aligned} && \sum_{j=1}^{n} \lambda_{jk}^t x_{ij}^t \leq x_{ik}^t, \ i=1,…,m\\ &&\sum_{j=1}^{n} \lambda_{jk}^t y_{rj}^t \geq \phi k{}^t y_{rk}^t, \ r=1,…,s\\ &&\sum_{j=1}^{n} \lambda_{jk}^t z_{lj}^t \geq z_{lk}^t, \ l=1,…,s\\ &&\sum_{j=1}^{n} \lambda_{jk}^t=1 \\ &&\lambda_{jk}^t \geq 0, \ j=1,…,n.\end{aligned}\qquad(10)

In model [ec5], the exogenous variables have been incorporated to model [ec4] through additional constraints in such a way that the assessed DMU, unit $$k$$ , is evaluated avoiding its comparison with units that present a more favorable production context. In our empirical study, we resort to exogenous variables as, for example, kilometers of coastline. In this way, model [ec5] does not allow the comparison between a country with a certain number of kilometers of coastline and another one with less kilometers to be defended.

In this paper, we evaluate the performance of the technical efficiency of a panel of NATO countries over the years 2010-2017, (2017 Annual Summary of the NATO Secretary General). To do this, we resorted to the resolution of the optimization program [ec5] for each country and year and we will report the main results year by year.

## Global Peace Index

Peace is difficult to define. The simplest formula is in terms of the harmony achieved by the absence of violence or fear of violence, which is described as negative peace, being a complement to positive peace, which is defined as the attitudes, institutions and structures that create and sustain peaceful societies. [Global Peace Index, Institute for Economics and Peace. Sydney, June 2019 https://www.visionofhumanity.org/resources/ (accessed-01-05-2021)].

In this paper, we use of the Global Peace Index as the output associated with the performance of the defense sector of NATO countries. This Index created by the Institute for Economics and Peace, has developed metrics to analyze peace and quantify its economic benefits. It measures the level of negative peace of a country using different domains of peace: ongoing domestic and international conflict, investigating to what extent countries are involved in internal and external conflicts, as well as their role and duration of participation, evaluating the level of harmony or discord of a nation. Through the use of various indicators, they determine the safety and protection of society. Other indicators are related to militarization and the link between the level of military accumulation, access to weapons and their level of peace, both nationally and internationally, military expenditure as a percentage of GDP and the number of armed officers. The data comes from various sources of information2. It includes 23 indicators of absence of violence or fear of violence.

## Selection of variables

As it has been pointed out, the sample consists of 27 countries of the North Atlantic Treaty (NATO), taking into account that those countries are not providing complete economic data/indices have been disregarded. All of them, through their ministries of Defense, make an economic contribution of a percentage of their GDP and a number of military personnel to the Alliance. In this way, each country is rewarded with citizen security index. Luxembourg and Iceland are excluded in the study because they do not meet all the requirements necessary for the analysis of at least some of the variables used in our calculations.

Based on data from the Institute for Economics and Peace and the Center for Peace and Conflict Studies of the University of Sydney, the variable of the Safety and Security or Peace Index of each country is selected as the output variable On the other hand, we consider various inputs from each country: personnel expenses, equipment expenses, infrastructure expenses and other expenses (operations, maintenance, R&D)

And, finally, as uncontrollable variables: population, Surface area and number of kilometers of the country’s coastlines Table 1 ,2, 3, 4, 5, 6, 7, 8.

Regarding the period under study, we have selected the period from 2010 to 2017, for several reasons: (1) Period sufficiently close to reality, with reliable data from official NATO websites and the Institute for Economics and Peace; (2) Search for the current trend of the variables, taking into account that the 2007 crisis is a period of reduction/ containment of defense spending, although from 2016 it tends to improve, but very little. In this sense it is a homogeneous period.

Global peace index.Institute For Economics and Peace
Country / Years 2010 2011 2012 2013 2014 2015 2016 2017
Albania 1.93 1.91 1.93 1.96 1.94 1.82 1.87 1.91
Belgium 1.40 1.41 1.38 1.34 1.35 1.37 1.53 1.53
Bulgaria 1.79 1.41 1.70 1.66 1.64 1.61 2.00 1.63
Croatia 1.71 1.70 1.65 1.57 1.55 1.55 1.63 1.67
R. Czech 1.36 1.32 1.40 1.40 1.38 1.34 1.36 1.36
Denmark 1.34 1.29 1.24 1.21 1.19 1.15 1.25 1.34
Estonia 1.75 1.80 1.72 1.71 1.64 1.68 1.73 1.71
France 1.64 1.70 1.71 1.86 1.81 1.74 1.83 1.84
Germany 1.40 1.42 1.42 1.43 1.42 1.38 1.49 1.50
Greece 1.89 1.95 1.98 1.96 2.05 1.88 2.04 2.00
Hungary 1.50 1.50 1.48 1.52 1.48 1.46 1.53 1.49
Italy 1.70 1.78 1.69 1.66 1.68 1.67 1.77 1.74
Latvia 1.83 1.79 1.77 1.77 1.75 1.70 1.68 1.67
Lithuania 1.71 1.76 1.74 1.78 1.80 1.67 1.74 1.73
Montenegro 2.06 2.11 2.01 1.98 1.86 1.85 1.88 1.95
The Netherlands 1.61 1.63 1.61 1.51 1.48 1.43 1.54 1.53
Norway 1.32 1.36 1.48 1.36 1.37 1.39 1.50 1.49
Poland 1.62 1.55 1.52 1.53 1.53 1.43 1.56 1.68
Portugal 1.37 1.45 1.47 1.47 1.43 1.34 1.36 1.24
Romania 1.75 1.74 1.63 1.58 1.68 1.54 2.00 1.60
R. Slovakia 1.54 1.58 1.59 1.62 1.38 1.48 1.60 1.61
Slovenia 1.36 1.36 1.33 1.37 1.40 1.38 1.41 1.36
Spain 1.59 1.64 1.55 1.56 1.55 1.45 1.60 1.57
Turkey 2.42 2.41 2.34 2.44 2.40 2.36 2.71 2.78
U. Kingdom 1.63 1.63 1.61 1.79 1.80 1.69 1.83 1.79
Canada 1.39 1.35 1.32 1.31 1.31 1.29 1.39 1.37
U.S 2.06 2.06 2.06 2.13 2.14 2.04 2.15 2.23
Source: Own elaboration

[tab:tab1]

Personal expenses (US $1 billion constant 2010 prices and rate) Country / Years 2010 2011 2012 2013 2014 2015 2016 2017 Albania 141 152 129 133 117 119 101 106 Belgium 3962 3898 4023 3864 3813 3670 3666 3590 Bulgaria 535 459 447 495 506 508 469 494 Croatia 658 639 607 576 560 510 497 494 R. Czech 1348 1271 1361 1326 1249 1282 1370 1422 Denmark 2288 2238 2169 2096 1976 1979 2015 2035 Estonia 115 114 123 170 173 189 196 181 France 24759 24892 24909 24965 24342 23713 24150 24516 Germany 24358 23728 23618 21830 21891 21815 21865 23356 Greece 5142 4928 4232 4027 4182 4079 4300 4220 Hungary 761 705 646 619 599 640 749 685 Italy 21515 20748 19920 18 16910 16161 16510 15749 Latvia 140 131 130 132 136 148 185 197 Lithuania 214 209 206 215 221 246 309 348 Montenegro 54 62 57 55 52 50 50 55 The Netherlands 5866 5832 5965 5705 5518 5435 5293 5408 Norway 2774 2836 2778 2732 2734 2644 2714 2777 Poland 4823 5010 5106 5141 5107 5180 5382 5699 Portugal 2484 2732 2473 2558 2380 2476 2406 2422 Romania 1649 1725 1756 1788 1750 1741 1818 2061 R. Slovakia 710 694 680 655 667 642 687 699 Slovenia 476 468 435 395 384 375 386 391 Spain 9344 8632 8194 8544 8458 8558 8569 8584 Turkey 7032 7437 8005 8077 8481 8596 9469 9370 U. Kingdom 21507 22293 21207 22055 21002 20520 20510 20142 Canada 8467 9659 9111 8998 9170 11620 11207 11424 U.S 336438 239660 220433 221673 216631 217545 271431 259853 Source: Own elaboration [tab:tab2] Equipment expenses (US$ 1 billion constant 2010 prices and rate)
Country / Years 2010 2011 2012 2013 2014 2015 2016 2017
Albania 29 26 27 29 29 14 12 11
Belgium 356 322 183 142 172 161 222 250
Bulgaria 128 43 25 34 7 24 65 267
Croatia 75 150 131 91 59 85 75 71
R. Czech 330 300 326 203 133 273 148 281
Denmark 635 415 399 456 424 438 557 503
Estonia 39 36 57 62 99 61 91 100
France 15695 14209 15510 12439 12344 12425 12312 12350
Germany 8136 7447 7678 5578 5591 5220 5522 6587
Greece 1421 380 432 651 443 589 791 904
Hungary 163 171 79 140 93 129 202 248
Italy 3129 3257 2293 3069 2417 2026 4452 4966
Latvia 39 28 24 30 19 40 80 91
Lithuania 33 29 35 30 54 109 204 255
Montenegro 3 1 3 1 5 3 3 6
The Netherlands 1762 1540 1390 1225 1043 1093 1446 1782
Norway 1178 1113 1164 1258 1471 1537 1751 1997
Poland 1540 1398 1350 1238 1870 4099 2468 2633
Portugal 467 421 295 277 247 263 294 320
Romania 184 165 87 242 388 540 571 1252
R. Slovakia 112 71 98 69 107 209 179 262
Slovenia 139 36 7 6 3 8 5 21
Spain 1784 898 3275 1549 1694 1946 785 2695
Turkey 3955 3446 3031 3979 3740 3802 4200 5346
U. Kingdom 14763 13067 10653 12755 13098 12128 12769 13032
Canada 2581 1983 1542 1915 2347 2263 2239 4705
U.S 173046 195953 185090 166545 158700 150869 151063 175603
Source: Own elaboration

[tab:tab3]

Infraestructure expenses (US $1 billion constant 2010 prices and rate) Country / Years 2010 2011 2012 2013 2014 2015 2016 2017 Albania 3.4 1.5 1.2 2.1 1.5 2.1 2 1.4 Belgium 91.8 86.8 81.5 113.9 88.7 43.6 45.2 61.8 Bulgaria 19.9 10.4 5.3 3.6 4.4 8.8 4.5 4.5 Croatia 13.1 6.8 5.1 10.2 13.2 21 12.6 24.3 R. Czech 154 56.7 35.5 58.2 47.6 77 86.4 101.2 Denmark 48.2 62.1 54.8 47 37.4 41.5 87.9 115.2 Estonia 45.6 47.8 36.7 49.2 36.8 40.5 61.6 58.4 France 1626.7 1351.8 1734.7 1120.7 1167.2 1389.3 1360.2 1471.6 Germany 2386.8 1874.1 1647.6 1554.3 1620.2 1575.1 1533.1 1873.2 Greece 60.1 81.7 45.7 34 59.6 36.8 34.1 21.6 Hungary 28 18.2 28.6 29.4 12.9 16.1 17 26.5 Italy 401.2 363.5 263.7 385.2 309.8 270.9 163.3 305.9 Latvia 14.5 23.8 9.7 15.7 22.9 19.6 54.1 93.1 Lithuania 6.4 4.3 4.5 6.6 8.4 11 24.4 42.7 Montenegro 4.3 1.9 0 0.1 0.6 1.6 1.6 1.2 The Netherlands 389.3 402.3 383.6 267.1 465.8 312.3 398.8 354.4 Norway 340.6 275.6 318.6 375.6 416.8 382.7 506.8 594.8 Poland 336.3 416 423.8 500.7 543 585.2 527.4 561.3 Portugal 15.2 0.4 1.3 1.3 3.2 7.6 1.8 0.3 Romania 37.8 32.1 24.9 26.3 26.8 34.9 77.5 78.8 R. Slovakia 48 10.1 3.8 2.7 5.5 22.7 43.9 50.7 Slovenia 20.6 16.4 11.1 6.5 3 2.8 5.8 2.3 Spain 184.3 250.4 121.8 83.9 82.9 127.4 114.5 127 Turkey 401.4 408.2 528.7 402.5 413 387.3 397.2 351.7 U. Kingdom 977.3 973.6 1041.3 1188.7 1119.3 908.9 1160.9 1153.5 Canada 768.2 1123.6 1015.1 706.9 686.4 784.6 639.4 874.7 U.S 6988.1 22797.1 16333.5 13411.3 10449.6 8609.2 7357.2 7473.8 Source: Own elaboration [tab:tab4] Other Expenses (US$ 1 billion constant 2010 prices and rate)
Country / Years 2010 2011 2012 2013 2014 2015 2016 2017
Albania 13 17 28 13 25 18 34 37
Belgium 836 830 836 876 824 816 821 817
Bulgaria 149 169 213 224 177 149 176 139
Croatia 174 155 148 169 176 186 156 197
R. Czech 828 630 484 551 605 688 606 726
Denmark 1532 1571 1798 1452 1418 1347 1410 1504
Estonia 132 155 198 145 139 188 159 179
France 10030 9987 8567 12186 12238 12092 12554 12759
Germany 11369 12329 13732 14816 14097 15143 16303 16088
Greece 1279 1092 1073 689 734 957 755 700
Hungary 398 498 601 476 498 542 540 656
Italy 3611 3377 3376 2682 2494 2380 2197 2696
Latvia 57 73 68 72 79 88 102 148
Lithuania 73 70 64 72 101 141 142 175
Montenegro 12 10 9 7 9 9 12 13
The Netherlands 3203 2896 2627 2550 2739 2951 3088 3066
Norway 2205 2306 2295 2294 2324 2269 2309 2457
Poland 1794 1843 2024 2030 2406 2483 3038 2998
Portugal 573 336 386 367 298 277 255 362
Romania 215 258 223 207 295 434 330 379
R. Slovakia 268 224 241 207 185 268 260 271
Slovenia 136 107 98 83 77 70 111 104
Spain 3429 3540 2738 2342 2324 2499 2334 2551
Turkey 2746 2734 2725 2338 2277 2343 2347 2517
U. Kingdom 23082 23035 21611 22270 22173 22204 24787 24827
Canada 6872 7740 6888 5539 5812 6947 7016 7225
U.S 203880 267611 264424 243208 225309 216773 173255 174739
Source: OTAN. Own elaboration

[tab:tab5]

Real GDP (US \$ 1 billion constant 2010 prices and rate)
Country / Years 2010 2011 2012 2013 2014 2015 2016 2017
Albania 0.012 0.012 0.012 0.013 0.013 0.013 0.013 0.014
Belgium 0.484 0.492 0.493 0.494 0.501 0.508 0.516 0.525
Bulgaria 0.051 0.052 0.052 0.052 0.053 0.055 0.057 0.059
Croatia 0.06 0.059 0.058 0.058 0.057 0.059 0.06 0.062
R. Czech 0.207 0.211 0.209 0.208 0.214 0.225 0.231 0.241
Denmark 0.322 0.326 0.327 0.33 0.335 0.341 0.348 0.355
Estonia 0.019 0.021 0.022 0.022 0.023 0.023 0.024 0.025
France 2.647 2.702 2.707 2.722 2.748 2.778 2.811 2.861
Germany 3.417 3.542 3.56 3.577 3.646 3.71 3.782 3.878
Greece 0.299 0.272 0.252 0.244 0.246 0.245 0.244 0.248
Hungary 0.131 0.133 0.131 0.134 0.139 0.144 0.147 0.153
Italy 2.125 2.137 2.077 2.041 2.043 2.064 2.083 2.116
Latvia 0.024 0.025 0.026 0.027 0.027 0.028 0.029 0.03
Lithuania 0.037 0.039 0.041 0.042 0.044 0.045 0.046 0.047
Montenegro 0.004 0.043 0.004 0.004 0.004 0.005 0.005 0.005
The Netherlands 0.836 0.85 0.841 0.84 0.852 0.871 0.89 0.919
Norway 0.429 0.433 0.445 0.45 0.459 0.468 0.473 0.483
Poland 0.479 0.503 0.511 0.519 0.536 0.556 0.572 0.597
Portugal 0.238 0.234 0.225 0.222 0.224 0.228 0.232 0.238
Romania 0.168 0.17 0.171 0.177 0.182 0.19 0.198 0.21
R. Slovakia 0.09 0.092 0.094 0.095 0.098 0.101 0.105 0.108
Slovenia 0.048 0.048 0.047 0.047 0.048 0.049 0.051 0.053
Spain 1.432 1.417 1.376 1.352 1.371 1.418 1.464 1.51
Turkey 0.772 0.858 0.899 0.975 1.025 1.088 1.123 1.191
U. Kingdom 2.441 2.476 2.513 2.564 2.643 2.705 2.753 2.795
Canada 1.613 1.664 1.693 1.735 1.78 1.796 1.823 1.878
U.S 14.964 15.204 15.542 15.803 16.209 16.673 16.92 17.3
Source: OTAN. Own elaboration

[tab:tab6]

Population (millons)
Country / Years 2010 2011 2012 2013 2014 2015 2016 2017
Albania 2.92 2.88 2.88 2.88 2.89 2.90 2.90 2.91
Belgium 10.84 11.00 11.09 11.16 11.18 11.24 11.31 11.35
Bulgaria 7.42 7.37 7.33 7.28 7.25 7.20 7.15 7.10
Croatia 4.30 4.29 4.28 4.26 4.25 4.23 4.19 4.15
R. Czech 10.46 10.49 10.51 10.52 10.51 10.54 10.55 10.58
Denmark 5.53 5.56 5.58 5.60 5.63 5.66 5.71 5.75
Estonia 1.33 1.33 1.32 1.32 1.32 1.31 1.32 1.32
France 64.66 64.98 65.28 65.60 65.94 66.49 66.76 66.99
Germany 81.80 80.22 80.33 80.52 80.77 81.20 82.18 82.52
Greece 11.12 11.12 11.09 11.00 10.93 10.86 10.78 10.77
Hungary 10.01 9.99 9.93 9.91 9.88 9.86 9.83 9.80
Italy 59.19 59.36 59.39 59.69 60.78 60.80 60.67 60.59
Latvia 2.12 2.07 2.05 2.02 2.00 1.99 1.97 1.95
Lithuania 3.14 3.05 3.00 2.97 2.94 2.92 2.89 2.85
Montenegro 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6
The Netherlands 16.57 16.66 16.73 16.78 16.83 16.90 16.98 17.08
Norway 4.86 4.92 4.99 5.05 5.11 5.17 5.21 5.26
Poland 38.02 38.06 38.06 38.06 38.02 38.01 37.97 37.97
Portugal 10.57 10.57 10.54 10.49 10.43 10.37 10.34 10.31
Romania 20.29 20.20 20.10 20.02 19.95 19.87 19.76 19.64
R. Slovakia 5.39 5.39 5.40 5.41 5.42 5.42 5.43 5.44
Slovenia 2.05 2.05 2.06 2.06 2.06 2.06 2.06 2.07
Spain 46.49 46.67 46.82 46.73 46.51 46.45 46.45 46.53
Turkey 72.6 73.72 74.72 75.63 76.67 77.70 78.74 79.81
U. Kingdom 62.51 63.02 63.50 63.91 64.35 64.88 65.38 65.81
Canada 34.00 33.48 34.71 35.08 35.44 35.70 35.15 36.54
U.S 309.30 311.60 314.00 316.20 318.60 321.00 323.40 325.70
Source: OTAN. Own elaboration

[tab:tab7]

Extension, boders and coasts
Country Extension(thousands of $$km^2$$ ) Coasts($$km$$)
Albania 28.7 362
Belgium 30.5 67
Bulgaria 111.9 354
Croatia 56.6 5835
R. Czech 78.9 0
Denmark 43.1 7314
Estonia 45.2 3794
France 675.4 5500
Germany 357.0 2389
Greece 131.9 15021
Hungary 93.0 0
Italy 301.3 7600
Latvia 64.6 498
Lithuania 65.3 90
Montenegro 13.8 293
The Netherlands 41.5 798
Norway 323.8 25148
Poland 312.7 25148
Portugal 92.1 1793
Romania 237.5 225
R. Slovakia 48.8 0
Slovenia 20.3 47
Spain 504.6 4964
Turkey 783.6 7200
U. Kingdom 244.8 12429
U.S 9147.6 19924
Source: OTAN. Own elaboration

[tab:tab8]

# Results

In this section we will describe the results obtained after applying the methodology described above to NATO countries 3.

Firstly, it should be noted that, in the first stage of calculation Table 9 and assuming variable returns to scale (VRS), with output orientation4, the set of efficient countries was determined, by years, for the period 2010-2017. Technical efficiency was calculated for each year, (Figure 2) as well as the averages for each country both in the study period and annually. Once the calculation was performed in this regard, it was observed that four of the countries analyzed appear to be efficient: Albania, Belgium, Bulgaria, and Lithuania. Other countries appear as efficient in some of the years analyzed, such as: Croatia, Denmark, Germany , Hungary, Latvia, Poland, Portugal and the United Kingdom. The rest are not efficient in the period: Belgium, Montenegro, The Netherlands, Norway, Rumania, U. Kingdom, Canada, U.S., Slovakia and Slovenia. The average values of the efficiency indices are quite high in most countries, being around 0.853. These efficiency results are supported by an increasing trend during the analyzed period of 2.5%.

VRS Technical Efficiency
Country/couple of Years 10-11 11-12 12-13 13-14 14-15 15-16 16-17 Half
Albania 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
Belgium 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
Bulgaria 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
Croatia 0.759 1.000 0.795 0.756 0.785 0.748 0.778 0.799
R. Czech 0.768 0.734 0.746 0.739 0.762 0.805 0.770 0.760
Denmark 0.621 1.000 0.727 0.678 0.725 0.721 0.751 0.739
Estonia 0.637 0.878 0.668 0.683 0.736 0.776 0.744 0.728
France 0.764 0.853 0.753 0.769 0.819 0.752 0.791 0.785
Germany 0.730 1.000 0.758 0.770 0.764 0.819 0.852 0.809
Greece 0.644 1.000 0.731 0.742 0.765 0.709 0.695 0.749
Hungary 1.000 0.665 0.731 0.718 0.719 0.720 1.000 0.783
Italy 0.878 0.640 0.843 0.823 0.933 0.841 0.879 0.829
Latvia 0.874 1.000 0.817 0.874 0.858 0.899 0.852 0.880
Lithuania 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
Montenegro 1.000 0.871 1.000 1.000 1.000 1.000 1.000 0.980
The Netherlands 1.000 0.878 1.000 1.000 1.000 1.000 1.000 0.982
Norway 1.000 0.731 1.000 1.000 1.000 1.000 1.000 0.956
Poland 0.705 0.733 0.724 0.752 0.787 0.676 0.767 0.734
Portugal 0.750 0.987 0.743 0.746 0.716 0.787 0.698 0.771
Romania 1.000 1.000 1.000 1.000 1.000 0.898 1.000 0.985
R. Slovakia 1.000 1.000 1.000 0.996 0.998 1.000 1.000 0.999
Slovenia 0.740 1.000 0.753 0.845 0.889 0.790 0.833 0.832
Spain 0.740 0.908 0.837 0.849 0.833 0.858 0.812 0.832
Turkey 0.618 0.865 0.606 0.598 0.619 0.571 0.602 0.634
U. Kingdom 0.600 1.000 0.593 0.595 0.610 0.617 0.591 0.646
Canada 0.850 1.000 0.844 0.873 0.890 0.752 0.776 0.852
U.S 0.851 1.000 0.873 0.876 0.848 0.795 0.804 0.862
Socks 0.834 0.916 0.835 0.848 0.854 0.835 0.852 0.853
Source: Own elaboration

[tab:tab9]

Subsequently, a Ranking was made with the averages of the efficiencies of the period of the different countries Table 10.

Ranking of NATO country efficiencies 2010-2017
Country Index Country Index
1. Albania 1.000 12. Italy 0.829
1. Belgium 1.000 13. Germany 0.809
1. Bulgaria 1.000 14. Croatia 0.799
1. Lithuania 1.000 15. France 0.785
2. R. Slovakia 0.999 16. Hungary 0.783
3. Romania 0.985 17. Portugal 0.771
4. The Netherlands 0.982 18. R. Czech 0.760
5. Montenegro 0.980 19. Greece 0.749
6. Norway 0.956 20. Denmark 0.739
7. Latvia 0.880 21. Poland 0.734
8. U.S. 0.862 22. Estonia 0.728
9. Canada 0.852 23. U.Kingdom 0.646
10. Spain 0.832 24. Turkey 0.634
11. Slovenia 0.832
Source: Own elaboration.

[tab:tab10]

Secondly, an efficiency study is carried out Table 11, assuming variable returns to scale (VRS), with output orientation, with inputs and outputs. We rely on one of the advantages of the DEA methodology: its use as a benchmarking 5 technique. To associate each country with its benchmark pair and subsequently favor the application of best resource management practices in those most inefficient countries. For this, the measures of the intensity 6 variables of efficiency in the period 2010-2017 were calculated, analyzing them by years. Thus, the number of times that a country is taken as an efficiency reference -model- by other countries was obtained.

The study shows that the following countries are taken as a reference sometime during the period analyzed: Albania, Belgium, Bulgaria, Croatia, Denmark, Germany, Greece, Hungary, Latvia, Lithuania, Montenegro, The Netherlands, Norway, Romania, R. Slovakia, Slovenia, United Kingdom, Canada and the United States.

We highlight that Romania is the country that most countries take as a reference – 86 times in the period – in order to achieve maximum efficiency. Thus, a maximum is reached in 2012 (44 countries) and a minimum in 2011 (39 countries).

Intensity Variables of technical efficiencies (number of times other countries take it as a reference)
Country/couple of years 2010/11 2011/12 2012/13 2013/14 2014/15 2015/16 2016/17
Albania 19 3 1 3 3 3 3 3
Belgium 69 1 13 17 18 18 1 1
Bulgaria 54 16 1 1 1 1 18 16
Croatia 1 1
Denmark 1 1
Germany 1 1
Greece 1 1
Hungary 2 1 1
Latvia 1 1
Lithuania 7 1 1 1 1 1 1 1
Montenegro 6 1 1 1 1 1 1
The Netherlands 6 1 1 1 1 1 1
Norway 6 1 1 1 1 1 1
Romania 86 15 12 2 18 18 18 3
R. Slovakia 36 3 1 17 15
Slovenia 1 1
U. Kingdom 1 1
U.S. 2 2
43 39 44 44 44 44 43
Source: Own elaboration

[tab:tab11]

Figure 3 represents the number of times a country is taken as a reference in each couple of years of study.

Intensity Variables of technical efficiencies.Year 2010 reference countries and value of intensity variables
1 2 3 4 4 6 7 8 9 10
Albania 1.000
Belgium 1.000
Bulgaria 1.000
Croatia 0.964 0.036
R. Czech 0.964 0.036
Denmark 0.941 0.059
Estonia 0.940 0.060
France 0.979 0.021
Germany 0.979 0.021
Greece 0.967 0.033
Hungary 1.000
Italy 0.335 0.665
Latvia 0.335 0.665
Lithuania 1.000
Montenegro 1.000
The Netherlands 1.000
Norway 1.000
Poland 0.544 0.417 0.039
Portugal 0.740 0.260
Romania 1.000
R. Slovakia 1.000
Slovenia 0.700 0.300
Spain 0.700 0.300
Turkey 0.536 0.464
U. Kingdom 0.543 0.457
U.S 1.000
Source: Own elaboration

[tab:tab12]

1-Albania, 2-Belgium, 3-Bulgaria, 4-Hungary, 5-Lithuania, 6-Montenegro, 7-The Netherlands, 8-Norway, 9-Romania, 10-R.Slovakia

Third, the intensity variables for the year 2010 were calculated. Carrying out a study assuming variable returns to scale (VRS), with output orientation, with the inputs, outputs. Table 12 shows the values of the intensity variables for each country and the reference country –model- from which they could learn.

It follows that the following countries are taken as a reference sometime during 2010 from the 27 countries and are presented as -models-: Albania, Belgium, Bulgaria, Hungary, Lithuania, Montenegro, The Netherlands, Norway, Romania, R Slovakia Turkey, representing 27% of the countries under study. We highlight: Bulgaria and Romania, which were taken as a reference 16-15 times in the year. As an example and with the use of benchmarking techniques, we analyze the -intensity variables- taken from the DEA VRS analysis year 2010, from an inefficient country. Bulgaria, which has a technical efficiency of 90.8%. We see that it can be compared with its pairwise references -Intensity Variables- to: Croatia, R. Czech, Denmark, Estonia, France, Germany, Grecee, Italy, Latvia, Poland, Portugal, Slovenia, Spain, Turkey, and U. Kingdom, which could be considered as possible reference strategies, to increase its technical efficiency. Figure 4 shows the results of average efficiencies, assuming VRS returns with output orientation, of the countries analyzed in the period 2010-2017. As we can see countries such as the Albania, Belgium, Bulgariaand Lithuania, among others, stand out from the rest of the countries in terms of the efficiency index.

Taking into account what is presented in our literature review and having calculated the degree of technical efficiency of NATO countries year by year (Table 9), with regard to efficiency indices it can be highlighted that 40% of the countries are efficient, another 48.15% are efficient in some year and the remaining 47.9% are not efficient in any year. We mention that the average efficiency indices are quite high, being around 80%. However, the trend during the period shows a growth in average technical efficiency under VRS of 2.15%, on average in most countries in recent years, with the exception of Portugal, Turkey, U. Kingdom and U.S., which show a decreasing index. The index grew partially until 2011, decreasing until 2012, growing again until reaching in 2014 and it finally decreased .

This means that the countries continue to have a certain concern about their efficiency. From the results, it can be seen that the technical efficiency was 85.3%, deducing that countries can produce 14.7% more outputs without modifying the level of inputs used. In this sense, we observe that the countries that make the greatest contribution of resources are more efficient, highlighting the Albania, Bulgaria and Lithuania, among others.

Regarding the analysis of the intensity variables between countries in the 2010-2017 period (Table 11), used to obtain the number of times that each country is taken as an efficiency reference, we deduce that 66.6% of the 27 countries serve as a reference at some time. Thus, they are represented as -model-: Belgium, Denmark, Canada, Montenegro, The Netherlands, Norway, R. Slovakia, Slovenia, Canada, Albania, Hungary, Germany (8.69%), Romania, United States, Bulgaria, Croatia, Grecee, Latvia, Lithuania.

In relation to the calculation of the intensity variables for 2010, (Table 12). It follows that only 37% of the 27 countries are taken as a reference. Thus, they are presented as –models-: Albania, Belgium, Bulgaria, Hungary, Lithuania, Montenegro, Netherlands, Norway, Romania and R Slovakia being the countries that the majority take for reference.

# Discussion

Regarding the approach of the hypotheses initially proposed, we can say that, stemming from our research, it is observed that the defense ministries of each country may take certain countries as a reference to increase efficiency rates. That is, with the same inputs as their contributions, they produce more outputs and so are able to reduce their gaps in efficiency indices. We also note that an increase in defense spending indirectly affects achieving a higher rank in the efficiency index.

Across the board, it can be deduced that the country that contributes the most financially, offers greater collective security, that is, helping less secure neighboring countries. This implies that, by having more stability in neighboring countries, the environment is more stable and more security is obtained as a whole. However, it is necessary to consider what aspects are behind the results obtained, and various arguments can be derived that may shed light on certain factors that affect these results. Taking into consideration Driver (2016) burden sharing and the future of NATO, burden sharing is a key piece within NATO that involves important debates over time. Thus, and quoting Eisenhower, the American well had run dry, and it was only through unity that Europeans might be capable of assuming a greater share of the defense burden so that the US might, as he opined, sit back and relax somewhat. This situation is clearly reflected in the results of the analysis, bestowing the United States maximum relative efficiency. Likewise, the signing of the Newport agreement of 2014 according to which the countries promised to increase their defense spending to 2% of GDP7, implies that higher spending will generate higher levels of collective security not just individual security a result brought to light from this analysis.

It is just as necessary to take into account the different culture and defense strategies of the countries, since they determine both the expenditure incurred and how it is carried out, which in turn determines the different levels of efficiency. In this sense, both the historical evolution in the field of security, such as the geopolitical situation, the priorities of the various governments, their economic situation and the international commitments taken on board, make up a set of aspects that affect how spending on defense is carried out and what level of security is reached, Ghazalian and Hammoud (2020). It is therefore logical that the main countries United States, United Kingdom, Canada tend to achieve higher levels of efficiency, as the analysis shows. Something similar, but with limitations due to output the security index occurs with countries that have to face greater risks, either because of their geographical position close to conflicts or non friendly countries or because they have less developed defense systems that they need to boost.

The composition of defense spending is equally important since it determines the type of systems that provide citizen´s security. In this sense, the same threat can be faced using different types of strategies that will give rise to different weapons systems capabilities, which, in turn, will condition that defense spending is oriented one way or another, Davis (2011). Thus, its expression in the country’s security level will be equally different, and may be higher or lower depending on where such spending is directed.

In relation to the defense policies carried out through NATO, it is important to underline the need to pursue greater efficiency in spending, along with systems that provide higher levels of security, many of them far from the more traditional weapons systems and much more closely linked to the typology of new conflicts –hybrid warfare and gray zone-, which leads to substantial changes in the concept of security, expanding its range to areas such as economic security or cybersecurity, Hunter and Pernik (2015).

# Conclusions

Most studies in the field of defense economics are based on an analysis focused on the effects of public defense spending on the national economy. It is necessary to recognize that the existence of works that analyze efficiency to date are scarce. It is important to highlight the current problems in obtaining information on adequate inputs and outputs, in the NATO military environment, which has led us to use the following inputs in the study: personnel spending, equipment spending, infrastructure spending and other expenses (operations, maintenance, R&D) at the macroeconomic level. And as output, the global peace index and considering the following as uncontrollable variables (exogenous variables): the country’s population, the surface area and the kilometers of coastline. Thus we have adapted our methodology, Data Envelopment Analysis –DEA- to the measurement of the efficiency of the countries with this type of exogenous variables.

Therefore, this paper provides information on a little studied area, where it has been possible to observe levels of technical efficiency. We can say that quite high rates are reached and with an increasing trend in the period. This efficiency trend could be explained as follows. Year after year, several of the countries that make up the group of certain relative weight within NATO are on the production frontier. It is appreciated that, in turn, these countries tend to maintain, generally without great changes, their inputs, but if they greatly increase their outputs, this would tend to produce an efficient upward shift on the frontier, which in turn means that the least efficient countries are gradually positioned farther away from that frontier. This, in the end, implies a negative evolution of their technical efficiency.

In addition, the study allows the comparison of intensity variables (countries that can be used as a reference by others that are less efficient). In this way, the efficiency gap can be reduced, taking them as models for applying measures that enhance their efficiency and allowing more effective changes to be made within the defense ministries of each country.

The study shows that the most efficient countries could reduce their input-inputs, that is, reduce personnel spending, equipment spending, infrastructure spending and other expenses (operations, maintenance, R&D) at the macroeconomic level -up to a ceiling- to continue obtaining the same security indices, not forgetting that, although security is an intangible asset, today’s society takes it for granted and higher spending is not usually socially accepted.

Finally, we mention that the inefficiency of the countries may be due to what Leibenstein (1966) called X-inefficiency, where the source of the inefficiency is attributed to non-technological causes and that are linked to the behavior of individuals.

As future lines of work, we could point out that countries attempted to limit their efforts, maximizing their utility, instead of minimizing costs, using more production factors than necessary to achieve a certain level of output. And so, the least efficient countries could improve their situation by adopting appropriate strategic decisions such as a different combination of inputs or composition of systems to obtain the best combination of resources, reducing their efficiency gaps. That is, generate more output with the same inputs. This would lead us to calculate economic efficiency, which, together with technical efficiency, would allow us to estimate changes in productivity, as well as their decomposition into changes in both efficiency and those derived from technology. The research is open to its expansion and to carrying out more exhaustive analyzes with data, which, because they are classified and confidential, have not been used. According to Nayar et al. (2013), DEA is a promising tool to assess efficiency in conjunction with effectiveness, this could be applied to NATO countries. Thus, in the future, global efficiency measures may be based on the use of the efficiency levels granted by recognized organizations such as the European Foundation for Quality Management, the Joint Commission, or others. However, what seems clear is the need to undertake further work on measuring both aspects of efficiency and effectiveness in defense economics.

## Acknowledgments

J. Aparicio and M. Domínguez thank the financial support from the Spanish Ministry of Science and Innovation and the State Research Agency under grant: PID2019-105952GB-I00/AEI/10.13039/5011 00011033.

Juan Aparicio Doctor, Catedrático de Universidad del área de Estadística e Investigación Operativa, Director del Centro de Investigación Operativa de la Universidad Miguel Hernández de Elche, Director de la Cátedra Santander en Eficiencia y Productividad, coordinador de la Red de Institutos Universitarios de investigación en matemáticas de España, Investigador Principal de varios proyectos del Ministerio de Ciencia e Innovación, miembro de un proyecto PROMETEO de excelencia en la Comunidad Valenciana. Ha publicado más de 100 artículos en revistas de alto impacto y capítulos de libro en editoriales de prestigio, como Springer. Es editor asociado de varias revistas, como Omega y Journal of Productivity Analysis. Su principal línea de investigación es la medición de la eficiencia y la productividad.

Antonio Fonfría Licenciado y Doctor en Ciencias Económicas y Empresariales, Master en Economía Europea, Diplomado de Altos Estudios de la Defensa, Profesor de Economía de la Defensa en varios posgrados, colaborador: del Instituto Español de Estudios Estratégicos, del CESEDEN, del CESIA, del Ministerio de Defensa-DGAM, del Real Instituto Elcano, es miembro del consejo de la revista IEEE. Sus principales líneas de investigación son la economía e Industria de la defensa, políticas de seguridad y defensa y economía internacional. Ha dirigido más de 20 proyectos de investigación nacionales e internacionales y publicado en editoriales como Oxford University Press o Routledge.

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1. Win4Deap, version 2.1↩︎
2. Information sources: Uppsala Conflict Data Program, Sweden; Economist Intelligence Unit; Survey of Trends and Criminal Operations of the United Nations Criminal Justice System; International Center for Prison Studies at Kings College, UK; International Institute for Strategic Studies, Stockholm and Bonn International Center for Conversion↩︎
3. Albania, Belgium, Bulgaria, Croatia, Czech Republic, Denmark, Estonia, France, Germany, Greece, Hungary, Italy, Latvia, Lithuania, Montenegro, the Netherlands, Norway, Poland, Portugal, Romania, Slovak Republic, Slovenia, Spain, Turkey, United Kingdom, Canada and the United States.↩︎
4. VRS output orientation: Countries are asked to increase their output, with the same inputs.↩︎
5. Benchmarking technique: systematic and continuous process to evaluate the products, services and work processes of organizations that are recognized as representing best practices, with the purpose of making organizational improvements (Spendolini,1994)↩︎
6. Intensity variables. Country/ies to be taken as a reference to achieve greater efficiency.↩︎
7. However, the figure of 2% of GDP is arbitrary, but it supposes the need to tend towards higher efforts in country defense.↩︎

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