# The Long-Run Dynamic of the Nexus between Military Strength and National Power: An Econometric Analysis

Authors: Emilio Casetti
Journal: Discrete Dynamics in Nature and Society
 (2008)

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## Abstract

A number of literatures suggest that military strength has been losing centrality and importance to nonmilitary factors of national power. In this paper, logistic regressions and data from the Correlates of War (COW) project are used to investigate whether over the 1820_2000 time horizon, for the great powers and their proximate contenders, the importance of military capabilities to national power has declined vis-_-vis that of economic capabilities. Estimation was carried out using generalized estimating equations (GEEs). The overall picture that emerges from the analysis is that of a transition in progress from a systemic state in which military capabilities were the dominant determinants of national power to a state in which economic capabilities will become the dominant ones. The analysis is concerned with
long-run trends, and its results are not necessarily applicable to specific countries and circumstances.


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## Body

## 1. Introduction

A
substantial literature suggests that over the past two centuries the
comparative contribution of military capabilities to national power has
declined. However, there are also voices supporting the view that military
power has been and is the quintessential determinant of power upon which a
country's standing in the international system depends. This paper presents an
econometric analysis of the “decreasing comparative importance of military
capabilities” thesis. Specifically, it investigates whether over the 1820–2000 time
horizon, for the great powers and their proximate contenders, the importance of
military capabilities to national power has declined vis-à-vis that of economic
capabilities.The
results presented in this paper show that in fact early on realized military
capabilities were by far the most important determinants of national power, and
that their comparative importance vis-à-vis economic capabilities greatly
decreased over time. The overall picture that emerges is that of a
transition from a state of affairs in which military capabilities were the
dominant determinants of national power to one in which economic capabilities
may become dominant. Today’s international system is near the midpoint of this
transition: the military capabilities are still twice as important as the
economic ones, but are slowly moving toward parity.This paper is intended as a
contribution to assessing the comparative validity of contrasting views on the
importance of military capabilities, and to evolving realistic world views that
neither overestimate nor underestimate the role of military strength to a
country's security and international influence. Realistic views about the
declining importance of military capabilities constitute an important
background to the guns-versus-butter type of debates. To be sure, the decisions
about the military capabilities a country needs depend upon a myriad of
specifics. Yet, the historical decline in the importance of military
capabilities is very relevant to strategic decisions on the appropriate mix of
military and nonmilitary tools and policies.The methodology used in this paper
builds upon the literature that regards the perceptions of national power by “experts”
as indices of power. This literature focuses upon the specification and
estimation of relations between power rankings, dependent variable, and power
determinants, independent variables. Also, it shows that both observed and
predicted perceptions of power are closely correlated with the conventional
indices of national power obtained by combining indices of power determinants
on the basis of assumptions rather than by estimation.Here the power perceptions used are
in the form of a classification of the top countries in the international
system into major and minor powers. The binary variable implementing this
classification and the indices of power determinants employed to “explain” it
are from the Correlates of War (COW) project. The analyses consist of logistic
regressions carried out on an unbalanced time series of cross-sections.
Generalized estimating equations (GEEs) techniques are employed to address the
temporal autocorrelation in the data.This paper starts with a review of
the literature on the importance of military capabilities to national power.
The body of the paper is comprised of a methodology and an empirics sections.
In the methodology section, the mathematical models used are presented and
discussed, and the literatures on the indices of power are briefly reviewed. The empirics section
discusses the models’ estimation and its results. A conclusions section caps
the paper.


## 2. Literature

Let us review selected literature
threads concerning the historical changes in the importance of military
strength to national power. The two quotes that follow typify how both scholars
and the public viewed the importance of military capabilities in the pre WW2
era. In a textbook popular in the 1930s Simonds and  Emeny [1,
pages 27–29] wrote:  “… the world of today is a lawless world …
But in a lawless world, force must be the ultimate means of pursuing policy,
and resort to force must mean war. … [H]owever states … vary in the degree to
which they can clothe their national policies with force. As a consequence,
only a few [states] will posses the force necessary to support their national
policies effectively, and these alone constitute the Great Powers. Thus, ours
is not only a world without enforceable international law but also a Great
Powers world. Such, too, it has always been during the centuries which have
seen the development of the modern states system.” Carr [2, page
109] outlined the linkage between
this worldview and the importance of military capabilities in the following
terms: “The supreme importance of the military instrument lies in the fact that
the ultima ratio of power in international relations is war. Every act of the
state, in its power aspect, is directed to war, not as a desirable weapon, but
as a weapon which it may require in the last resort to use.”Recently however, in explaining
the changes in the comparative importance of military capabilities,
Nye [3] wrote: “Traditionally,
the test of a great power was “strength for war.” War was the ultimate game in
which the cards of international politics were played and estimates of relative
power were proven. Over the centuries, as technology evolved, the sources of
power have shifted. Today, the foundations of power have been moving away from the
emphasis on military force.”The result of a recent
international poll shows that indeed the international public opinion today
believes that the foundations of national power have been moving away from an
emphasis on military force. In a 2002 public opinion poll commissioned by the
Chicago Council on Foreign Relations and the
German Marshall Fund [4,
page 23], 1000 men and women over 18
from each of six European countries were asked: “Which of the following do you
think is more important in determining a country’s overall power and influence
in the world—a country’s economic strength or its military
strength?” The respondents who choose “economic strength” and “military
strength” were respectively 81% and 15% in Great
Britain, 89% and 9% in France,
80% and 16% in Germany, 89%
and 7% in The Netherlands, 88% and 10% in Italy,
83% and 11% in Poland.
The average percentages for the six countries (calculated as the mean of
country averages weighted by population) indicated that 84% to 12% of the
Europeans polled selected economic strength over military strength as the most
important determinant of national power.
The 1097 USA respondents who answered the same question [5,
page 40] choose 66% to 27% economic
strength over military strength as the most important determinant of power.
These polls can be accessed at http://www.worldviews.org/.
Clearly, today there is a remarkable popular consensus across the Atlantic that military power is less important than
economic power.The historical circumstances,
collective experiences, and trends impacting the importance of the military and
economic capabilities on national power have been extensively discussed, for
example in Keohane and  Nye [6],
Nye [7, 8],
Mansbach [9], Rothgeb
[10, page 27 ff], and Snow  [11, 12]. A few key points culled from
these writings are sketched hereafter.After WW2, military strength
retained a major role in the international relations, however the limitations
of, and constraints upon military actions became by far more prominent than
previously. The limitations of military superiority became apparent in a number
of conflicts between more powerful and less powerful countries. The
decolonization pitted militarily weak movements of national liberation against
militarily strong colonial powers, and the latter lost on a grand scale.
Stalin’s inability to squelch Tito’s independence, and the loss of the US to Vietnam and of the Soviet Union to Afghanistan
also demonstrated that an overwhelming military superiority does not
necessarily lead to the defeat of national movements that are militarily weak.
Today and in the recent past, countries that are militarily strong may greatly
damage or obliterate each other, may easily defeat countries that are
militarily weaker, but will still experience a great deal of difficulty to
overcome national movements.A major constraint upon the use of
military force is represented by the reaction of the public opinion to the loss
of blood and treasure it entails. War has probably always generated a domestic
opposition that grows larger and more visible as its costs and casualties
become larger and more visible. However, the ferocity of this opposition and
the speed at which it can unfold are greater today than in the past, especially
in the developed countries.It has been argued that the
destructiveness of the atomic weapons places a major constraint upon the use of
military force. Throughout the cold war, the USA and USSR
did certainly retain a major commitment to military strength and preparedness,
but their conflicts never led to a WW3 that could produce “mutual assured destruction.”
The destructiveness of the atomic weapons possibly was the major factor that
prevented an unrestrained reliance on military force. It can be conjectured
that in the absence of countervailing atomic weapons, a WW3 would have been
much more likely.On the other hand, the
nonmilitary factors of national power have become increasingly important.
Before WW2, the actors in the international system were almost exclusively
states. After it, they included also an increasing number of international and
transnational organizations such as the UN and its agencies and the
multinational corporations. The interactions among nations in the context of
international and transnational organizations involve cooperation and conflicts
that are essentially nonmilitary. International trade, international capital
flows, and the movement of people across international boundaries for work,
study, or tourism have
increased greatly, resulting in cooperation and conflicts that are primarily
nonmilitary. Although national security is still exceedingly important, other
issues international in scope have been acquiring prominence. Issues such as
those involving the environment, epidemics, and the movement across boundaries
of illegal drugs produce cooperation and conflicts among countries that are
dealt with primarily by nonmilitary instruments. All these trends taken in the
aggregate suggest that over time and especially after the end of WW2, the
economic and political factors of national power increased in importance while
the military factor did not.An econometric study that
indirectly supports the “declining comparative importance of military power”
thesis is due to Stoll [13]. Stoll defines three world views
that he calls, respectively, Classical, Bipolarist, and Interdependent. Here
they are referred to by the acronyms CWV, BWV, and IWV. The CWV depicts the pre
WW2 international relations, and in it military power is the paramount
component of national power. In the BWV, national power depends upon a
combination of military and economic capabilities. In the IWV, national power
is multidimensional, and military strength is only an important but not major
component of it. The BWV and IWV emerged after WW2.Stoll carried out factor andt-test analyses on 1850,
1900, 1950, and 1980 datasets. One of his conclusions is that all the three
worldviews are applicable to the current (the 1980s) international realities.
Since the CWV depicts primarily the pre WW2 international relations and
military strength is paramount in it, Stoll’s conclusion that all three
worldviews apply to the post WW2 international relations implies that WW2
separates the era in which military strength is supremely important, from the
subsequent one in which is only one of multiple sources of national power.However, there are contemporary
voices arguing for the primacy of military strength. For instance, the authors
of a Rand Corporation's report [14, page 41] wrote:
“… military forces remain the
final arbiter of disputes in the ‘anarchic’ realm of international politics.
The country that has the most effective military instruments—understood as an
amalgam of technology, doctrine, training, and organization—can shape the
operations of the international system to its advantage: it can define and
enforce, as it were, ‘the rules of the game’.”The rationales for these views were
summarized in the following three points: “First,… countries will remain the most important units of
the international system in comparison to individuals, nongovernment actors,
and transnational organizations, at least where issues of  ‘high politics’—those issues
relating to order and governance—are concerned. In
this environment, countries will continue as the ultimate arbiters of their own
political choices, and while these choices will be limited by the actions and
capabilities of others, countries will nonetheless continue to employ power in
defense of their own interests. Second, … the most important manifestation of
power will continue to be military capability because it pertains to the domain
of survival and conditions the freedom of action enjoyed by entities in an
environment where there is no other overarching ideological or moral constraint
on national action. Third, where military capability is concerned, the ability
to conduct diverse conventional operations effectively will remain critical
because, even though nuclear weapons have become the ultima ratio regum in international politics, their relative
inefficacy in most situations other than those involving national survival
implies that their utility will continue to be significant but highly
restricted. The ability to conduct different and sophisticated forms of
conventional warfare will, therefore, remain the critical index of national
power …” (ibidem pages 42–3).The thesis that over the past two centuries the
comparative importance of military capabilities to national
power decreased vis-à-vis that of economic capabilities is
investigated in the next two sections that are, respectively, concerned with
methodology and empirics.


## 3. Methodology

The research reported in this paper aims
at testing whether over the 1820–2000 time horizon
and for the great powers and their proximate contenders, the comparative
importance to national power of military capabilities declined vis-à-vis that of the economic capabilities. The economic
capabilities are viewed as proxies for most determinants of national power
except realized military strength.The approach used involves the following: (a) an Initial model
relating a binary variable with values 1 and 0, respectively, for major and
minor powers, to indices of military and economic capabilities is specified and
estimated; (b) an Expanded model generated by redefining the parameters of the
Initial model into functions of time is specified and estimated; (c) a
parsimonious Final model is extracted from the Expanded model and estimated;
(d) the results of the analyses are used to test the “decline” hypotheses.Two subsections follow. In the first one,
the Initial and Expanded models are specified and discussed. The second
subsection briefly discusses strands of the literatures on the indices of national
power that constitute the foundation on which the investigation presented in
this paper is built.


### 3.1. Models

Let MP be a binary variable with values
one and zero, respectively, for major and minor powers. Denote the probability
that a given country at a given point in time is regarded as a major power bypr=pr(MP=1),
and its logit by P,
where (3.1)P=ln(pr(MP=1)1−pr(MP=1)),P and pr are rank-equivalent indices of national power.
To clarify, consider the following: (a) two indices of national power are
rank-equivalent when they produce identical power rankings of the same
countries; (b) two indices yield same rankings when one is a monotonically increasing
function of the other; (c) the pr variable is an index of national power since
countries that “are” more powerful will tend to have a greater probability to “be
regarded” as major powers; (d) since P is a monotonically increasing function
of pr;P and pr are both rank-equivalent perceptual indices of
national power. A discussion of indices of national power, perceptual, or otherwise
can be found in the next subsection.Define the Initial model(3.2)P=α0+αMM+αEE, that relates the index of national
power P to the indices of military and economic
capabilities M and E.The empirical variablesMP, M,
and E are described in the data subsection. However,
let us note here that M and E index distinct determinants of national power,
that the military capabilities, M,
are “realized,” not “potential” capabilities, and that the economic
capabilities, E,
are a proxy for most other factors of national power unrelated to realized
military strength.The parametersαM and αE of (3.2) indicate how much P changes in response to unit changes in M and E.
Consequently, they also indicate to what extent M or E influences P and thus define the “importance” or “effect”
of the military and of the economic capabilities to national power. Since
positive increments in M or E cannot affect negatively the national power,
these “importance parameters” αM and αE are restricted to be non-negative.The parameterα0 represents the net effect of factors of
national power that are not represented or proxied by M and E. This follows
directly from the fact that P=α0, if M=E=0 and/or if αM=αE=0. In other
words, if the military and economic capabilities equal zero, and/or the effects
of military and economic capabilities on national power are nil, the index of
national power P equals α0.
Consequently, P−α0 represents the portion of national power that
results from the capabilities M and E.  The ratio (3.3)RI=αMαE
denotes the comparative importance
of the military/economic capabilities to national power.A model suited to test for the temporal
decline in the comparative importance of military capabilities can be arrived
at by “expanding” the parameters of (3.2) into functions of time t [15]. Here this was accomplished by redefining
the parameters α0, αM, and αE into quadratic polynomials in time (3.4)α0=α00+α01t+α02t2,(3.5)αM=αM0+αM1t+αM2t2,(3.6)αE=αE0+αE1t+αE2t2.
These polynomials allow α0, αM, and αE to increase or decrease over time at accelerating
or decelerating rates, and are adequate to investigate the potential occurrence
and modalities of the parameters' long-run temporal change.Upon replacing the right-hand sides of
(3.4), (3.5),
and (3.6) for the parameters α0, αM, and αE in (3.2), the following “expanded” model is
produced: (3.7)P=α00+α01t+α02t2+αM0M+αM1Mt+αM2Mt2+αE0E+αE1Et+αE2Et2.
It should be noted that αM and αE defined by (3.5) and
(3.6) are also restricted to
be greater than or equal to zero throughout any time horizon to which the
Expanded model is applied.The comparative “importance” of the
military/economic capabilities,RI,
that correspond to the expanded model (3.7) is(3.8)RI=αM0+αM1t+αM2t2αE0+αE1t+αE2t2.
The notions that the comparative
importance of the military/economic capabilities to national power declined
over a given time horizon is validated if, over this time horizon, the estimated RI is a decreasing function of time, and
the two polynomials in RI are greater than zero.


### 3.2. Power Indices

The analyses in this paper are built upon the literature on the “perceptual
indices” of national power, and on the “estimated perceptual indices” of
national power obtained by regressing a perceptual measure of power versus
indices of power determinants. Let us place this literature in
perspective.Most indices of national power are either perceptual measures of power, or are
generated by regressing perceptual measures of power versus indices of power
determinants, or are obtained by combining indices of power determinants on the
basis of assumed weights.The indices of national power obtained by combining indices
of power determinants on the basis of assumed weights are the most common. A
prominent example of them is theCINC index [16–18]. CINC is arrived at by averaging
six indicators of factors of power, namely, by assigning a weight of 1/6 to
each indicator. Thus, CINC is based on assumed weights that define the
comparative “importance” or “effect” of each determinant of national power. In
addition to CINC, the best known indices of this type are the GDP
([19,  page 346], [20,
page 436], [21]), and the
indices by Cline [22, 23]
and German [24].A second literature strand is concerned with obtaining measures of
national power and then regressing them versus indices of power determinants.
Doran et al. [25], Alcock and Newcombe [26],
and Shinn [27] produced perceptual measures of power in
the form of rankings of countries in terms of their power as perceived by “experts.”
These measures were then regressed versus indices of economic development,
economic strength, and military strength to produce estimated perceptual
indices of national power.The case for perceptual measures of national power was effectively
made by Doran et al. [25] who wrote: “Instead of beginning
with a formal definition of power as previous theorists advocate, we have
followed Alcock and  Newcombe [26] and
Shinn Jr.  [27] in simply asking individual respondents
to use their own concept of power to rank nations. We have not forced a
definition of power upon our sample of respondents; rather, we have naively
assumed that most people have experienced power in their lives and that, based
on that experience, they would be able to rank states in terms of their own
intuitive appreciation of the power concept.” (page 432).  On the advantages of ranking countries by
perceived power they commented: “It is the actual perceptions rather than
idealized or so-called objective measures of
… [determinants of power] … that we hope will enable us to escape the
jungle of competing definitions and formulations … Our solution is neither to
delineate the power concept more finely nor to banish it altogether. Rather, a
high level of agreement about hierarchy within the international system can
exist, we argue, despite high disagreement regarding an operational definition
of the concept.” (page 433).There is empirical support to the notion that the perceptual
measures of power, the estimated perceptual indices of power, and theCINC types of power indices are all indices of national power.
Merritt and  Zinnes [28],
Taber [29], and Sullivan
[30] found that the perceptual measures of
power, the indices of power obtained by combining indices of power determinants
on the basis of assumed weights, and the estimated perceptual indices agree
significantly. Sullivan (1990 page 110) referred to this agreement as “convergent
validation,” and commented that “If different studies using different
indicators or manipulating them in different ways, produce fairly similar
rankings of nations' power, then there is probably some merit to those
measures. And they are more likely reflecting power levels that actually exist
in the real world.”This paper builds upon the literature on the indices obtained by
regressing a perceptual ranking of countries in terms of their power versus
indices of national power's determinants. Let us articulate why so.Ranking a group of countries in terms of power is tantamount to
classifying the countries into mutually exclusive classes ordered in terms of
power. However, rankings may differ in the number of classes (two or more) and
in the number of countries in each class (one or more). Thus, the
classification of many countries in two classes qualifies as a ranking. Hence,
the classification of countries into major and minor powers by a binary
variable taking the values of one/zero constitutes an empirical perceptual
measure of power in the tradition of the Alcock and Newcombe, Shinn, and Doran.
A logistic regression with such a binary dependent variable yields the
estimated logit of the probability that a country is a major power. Hence,
within this tradition also this estimated logit is a perceptual estimated index
of power.


## 3.1. Models

Let MP be a binary variable with values
one and zero, respectively, for major and minor powers. Denote the probability
that a given country at a given point in time is regarded as a major power bypr=pr(MP=1),
and its logit by P,
where (3.1)P=ln(pr(MP=1)1−pr(MP=1)),P and pr are rank-equivalent indices of national power.
To clarify, consider the following: (a) two indices of national power are
rank-equivalent when they produce identical power rankings of the same
countries; (b) two indices yield same rankings when one is a monotonically increasing
function of the other; (c) the pr variable is an index of national power since
countries that “are” more powerful will tend to have a greater probability to “be
regarded” as major powers; (d) since P is a monotonically increasing function
of pr;P and pr are both rank-equivalent perceptual indices of
national power. A discussion of indices of national power, perceptual, or otherwise
can be found in the next subsection.Define the Initial model(3.2)P=α0+αMM+αEE, that relates the index of national
power P to the indices of military and economic
capabilities M and E.The empirical variablesMP, M,
and E are described in the data subsection. However,
let us note here that M and E index distinct determinants of national power,
that the military capabilities, M,
are “realized,” not “potential” capabilities, and that the economic
capabilities, E,
are a proxy for most other factors of national power unrelated to realized
military strength.The parametersαM and αE of (3.2) indicate how much P changes in response to unit changes in M and E.
Consequently, they also indicate to what extent M or E influences P and thus define the “importance” or “effect”
of the military and of the economic capabilities to national power. Since
positive increments in M or E cannot affect negatively the national power,
these “importance parameters” αM and αE are restricted to be non-negative.The parameterα0 represents the net effect of factors of
national power that are not represented or proxied by M and E. This follows
directly from the fact that P=α0, if M=E=0 and/or if αM=αE=0. In other
words, if the military and economic capabilities equal zero, and/or the effects
of military and economic capabilities on national power are nil, the index of
national power P equals α0.
Consequently, P−α0 represents the portion of national power that
results from the capabilities M and E.  The ratio (3.3)RI=αMαE
denotes the comparative importance
of the military/economic capabilities to national power.A model suited to test for the temporal
decline in the comparative importance of military capabilities can be arrived
at by “expanding” the parameters of (3.2) into functions of time t [15]. Here this was accomplished by redefining
the parameters α0, αM, and αE into quadratic polynomials in time (3.4)α0=α00+α01t+α02t2,(3.5)αM=αM0+αM1t+αM2t2,(3.6)αE=αE0+αE1t+αE2t2.
These polynomials allow α0, αM, and αE to increase or decrease over time at accelerating
or decelerating rates, and are adequate to investigate the potential occurrence
and modalities of the parameters' long-run temporal change.Upon replacing the right-hand sides of
(3.4), (3.5),
and (3.6) for the parameters α0, αM, and αE in (3.2), the following “expanded” model is
produced: (3.7)P=α00+α01t+α02t2+αM0M+αM1Mt+αM2Mt2+αE0E+αE1Et+αE2Et2.
It should be noted that αM and αE defined by (3.5) and
(3.6) are also restricted to
be greater than or equal to zero throughout any time horizon to which the
Expanded model is applied.The comparative “importance” of the
military/economic capabilities,RI,
that correspond to the expanded model (3.7) is(3.8)RI=αM0+αM1t+αM2t2αE0+αE1t+αE2t2.
The notions that the comparative
importance of the military/economic capabilities to national power declined
over a given time horizon is validated if, over this time horizon, the estimated RI is a decreasing function of time, and
the two polynomials in RI are greater than zero.


## 3.2. Power Indices

The analyses in this paper are built upon the literature on the “perceptual
indices” of national power, and on the “estimated perceptual indices” of
national power obtained by regressing a perceptual measure of power versus
indices of power determinants. Let us place this literature in
perspective.Most indices of national power are either perceptual measures of power, or are
generated by regressing perceptual measures of power versus indices of power
determinants, or are obtained by combining indices of power determinants on the
basis of assumed weights.The indices of national power obtained by combining indices
of power determinants on the basis of assumed weights are the most common. A
prominent example of them is theCINC index [16–18]. CINC is arrived at by averaging
six indicators of factors of power, namely, by assigning a weight of 1/6 to
each indicator. Thus, CINC is based on assumed weights that define the
comparative “importance” or “effect” of each determinant of national power. In
addition to CINC, the best known indices of this type are the GDP
([19,  page 346], [20,
page 436], [21]), and the
indices by Cline [22, 23]
and German [24].A second literature strand is concerned with obtaining measures of
national power and then regressing them versus indices of power determinants.
Doran et al. [25], Alcock and Newcombe [26],
and Shinn [27] produced perceptual measures of power in
the form of rankings of countries in terms of their power as perceived by “experts.”
These measures were then regressed versus indices of economic development,
economic strength, and military strength to produce estimated perceptual
indices of national power.The case for perceptual measures of national power was effectively
made by Doran et al. [25] who wrote: “Instead of beginning
with a formal definition of power as previous theorists advocate, we have
followed Alcock and  Newcombe [26] and
Shinn Jr.  [27] in simply asking individual respondents
to use their own concept of power to rank nations. We have not forced a
definition of power upon our sample of respondents; rather, we have naively
assumed that most people have experienced power in their lives and that, based
on that experience, they would be able to rank states in terms of their own
intuitive appreciation of the power concept.” (page 432).  On the advantages of ranking countries by
perceived power they commented: “It is the actual perceptions rather than
idealized or so-called objective measures of
… [determinants of power] … that we hope will enable us to escape the
jungle of competing definitions and formulations … Our solution is neither to
delineate the power concept more finely nor to banish it altogether. Rather, a
high level of agreement about hierarchy within the international system can
exist, we argue, despite high disagreement regarding an operational definition
of the concept.” (page 433).There is empirical support to the notion that the perceptual
measures of power, the estimated perceptual indices of power, and theCINC types of power indices are all indices of national power.
Merritt and  Zinnes [28],
Taber [29], and Sullivan
[30] found that the perceptual measures of
power, the indices of power obtained by combining indices of power determinants
on the basis of assumed weights, and the estimated perceptual indices agree
significantly. Sullivan (1990 page 110) referred to this agreement as “convergent
validation,” and commented that “If different studies using different
indicators or manipulating them in different ways, produce fairly similar
rankings of nations' power, then there is probably some merit to those
measures. And they are more likely reflecting power levels that actually exist
in the real world.”This paper builds upon the literature on the indices obtained by
regressing a perceptual ranking of countries in terms of their power versus
indices of national power's determinants. Let us articulate why so.Ranking a group of countries in terms of power is tantamount to
classifying the countries into mutually exclusive classes ordered in terms of
power. However, rankings may differ in the number of classes (two or more) and
in the number of countries in each class (one or more). Thus, the
classification of many countries in two classes qualifies as a ranking. Hence,
the classification of countries into major and minor powers by a binary
variable taking the values of one/zero constitutes an empirical perceptual
measure of power in the tradition of the Alcock and Newcombe, Shinn, and Doran.
A logistic regression with such a binary dependent variable yields the
estimated logit of the probability that a country is a major power. Hence,
within this tradition also this estimated logit is a perceptual estimated index
of power.


## 4. Empirics

The analyses discussed in this section are based on a dataset
consisting of 291 observations and six variables. Each observation refers to a
country year duplet. The observations' identifiers are the variables “name” and
“year.”  The years are 1820, 1830,…,
2000. The other variables in the dataset are: a binary variable, “MP,” with
values one for the major powers and zero for the minor powers; a military
capability shares variable, “M”; an economic capability shares variable, “E”;
and a time variable, “t,” obtained by the transformation t=year−1800. The dataset
consists of an unbalanced time series of cross-sections. The source data, the
salient characteristics of the variables, their suitability, and the rationale
for the selection of the observations included in the study are discussed in
the next subsection.The analyses are concerned with the estimation of the
Initial, Expanded, and Final models, and with the investigation of theRI ratio calculated using the estimated Final model. This ratio allows testing the
hypothesis that the comparative importance to national power of
military/economic capabilities declined over time.The Initial, Expanded, and Final models
were estimated by logistic regressions [31–35] using generalized estimating equations
(GEEs) techniques [36–40]. The use of GEEs techniques
is necessitated by the data’s unbalanced panel structure and by the temporal
autocorrelation of the dependent variable MP. This autocorrelation should be
assumed since a country’s status as a major or minor power changes slowly over
time, and since here the data generating process consists in an iterated reevaluation
of each country’s current status as a major or minor power. The GEE technique
is well suited to estimate a logistic regression from unbalanced panel data
characterized by within-group
temporal autocorrelation.


### 4.1. Data

This subsection describes the “dataset” used in the analyses and
the research choices made to assemble it. The source data were downloaded fromhttp://www.cow2.la.psu.edu/. They can be also extracted from the EUGene database [41] downloadable from http://eugenesoftware.org/.
The “dataset” consists of 291 observations and six variables. Each observation
refers to a country year duplet. The observations' identifiers are the
variables  “name”  and  “year.” The years are 1820, 1830, …, 2000.
The other variables in the dataset are: a binary variable, “MP,” with
values one for the major powers and zero for the other countries in the sample;
a military capability shares variable, “M,” an economic capability
shares variable, “E”; and a time variable, “t,” obtained by the
transformation t=year−1800.
Let us remark again for emphasis that  “M”
and “E” are “shares” variables since they denote, respectively, the
ratios of military or economic capabilities of each country at a point in time
divided by the military or economic capabilities of all the countries in the
international system at that point in time. The dataset has a panel structure
and consists of an unbalanced time series of cross-sections.The source data
forMP were extracted from the COW2 “State System Membership file”
(major2002.csv). The major 2002.cvs file defines the dummy variable (here, MP)
with value one for the countries classified as “major powers.” The coding of MP produced by the COW project reflects the best judgment of generations of
scholars as to which countries play a major systemic role and project their
influence worldwide [13].The source data forM and E were extracted from the
COW2 file “National Material Capabilities” (NMC_3.0.csv). The articles of
record for the NMC dataset are Singer [16, 42]. The NMC file contains, for all the
states in the “International System” and for the 1816–2001 time
interval, the annual values of total population, urban population, iron and
steel production, energy consumption, military personnel, military
expenditures, and the year and country to which each observation refers.In order to obtain the indicesM, E, and CINC, (a) the raw indicators of material
capabilities were converted in yearly capability “shares” by dividing each
indicator’s value for a country and year by its aggregate value for the
international system for the year; (b) these shares were then aggregated into a
military capability shares index, M, an economic capability shares
index, E, and a demographic capability shares index, D, by
averaging, respectively, the military personnel and the military expenditures
shares, the iron and steel production and the energy consumption shares, and
the total population and the urban population shares; and (c) the Combined
Index of National Capabilities (CINC) was obtained by averaging M, E, and D.TheM and E variables index conceptually distinct
dimensions of national power. Specifically, E is an index of economic
strength, and a proxy for most nonmilitary determinants of national power. M is an index of “realized military strength,” that is virtually identical to
what Knorr in “The War Potential of Nations” calls the ready military
strength of a nation. He writes: “Mobilized manpower, munitions supplies,
and such establishments as army camps, airfields, and naval bases make up the
ready military strength of a nation.”
Knorr [43, page 19].The dataset used in this paper was obtained from the source data
in four steps. First, the observations for the years 1820, 1830,…, 2000 were
extracted from the source data. Second, for each of these years, the
observations with a rank higher than 20 on the CINC index were dropped.
Third, the observations with missing or zero values on M or E were dropped. Fourth, for each of the extant countries, the sequences of
temporally contiguous observations made of two or fewer observations were
dropped.The rationale for selecting observations with a 10 years spacing
is that the dependent variableMP changes over time very slowly since
countries tend to
persist in the major or minor power status for very long periods. This implies
that MP tends to possess a high temporal autocorrelation. Since,
everything else being equal, temporal autocorrelation tends to be smaller for
measurements taken at points in time more distant from each other, it can be
presumed that measurements at 10-year intervals are less autocorrelated than
measurements taken at one year intervals. This research decision follows the lead of
Kugler and Arbetman [44, page 49 ff] who in a study of national capabilities
used data at 10 year intervals since “national capabilities change at a
relatively slow pace” (page 55).The decision to select observations for the great powers and their
proximate contenders is based on the stated objective of this study, which is
to investigate whether the comparative importance of the military versus the
economic components of national power tended to decline over the 1800–2000 interval and
for the countries at the top of the power hierarchy. The rationale for this
choice rests on the hierarchical nature of the international system, in which
most power as well as most of the ability to project power at great distances
are concentrated at the top. Therefore, the decreasing comparative importance
of military capabilities is of special consequence if it occurs at the top of
the power hierarchy, where the “rules of the game” in the international system
are set. Selecting for each cross-section the top 20 countries on theCINC index is an arbitrary but plausible operational rule to select the top of the
power hierarchy.The decision to use theCINC index to select the top 20
countries was inspired by the finding that all the major indices of national
power in the literature tend to produce very similar power rankings, especially
so as regards to the
countries at the top ranks [28–30]. If this is the case, an index as
commonly used as CINC can be expected to be well suited to implement
this selection.


### 4.2. Analyses

The Initial model defined by (3.2) is
estimated under the assumption that its parameters did not change over the 1820–2000 time
horizon. The estimation results in column 1 of Table 1 suggest that the
military and economic capabilities contributed to national power to a very
different extent. In fact, their ratio RI=aM/aE=9.994 means that, in the average, during the 1820–2000 horizon,
military capability was ten times more important to national power than
economic capability.Table 1
GEEs estimates.
(1) Initial model(2) Expanded model(3) Final modelM6.74e+012.10e+027.12e+01(2.17)*(0.89)(2.18)*E6.74e+001.25e+01—(1.03)(0.18)t—1.26e−01—(1.27)t2—−5.12e−04—(1.29)Mt—−2.71e+00—(0.60)Et—−2.88e−01—(0.23)Mt2—1.21e−02—(0.66)Et2—2.09e−038.11e−04(0.40)(2.31)*Const−3.37e+00−1.08e+01−3.72e+00(4.47)**(2.05)*(4.36)**#obs291291291z
statistics in parentheses;
*Significant at 5%; **Significant at
1%.The estimate of the Expanded model
defined by (3.7) is shown in Table 1, column 2. A Wald test was carried out in
order to determine whether the block of the six expansion parameters in (3.7)
adds significantly to the
explanatory power of the Initial model. The test was significant at better than
the 1% level, indicating that the expansion of α0, αM, and αE with respect to time was warranted. However,
none of the coefficients
of the six expansion variables is significant and the collinearity diagnostics
CN and Max(VIF) reported in Table 4, column 2, indicate a strong degrading
collinearity.Let us discuss next the approach
used to extract from the overparametrized Expanded model a parsimonious Final model.
The approach does not presuppose that either the Expanded or the Final models
are “true” models. Today many scholars are in sympathy with this line of
thinking. To exemplify, consider a couple of quotes: Kennedy
[45, page 73] wrote “It is now generally
acknowledged that econometric models are ‘false’ and that there is no hope, or
pretense, that through them ‘truth’ will be found.
“Feldstein [46,  page 829] remarked” … in practice
all econometric specifications are necessarily ‘false’ models … The applied
econometrician, like the theorist, soon discovers from experience that a useful
model is not one that is ‘true’ or ‘realistic,’ but one that is parsimonious,
plausible and informative.”The Final model is arrived at
by removing some of the variables that appear in the Expanded model. The
rationale for retaining in a model only a parsimonious number of variables has
been articulated as follows by
Hosmer Jr.   and  Lemeshow [34,
pages 82-83]: “The
traditional approach to statistical model building involves seeking the most
parsimonious model that still explains the data. The rationale for minimizing
the variables in the model is that the resultant model is more likely to be
numerically stable … The more variables included in a model, the greater the
estimated standard errors become, and the more dependent the model becomes on
the observed data. Recently there has been a move … to include all
scientifically relevant variables in the model, irrespective of their
contribution to the model. … The major problem with this approach is that the
model may be overfitted and produce numerically unstable estimates. Overfitting
is typically characterized by unrealistically large estimated coefficients
and/or estimated standard errors.”The model selection approach used
here is inspired by Hendry’s  “General to
Specific” methodology ([47, 48], [49, Chapter 20],
[50], [51,
pages 58–83], [52]). Specifically, the approach used
starts with a heuristic iterated estimation of the Initial model over a
sequence of overlapping intervals spanning the 1820–2000 time
horizon. The parameter sequences thus obtained show which parameters of the
Initial model changed over time how much, and therefore suggest which blocks of
parameters should be tested for significance.
These suggestions lead to iterated Wald tests followed by the sequential
elimination of blocks of nonsignificant variables. The Final model arrived at
by this process is then analyzed for congruence with the hypothesized long-term
change in the comparative importance of the military and economic capabilities.The moving windows analyses were
carried out by estimating the initial model by logistic GEE regressions over
the nine overlapping intervals 1820–1920, 1830–1930,…, 1900–2000. Wide
overlapping intervals (“windows”) were selected in order to obtain parameter
traces reflecting primarily long-run trends. The three time sequences of
estimated αM, αE, and α0 obtained were subsequently converted into the
dimensionless indices iaM, iaE,
and ia0 by dividing each parameter sequence by its
first value. These dimensionless and comparable indices can suggest whether and
in which manner the parameters of the Initial model tend to change in the long
run. The indices are given in Table 3. Each line in the
table corresponds to a
logistic GEE regression over a time interval with end points year0 and year1,
and shows the iaM, iaE,
and ia0 indices computed from estimated regression parameters.
The table suggests that over time, αE increased substantially and at an accelerating
rate, while αM and α0 remained quasiconstant.In order to quantify the extent of
these indices’ variation over time, their coefficients of variationCV(iaM), CV(iaE),
and CV(ia0) were calculated by dividing their standard
deviations by their means. These CVs
are dimensionless measures of variation and allow to compare the temporal
variation of iaM, iaE,
and ia0.
Their values are, respectively, 0.161, 1.049, and 0.095.Clearly, the variation ofiaM is only slightly greater than that of ia0,
and the variations of both iaM and ia0 are much smaller than that of iaE.
This implies that the expansion terms associated with α0 (namely, t and t2) are less likely to be significant than those
associated with αM (namely, Mt and Mt2) which in turn are less likely to be
significant than those associated with αE (namely, Et and Et2). These results suggest to test for
significance as a group, and if appropriate, to remove first the expansion
terms associated with the parameter with the smallest CV, α0,
and subsequently the ones associated with αM,
that have the next smallest CV.The sequence of steps that produce the Final model
is documented in Table4. The table summarizes the collinearity diagnostics and
Wald tests that justify these steps. The columns in the table correspond to the
Initial, Expanded, and Final models plus the two intermediate models referred
to as Temp1 and Temp2. In the body of the table, we can distinguish three
segments separated by rows of blanks. In the first segment, we find vertical
sequences of the symbols “×” and “—” indicating, respectively, whether a given
variable in the left stub is included in a given model. A second “×” in the columns
corresponding to the Expanded, Temp1, and Temp2 models identifies the variables
tested for significance as a block by Wald tests. The collinearity diagnostics
CN, that stands for condition number, and Max(VIF), that stands for maximum variance
inflation factor are located in the second segment of Table 4. The results of
the Wald tests are shown in the third segment.The CN and VIF entries document the
possible occurrence of “harmful collinearity.”
Following the guidelines in Kennedy [53, page 213],
in Belsley et al.  [54], and in Belsley et al.
[55, Chapter 3], harmful collinearity is
signaled by a CN > 30 and/or by a VIF > 10. Clearly the collinearity in the
Expanded model is intolerably high.In keeping with the first
suggestion emanating from the moving window regressions, a Wald test of the
null hypothesis that the parameters of the terms t andt2 in the Expanded model are equal to zero was
carried out. The test yielded a chi2 = 1.69 and a p>chi2=0.43, meaning that
the null hypothesis α01=α02=0 cannot be rejected. This result justifies
dropping the t and t2 variables to produce
the Temp1 model.Upon estimation, Temp1 showed a
collinearity lower than that in the Expanded model but still very high. To
implement the second suggestion from the moving window regressions, a Wald test
of the null hypothesis that the parameters ofMt and Mt2 in Temp1 are equal to zero was carried out. The test yielded a chi2 = 0.13 and a
p>chi2=0.93   indicating that the null hypothesis αM1=αM2=0 cannot be rejected. This result justifies
dropping Mt and Mt2 from Temp1, thus
producing the Temp2 model.Moving from the Expanded, to Temp1, to Temp2
models the collinearity declines, as shown by the decrease of the CNs from 63.3
to 46.8 to 22.8, and by the decrease of Max(VIF) from 159.6 to 117.2 to 62.0.
Yet, the collinearity in the Temp2 model is still too high since its Max(VIF)
of 62 is still much larger than the VIF = 10 threshold. Some relevant clues from
the literature provide an avenue for improving upon the Temp2 model.TheiaE trace in column 4 of
Table 3 shows that the
importance of the economic capabilities to national growth, αE,
grew at accelerating rates over the 1800–2000 time
horizon. The term in Temp2 that reflects this accelerated growth is αE2Et2.  The parameters αE0 in the αE0E term and αE1 in the αE1Et term denote, respectively, the importance of
economic capabilities and the rate of growth of such importance at time zero.
The literature reflects a consensus to the effect that military capabilities
were by far the most important determinant of power for centuries until
sometime after 1800. Consequently, during this time the direct contribution of
the economic capabilities to national power was small. And since this state of
affairs lasted centuries it follows that at the beginning of the nineteenth
century the rate of growth of the economic capabilities’ importance was also
small. This line of reasoning suggests that both the parameters αE0 and αE1 are approximately zero.  A Wald test of the null hypothesis that in
Temp2 these parameters are not significantly different from zero yielded a
chi2 =  0.40 and a p>chi2=0.82. This means that the null hypothesis αE0=αE1=0 cannot be rejected, so that it is warranted to
drop E and Et thus producing the Final model.The estimate of the
Final model (see
Table1 column 3) shows that all its coefficients are
significant. Also, the CN and Max(VIF) of the Final model are, respectively,
2.5 and 1.22 (see Table 4) that is well below the harmful collinearity
thresholds. These results tell us that the Final model provides a parsimonious
depiction of the long-run trends investigated in this study.In a capsule, the approach used to
extract a parsimonious Final model from the overparametrized Expanded model
involved the following: (a) the Initial model was estimated over a sequence of
overlapping intervals spanning the 1820–2000 time
horizon; (b) the temporal sequence of parameters thus obtained produced “suggestions”
as to which parameters of the Initial model changed over time how much; (c)
these suggestions plus others were translated into the sequential testing and
elimination of blocks of the Expanded model’s variables that produced the Final
model.The estimated Final model
(see Table1 column 3) shows that all the coefficients in it are significant
and the collinearity diagnostics in Table 4 are well below the harmful
collinearity thresholds. Since all the estimated parameters of the Final model
are statistically significant, and since the estimated αM(t) and αE(t) are greater than zero over the 1820–2000 time horizon,
it is safe to conclude that the ratio RI based on them portrays the estimated temporal
change in the comparative importance of the military and economic capabilities
over the 1820–2000 time
horizon.Equation (4.1) shows
the estimated ratio RI based on the Final model’s estimated
parameters, (4.1)RI=71.18519.0008114t2.
Clearly RI is a decreasing function of time, and this
supports the thesis that, for the countries at the top of the power hierarchy,
and over the 1820–2000 time
interval, the comparative importance of the military/economic capabilities to
national power did decline.Table2 shows the estimated
change of RI over 1820–2000, and its
projected change over 2000–2100. The table
shows that RI declined much more quickly in the earlier than
in the later portion of the estimation horizon. Specifically, it declined from
219 to 8.8 between 1820 and 1900, and from 8.8 to 2.2 between 1900 and 2000.
Over the 2000–2100 forecast
horizon, RI is projected to decline from 2.2 to about 1.0.
Also, (4.1) shows that RI approaches zero as t grows large.Table 2
Temporal change
in the importance of  the military and economic capabilities
to national
power.
YearaM(t)aE(t)R(t)182071.2.325219184071.21.354.8186071.22.9224.4188071.25.1913.7190071.28.118.77192071.211.76.09194071.215.94.48196071.220.83.43198071.226.32.71200071.232.52.19292071.239.31.81294071.246.71.52296071.254.81.30298071.263.61.12210071.273.00.97aM(t)
and aE(t) = importance of M and E,   aM(t)/aE(t) = comparative importance   of M and E.Table 3
Parameter indices from  window regressions.
Time windowIndicest0t1iaMiaEia0182019201.001.001.00183019301.151.051.05184019400.813.820.85185019500.813.990.83186019600.854.220.86187019700.814.340.83188019800.814.910.82189019900.796.700.82190020000.6820.500.86Table 4
Collinearity diagnostics
and Wald tests. The columns in the table correspond to the Initial, Expanded, and Final models plus
the two intermediate models referred to as Temp1 and Temp2. In the body of the
table we can distinguish three segments separated by rows of blanks. In the first
segment we find vertical sequences of the symbols “×” and
“—” that indicate
whether a given variable in the left stub is included in a given model. A second “x”   in the columns corresponding to the Expanded, Temp1 and Temp2 models identifies
the variables tested for significance as a block by Wald tests. The collinearity
diagnostic CN, that stands for Condition Number, and Max(VIF), that stands for
Maximum Variance Inflation Factor are located in the second segment of Table 4 the results of the Wald tests are shown in the third segment.
(1) Initial model(2) Expanded model(3) Temp1 model(4) Temp2 model(5) Final modelM×××××E×××××—t—××———t2—××———Mt—×××——Et—××××—Mt2—×××——Et2—××××Const×××××CN2.4563.3046.7921.772.46Max(VIF)1.22159.59117.1662.021.22d.o.f—222—chi2—1.690.130.40—p>chi2—.4294.9390.8185—


## 4.1. Data

This subsection describes the “dataset” used in the analyses and
the research choices made to assemble it. The source data were downloaded fromhttp://www.cow2.la.psu.edu/. They can be also extracted from the EUGene database [41] downloadable from http://eugenesoftware.org/.
The “dataset” consists of 291 observations and six variables. Each observation
refers to a country year duplet. The observations' identifiers are the
variables  “name”  and  “year.” The years are 1820, 1830, …, 2000.
The other variables in the dataset are: a binary variable, “MP,” with
values one for the major powers and zero for the other countries in the sample;
a military capability shares variable, “M,” an economic capability
shares variable, “E”; and a time variable, “t,” obtained by the
transformation t=year−1800.
Let us remark again for emphasis that  “M”
and “E” are “shares” variables since they denote, respectively, the
ratios of military or economic capabilities of each country at a point in time
divided by the military or economic capabilities of all the countries in the
international system at that point in time. The dataset has a panel structure
and consists of an unbalanced time series of cross-sections.The source data
forMP were extracted from the COW2 “State System Membership file”
(major2002.csv). The major 2002.cvs file defines the dummy variable (here, MP)
with value one for the countries classified as “major powers.” The coding of MP produced by the COW project reflects the best judgment of generations of
scholars as to which countries play a major systemic role and project their
influence worldwide [13].The source data forM and E were extracted from the
COW2 file “National Material Capabilities” (NMC_3.0.csv). The articles of
record for the NMC dataset are Singer [16, 42]. The NMC file contains, for all the
states in the “International System” and for the 1816–2001 time
interval, the annual values of total population, urban population, iron and
steel production, energy consumption, military personnel, military
expenditures, and the year and country to which each observation refers.In order to obtain the indicesM, E, and CINC, (a) the raw indicators of material
capabilities were converted in yearly capability “shares” by dividing each
indicator’s value for a country and year by its aggregate value for the
international system for the year; (b) these shares were then aggregated into a
military capability shares index, M, an economic capability shares
index, E, and a demographic capability shares index, D, by
averaging, respectively, the military personnel and the military expenditures
shares, the iron and steel production and the energy consumption shares, and
the total population and the urban population shares; and (c) the Combined
Index of National Capabilities (CINC) was obtained by averaging M, E, and D.TheM and E variables index conceptually distinct
dimensions of national power. Specifically, E is an index of economic
strength, and a proxy for most nonmilitary determinants of national power. M is an index of “realized military strength,” that is virtually identical to
what Knorr in “The War Potential of Nations” calls the ready military
strength of a nation. He writes: “Mobilized manpower, munitions supplies,
and such establishments as army camps, airfields, and naval bases make up the
ready military strength of a nation.”
Knorr [43, page 19].The dataset used in this paper was obtained from the source data
in four steps. First, the observations for the years 1820, 1830,…, 2000 were
extracted from the source data. Second, for each of these years, the
observations with a rank higher than 20 on the CINC index were dropped.
Third, the observations with missing or zero values on M or E were dropped. Fourth, for each of the extant countries, the sequences of
temporally contiguous observations made of two or fewer observations were
dropped.The rationale for selecting observations with a 10 years spacing
is that the dependent variableMP changes over time very slowly since
countries tend to
persist in the major or minor power status for very long periods. This implies
that MP tends to possess a high temporal autocorrelation. Since,
everything else being equal, temporal autocorrelation tends to be smaller for
measurements taken at points in time more distant from each other, it can be
presumed that measurements at 10-year intervals are less autocorrelated than
measurements taken at one year intervals. This research decision follows the lead of
Kugler and Arbetman [44, page 49 ff] who in a study of national capabilities
used data at 10 year intervals since “national capabilities change at a
relatively slow pace” (page 55).The decision to select observations for the great powers and their
proximate contenders is based on the stated objective of this study, which is
to investigate whether the comparative importance of the military versus the
economic components of national power tended to decline over the 1800–2000 interval and
for the countries at the top of the power hierarchy. The rationale for this
choice rests on the hierarchical nature of the international system, in which
most power as well as most of the ability to project power at great distances
are concentrated at the top. Therefore, the decreasing comparative importance
of military capabilities is of special consequence if it occurs at the top of
the power hierarchy, where the “rules of the game” in the international system
are set. Selecting for each cross-section the top 20 countries on theCINC index is an arbitrary but plausible operational rule to select the top of the
power hierarchy.The decision to use theCINC index to select the top 20
countries was inspired by the finding that all the major indices of national
power in the literature tend to produce very similar power rankings, especially
so as regards to the
countries at the top ranks [28–30]. If this is the case, an index as
commonly used as CINC can be expected to be well suited to implement
this selection.


## 4.2. Analyses

The Initial model defined by (3.2) is
estimated under the assumption that its parameters did not change over the 1820–2000 time
horizon. The estimation results in column 1 of Table 1 suggest that the
military and economic capabilities contributed to national power to a very
different extent. In fact, their ratio RI=aM/aE=9.994 means that, in the average, during the 1820–2000 horizon,
military capability was ten times more important to national power than
economic capability.Table 1
GEEs estimates.
(1) Initial model(2) Expanded model(3) Final modelM6.74e+012.10e+027.12e+01(2.17)*(0.89)(2.18)*E6.74e+001.25e+01—(1.03)(0.18)t—1.26e−01—(1.27)t2—−5.12e−04—(1.29)Mt—−2.71e+00—(0.60)Et—−2.88e−01—(0.23)Mt2—1.21e−02—(0.66)Et2—2.09e−038.11e−04(0.40)(2.31)*Const−3.37e+00−1.08e+01−3.72e+00(4.47)**(2.05)*(4.36)**#obs291291291z
statistics in parentheses;
*Significant at 5%; **Significant at
1%.The estimate of the Expanded model
defined by (3.7) is shown in Table 1, column 2. A Wald test was carried out in
order to determine whether the block of the six expansion parameters in (3.7)
adds significantly to the
explanatory power of the Initial model. The test was significant at better than
the 1% level, indicating that the expansion of α0, αM, and αE with respect to time was warranted. However,
none of the coefficients
of the six expansion variables is significant and the collinearity diagnostics
CN and Max(VIF) reported in Table 4, column 2, indicate a strong degrading
collinearity.Let us discuss next the approach
used to extract from the overparametrized Expanded model a parsimonious Final model.
The approach does not presuppose that either the Expanded or the Final models
are “true” models. Today many scholars are in sympathy with this line of
thinking. To exemplify, consider a couple of quotes: Kennedy
[45, page 73] wrote “It is now generally
acknowledged that econometric models are ‘false’ and that there is no hope, or
pretense, that through them ‘truth’ will be found.
“Feldstein [46,  page 829] remarked” … in practice
all econometric specifications are necessarily ‘false’ models … The applied
econometrician, like the theorist, soon discovers from experience that a useful
model is not one that is ‘true’ or ‘realistic,’ but one that is parsimonious,
plausible and informative.”The Final model is arrived at
by removing some of the variables that appear in the Expanded model. The
rationale for retaining in a model only a parsimonious number of variables has
been articulated as follows by
Hosmer Jr.   and  Lemeshow [34,
pages 82-83]: “The
traditional approach to statistical model building involves seeking the most
parsimonious model that still explains the data. The rationale for minimizing
the variables in the model is that the resultant model is more likely to be
numerically stable … The more variables included in a model, the greater the
estimated standard errors become, and the more dependent the model becomes on
the observed data. Recently there has been a move … to include all
scientifically relevant variables in the model, irrespective of their
contribution to the model. … The major problem with this approach is that the
model may be overfitted and produce numerically unstable estimates. Overfitting
is typically characterized by unrealistically large estimated coefficients
and/or estimated standard errors.”The model selection approach used
here is inspired by Hendry’s  “General to
Specific” methodology ([47, 48], [49, Chapter 20],
[50], [51,
pages 58–83], [52]). Specifically, the approach used
starts with a heuristic iterated estimation of the Initial model over a
sequence of overlapping intervals spanning the 1820–2000 time
horizon. The parameter sequences thus obtained show which parameters of the
Initial model changed over time how much, and therefore suggest which blocks of
parameters should be tested for significance.
These suggestions lead to iterated Wald tests followed by the sequential
elimination of blocks of nonsignificant variables. The Final model arrived at
by this process is then analyzed for congruence with the hypothesized long-term
change in the comparative importance of the military and economic capabilities.The moving windows analyses were
carried out by estimating the initial model by logistic GEE regressions over
the nine overlapping intervals 1820–1920, 1830–1930,…, 1900–2000. Wide
overlapping intervals (“windows”) were selected in order to obtain parameter
traces reflecting primarily long-run trends. The three time sequences of
estimated αM, αE, and α0 obtained were subsequently converted into the
dimensionless indices iaM, iaE,
and ia0 by dividing each parameter sequence by its
first value. These dimensionless and comparable indices can suggest whether and
in which manner the parameters of the Initial model tend to change in the long
run. The indices are given in Table 3. Each line in the
table corresponds to a
logistic GEE regression over a time interval with end points year0 and year1,
and shows the iaM, iaE,
and ia0 indices computed from estimated regression parameters.
The table suggests that over time, αE increased substantially and at an accelerating
rate, while αM and α0 remained quasiconstant.In order to quantify the extent of
these indices’ variation over time, their coefficients of variationCV(iaM), CV(iaE),
and CV(ia0) were calculated by dividing their standard
deviations by their means. These CVs
are dimensionless measures of variation and allow to compare the temporal
variation of iaM, iaE,
and ia0.
Their values are, respectively, 0.161, 1.049, and 0.095.Clearly, the variation ofiaM is only slightly greater than that of ia0,
and the variations of both iaM and ia0 are much smaller than that of iaE.
This implies that the expansion terms associated with α0 (namely, t and t2) are less likely to be significant than those
associated with αM (namely, Mt and Mt2) which in turn are less likely to be
significant than those associated with αE (namely, Et and Et2). These results suggest to test for
significance as a group, and if appropriate, to remove first the expansion
terms associated with the parameter with the smallest CV, α0,
and subsequently the ones associated with αM,
that have the next smallest CV.The sequence of steps that produce the Final model
is documented in Table4. The table summarizes the collinearity diagnostics and
Wald tests that justify these steps. The columns in the table correspond to the
Initial, Expanded, and Final models plus the two intermediate models referred
to as Temp1 and Temp2. In the body of the table, we can distinguish three
segments separated by rows of blanks. In the first segment, we find vertical
sequences of the symbols “×” and “—” indicating, respectively, whether a given
variable in the left stub is included in a given model. A second “×” in the columns
corresponding to the Expanded, Temp1, and Temp2 models identifies the variables
tested for significance as a block by Wald tests. The collinearity diagnostics
CN, that stands for condition number, and Max(VIF), that stands for maximum variance
inflation factor are located in the second segment of Table 4. The results of
the Wald tests are shown in the third segment.The CN and VIF entries document the
possible occurrence of “harmful collinearity.”
Following the guidelines in Kennedy [53, page 213],
in Belsley et al.  [54], and in Belsley et al.
[55, Chapter 3], harmful collinearity is
signaled by a CN > 30 and/or by a VIF > 10. Clearly the collinearity in the
Expanded model is intolerably high.In keeping with the first
suggestion emanating from the moving window regressions, a Wald test of the
null hypothesis that the parameters of the terms t andt2 in the Expanded model are equal to zero was
carried out. The test yielded a chi2 = 1.69 and a p>chi2=0.43, meaning that
the null hypothesis α01=α02=0 cannot be rejected. This result justifies
dropping the t and t2 variables to produce
the Temp1 model.Upon estimation, Temp1 showed a
collinearity lower than that in the Expanded model but still very high. To
implement the second suggestion from the moving window regressions, a Wald test
of the null hypothesis that the parameters ofMt and Mt2 in Temp1 are equal to zero was carried out. The test yielded a chi2 = 0.13 and a
p>chi2=0.93   indicating that the null hypothesis αM1=αM2=0 cannot be rejected. This result justifies
dropping Mt and Mt2 from Temp1, thus
producing the Temp2 model.Moving from the Expanded, to Temp1, to Temp2
models the collinearity declines, as shown by the decrease of the CNs from 63.3
to 46.8 to 22.8, and by the decrease of Max(VIF) from 159.6 to 117.2 to 62.0.
Yet, the collinearity in the Temp2 model is still too high since its Max(VIF)
of 62 is still much larger than the VIF = 10 threshold. Some relevant clues from
the literature provide an avenue for improving upon the Temp2 model.TheiaE trace in column 4 of
Table 3 shows that the
importance of the economic capabilities to national growth, αE,
grew at accelerating rates over the 1800–2000 time
horizon. The term in Temp2 that reflects this accelerated growth is αE2Et2.  The parameters αE0 in the αE0E term and αE1 in the αE1Et term denote, respectively, the importance of
economic capabilities and the rate of growth of such importance at time zero.
The literature reflects a consensus to the effect that military capabilities
were by far the most important determinant of power for centuries until
sometime after 1800. Consequently, during this time the direct contribution of
the economic capabilities to national power was small. And since this state of
affairs lasted centuries it follows that at the beginning of the nineteenth
century the rate of growth of the economic capabilities’ importance was also
small. This line of reasoning suggests that both the parameters αE0 and αE1 are approximately zero.  A Wald test of the null hypothesis that in
Temp2 these parameters are not significantly different from zero yielded a
chi2 =  0.40 and a p>chi2=0.82. This means that the null hypothesis αE0=αE1=0 cannot be rejected, so that it is warranted to
drop E and Et thus producing the Final model.The estimate of the
Final model (see
Table1 column 3) shows that all its coefficients are
significant. Also, the CN and Max(VIF) of the Final model are, respectively,
2.5 and 1.22 (see Table 4) that is well below the harmful collinearity
thresholds. These results tell us that the Final model provides a parsimonious
depiction of the long-run trends investigated in this study.In a capsule, the approach used to
extract a parsimonious Final model from the overparametrized Expanded model
involved the following: (a) the Initial model was estimated over a sequence of
overlapping intervals spanning the 1820–2000 time
horizon; (b) the temporal sequence of parameters thus obtained produced “suggestions”
as to which parameters of the Initial model changed over time how much; (c)
these suggestions plus others were translated into the sequential testing and
elimination of blocks of the Expanded model’s variables that produced the Final
model.The estimated Final model
(see Table1 column 3) shows that all the coefficients in it are significant
and the collinearity diagnostics in Table 4 are well below the harmful
collinearity thresholds. Since all the estimated parameters of the Final model
are statistically significant, and since the estimated αM(t) and αE(t) are greater than zero over the 1820–2000 time horizon,
it is safe to conclude that the ratio RI based on them portrays the estimated temporal
change in the comparative importance of the military and economic capabilities
over the 1820–2000 time
horizon.Equation (4.1) shows
the estimated ratio RI based on the Final model’s estimated
parameters, (4.1)RI=71.18519.0008114t2.
Clearly RI is a decreasing function of time, and this
supports the thesis that, for the countries at the top of the power hierarchy,
and over the 1820–2000 time
interval, the comparative importance of the military/economic capabilities to
national power did decline.Table2 shows the estimated
change of RI over 1820–2000, and its
projected change over 2000–2100. The table
shows that RI declined much more quickly in the earlier than
in the later portion of the estimation horizon. Specifically, it declined from
219 to 8.8 between 1820 and 1900, and from 8.8 to 2.2 between 1900 and 2000.
Over the 2000–2100 forecast
horizon, RI is projected to decline from 2.2 to about 1.0.
Also, (4.1) shows that RI approaches zero as t grows large.Table 2
Temporal change
in the importance of  the military and economic capabilities
to national
power.
YearaM(t)aE(t)R(t)182071.2.325219184071.21.354.8186071.22.9224.4188071.25.1913.7190071.28.118.77192071.211.76.09194071.215.94.48196071.220.83.43198071.226.32.71200071.232.52.19292071.239.31.81294071.246.71.52296071.254.81.30298071.263.61.12210071.273.00.97aM(t)
and aE(t) = importance of M and E,   aM(t)/aE(t) = comparative importance   of M and E.Table 3
Parameter indices from  window regressions.
Time windowIndicest0t1iaMiaEia0182019201.001.001.00183019301.151.051.05184019400.813.820.85185019500.813.990.83186019600.854.220.86187019700.814.340.83188019800.814.910.82189019900.796.700.82190020000.6820.500.86Table 4
Collinearity diagnostics
and Wald tests. The columns in the table correspond to the Initial, Expanded, and Final models plus
the two intermediate models referred to as Temp1 and Temp2. In the body of the
table we can distinguish three segments separated by rows of blanks. In the first
segment we find vertical sequences of the symbols “×” and
“—” that indicate
whether a given variable in the left stub is included in a given model. A second “x”   in the columns corresponding to the Expanded, Temp1 and Temp2 models identifies
the variables tested for significance as a block by Wald tests. The collinearity
diagnostic CN, that stands for Condition Number, and Max(VIF), that stands for
Maximum Variance Inflation Factor are located in the second segment of Table 4 the results of the Wald tests are shown in the third segment.
(1) Initial model(2) Expanded model(3) Temp1 model(4) Temp2 model(5) Final modelM×××××E×××××—t—××———t2—××———Mt—×××——Et—××××—Mt2—×××——Et2—××××Const×××××CN2.4563.3046.7921.772.46Max(VIF)1.22159.59117.1662.021.22d.o.f—222—chi2—1.690.130.40—p>chi2—.4294.9390.8185—


## 5. Conclusions

The picture emerging from the results of the analyses reported in this paper
is that the major powers and their proximate contenders are in the midst of a
transition from a past in which military strength was the dominant determinant
of national power, to a future in which economic strength will replace it in
this capacity. Two caveats, though, need to be seriously considered. First,
this picture of a transition in the importance of military power involves an
extrapolation beyond the time horizon spanned by the analyses, and any
extrapolation has to be considered cautiously and questioned. The second caveat
is that since the analyses in the study are concerned with long-run trends,
their results are not necessarily applicable to specific countries and
circumstances. However, they can still provide a useful background to the
ongoing debates about the importance and role of military capabilities in
today's world.The comparative importance of
military strength figures prominently in the worldviews that attempt to explain
and shape the international relations. This is especially true with respect to
the realist and the liberal worldviews. Let us briefly relate this study to the
debates about the realist and liberal perspectives.Realism and liberalism reflect
traditions of political and philosophical thought that span centuries and
encompass a number of variants [56–63]. However, the central tenets
present in all these variants reflect contrasting views on the role and
importance of military strength.The realism postulates that states
only are major actors in the international system, and that the structure of
the international system is “anarchic” since above the states there is not a “world
government” with laws, courts, and police that can adjudicate and enforce
solutions to international conflicts. In an anarchic world, the states depend
on military strength to pursue their objectives and for the defense of their
national interests. Even when nonmilitary policy tools prove successful, it is
the implicit threat represented by military strength that makes them effective.
Thus, in terms of a realist frame of reference, military strength is of
paramount importance, and the major powers are such because of their greater
military strength.The liberal perspective postulates
that the actors in the international system include international and
transnational organizations as well as states; that countries are bound to each
other by treaties, common interests, and common problems; that war is evitable
even in an anarchic system because of the interdependencies, interactions,
common interests among countries; and that the supranational organizations
provide opportunities and avenues for mediating conflicts and crises. Within a
liberal frame of reference, both the military and nonmilitary components of
national power are important.Realism
and liberalism can be regarded as perspectives that emphasize distinct facets
of the international realities. However, there are historical situations that
are best characterized in terms of a realist perspective, and others that are
best understood and explained in terms of a liberal perspective. The results of
this study support the notion that during the 1820–2000 time horizon,
the comparative validity of the two perspectives has shifted, and that the
happenings in, and structure of, the international system are best described
and explained by the realist perspective at the beginning of the horizon, while
the liberal perspective is to a greater extent applicable at the end of it.



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*Source: 286836-2008-09-15.xml*