# Zipf’s Law and World Military Expenditures

• Paschalis Arvanitidis and Christos Kollias

## Abstract

The paper employs Zipf’s law to examine the distribution of military spending across countries in the world over the period 1988–2012. Military spending can cautiously be treated as a crude and distant proxy for military capacity and strength, and hence states’ hard power. The paper finds that the first-in-rank country (the USA) consistently spends more on the production of military capabilities than what is projected by Zipf’s law to correspond to a balanced international structure. This, tentatively interpreted, implies the use of military strength (and the concomitant costs for acquiring it) as a tool of hegemonic status consolidation, perhaps vis-à-vis other rising global players. In turn, the countries at the lower end of the rank, although they have overall increased their military outlays, seem to spend less on defence than this is anticipated by the law. This finding may be pointing to free-riding on the military strength of allies and other major powers.

Corresponding author: Christos Kollias, Department of Economics, University of Thessaly, 43 Korai Street, 38333, Volos, Greece, E-mail:

## Appendix

Table A1

Country rank of military expenditure over 1 bil US$(2011 constant US$ bil).

Rank199019952000200520102012
Average 1988–1990Average 1993–1995Average 1998–2000Average 2003–2005Average 2008–2010Average 2011–2012
1USA545.512USA436.817USA384.051USA547.018USA690.161USA690.122
2Russia/USSR335.410France67.097France62.079France65.466China. P.R.124.037China. P.R.151.879
3France70.450Japan55.872Japan59.148China. P.R.64.149Russia70.823Russia84.488
4Germany69.452Germany55.217Germany50.949Japan61.316France66.905France62.662
5UK58.603Russia54.284UK47.207UK57.611UK63.440UK60.040
6Japan46.697UK51.006Italy40.760Germany48.106Japan59.293Japan59.407
7Italy37.767Italy34.899China. P.R.33.798Russia45.847Germany48.749Saudi Ar.51.375
8Brazil32.591China. P.R.22.982Saudi Ar.26.670Italy43.407India46.569India48.945
9Saudi Ar.21.648Saudi Ar.20.456Russia26.468India33.033Saudi Ar.45.864Germany48.391
11China. P.R.19.078India19.202Brazil23.701Brazil24.856Brazil34.650Brazil36.842
13Spain15.854Korea. S.17.836Korea. S.19.434Australia20.656Australia26.167Australia26.083
16Israel14.158Spain14.119Israel14.033Israel16.564Turkey16.790Turkey17.798
17Netherlands13.768Israel13.988Spain13.915Spain15.108Israel15.709Israel15.350
18German DR11.590Taiwan13.020Netherlands11.393Iran12.321UAE14.566Spain13.088
19Turkey11.229Netherlands11.641Taiwan11.343Netherlands11.778Netherlands12.325Colombia10.877
20Taiwan10.691Sweden7.687Greece9.264Taiwan9.653Colombia10.950Netherlands10.870
21Czechoslovakia10.596Greece7.025UAE8.183UAE9.558Greece10.440Taiwan10.256
22Kuwait8.580Switzerland6.979Sweden7.903Greece8.777Taiwan10.037Poland9.680
23Belgium8.488Belgium6.341Singapore7.446Singapore8.257Iran9.999Singapore9.234
24Sweden8.293Kuwait6.023Iran7.147Colombia7.750Singapore9.269Algeria8.878
25Romania8.212Norway5.786Poland6.514Poland7.293Poland8.855Norway7.211
26Switzerland8.032Poland5.549Belgium6.099Sweden7.138Norway7.034Mexico6.788
27Poland7.673Thailand4.939Switzerland6.035Norway6.576Sweden6.426Greece6.841
28South Africa7.417Pakistan4.779Colombia5.897Pakistan5.921Pakistan6.076Pakistan6.589
29Greece7.274Singapore4.705Norway5.794Belgium5.591Belgium5.992Indonesia6.377
30Norway5.824Denmark4.661Denmark4.644Switzerland5.204Algeria5.672Sweden6.374
31Denmark4.785South Africa4.516Pakistan4.607Kuwait5.045Mexico5.637Iraq5.799
32Egypt4.742Colombia4.217Egypt4.250Egypt5.036Thailand5.369Oman5.390
33Pakistan4.111Egypt4.213Portugal4.238Portugal4.816Portugal5.087Kuwait5.669
34Bulgaria4.085Portugal4.051Kuwait4.071Denmark4.559Oman5.023Chile5.399
35Hungary3.876Iran4.028Mexico3.979Malaysia4.397Chile4.974Thailand5.427
36Portugal3.798Mexico3.640Austria3.555South Africa4.294Switzerland4.960Belgium5.448
37Thailand3.640Austria3.510Thailand3.496Oman4.276Kuwait4.795Switzerland5.055
38Argentina3.599Venezuela3.181Chile3.185Indonesia3.972Denmark4.748Malaysia4.735
39Austria3.550Croatia3.167Czech Rep.3.155Mexico3.940Malaysia4.685South Afr.4.691
40Singapore3.369Czech Rep.2.952South Afr.3.101Chile3.924Egypt4.602Ukraine4.394
41Yemen2.958Malaysia2.802Finland2.869Czech Rep.3.701Indonesia4.526Denmark4.599
42Finland2.742Finland2.739Angola2.705Algeria3.497South Africa4.469Egypt4.231
43Oman2.605Oman2.736Oman2.604Austria3.444Ukraine4.069Argentina4.204
44Colombia2.570Chile2.540Algeria2.571Finland3.356Angola3.758Portugal4.423
45Mexico2.531Romania2.496Venezuela2.483Thailand3.165Finland3.686Angola3.737
46Iran2.493Argentina2.445Malaysia2.373Venezuela2.824Austria3.586Finland3.804
47Chile2.438Morocco2.105Romania2.361Ukraine2.818Venezuela3.482Morocco3.463
48Philippines1.952Philippines2.070Argentina2.220Romania2.539Iraq3.469Austria3.411
49Morocco1.908Indonesia1.992Ukraine2.150Morocco2.467Argentina3.207Venezuela2.851
50New Zealand1.845Hungary1.938Philippines2.116Philippines2.340Morocco3.108Viet Nam3.042
51Malaysia1.631Angola1.743Indonesia1.952Syria2.329Czech Rep.2.905Azerbaijan3.079
52Indonesia1.616Algeria1.559Croatia1.942Hungary2.213Philippines2.606Libya2.800
53Viet Nam1.440Ukraine1.557Hungary1.843Iraq2.212Viet Nam2.603Philippines2.758
54Syria1.167N. Zealand1.493Morocco1.748Angola2.188Romania2.578Syria2.495
57Yemen1.339N. Zealand1.507Viet Nam1.517Qatar2.015Romania2.393
58Peru1.328Sri Lanka1.439Peru1.512Nigeria1.903Peru2.196
59Lebanon1.263Ireland1.334N. Zealand1.486Peru1.877Nigeria2.243
60Ireland1.125Serbia1.322Yemen1.480N. Zealand1.784Kazakhstan2.080
61Sri Lanka1.122Sudan1.187Ireland1.391Azerbaijan1.754N. Zealand1.801
62Bulgaria1.016Slovak Re.1.182Slovak Rep.1.372Sri Lanka1.734Lebanon1.625
63Lebanon1.145Lebanon1.280Hungary1.629Sri Lanka1.625
65Ethiopia1.057Serbia1.134Yemen1.526Jordan1.361
66Nigeria1.124Lebanon1.509Yemen1.204
67Bulgaria1.114Jordan1.454Ireland1.268
68Sri Lanka1.091Ireland1.424Hungary1.239
70Croatia1.065Libya1.338Croatia1.053
72Croatia1.163
73Serbia1.055
74Bulgaria1.030

*Source: SIPRI.

Table A2

Change of military expenditure (%) per country rank (truncated set).

Rank1990–19951995–20002000–20052005–20102010–2012
1–24.88–13.7429.7920.74–0.01
2–399.89–8.085.1747.2218.33
3–26.095.547.809.4216.17
4–25.78–8.3816.918.35–6.77
5–7.96–14.9918.069.19–5.66
68.45–25.1415.2718.870.19
7–8.22–3.2626.285.955.11
8–41.8113.8338.566.794.85
9–5.8322.7219.8727.985.22
10–2.7222.2712.7825.96–9.04
110.6518.984.6528.265.95
12–2.0811.4111.2321.535.35
1311.118.225.9221.06–0.33
147.716.45–3.7624.061.37
156.25–0.877.803.078.90
16–0.27–0.6215.281.355.66
171.57–0.527.893.83–2.34
1810.98–14.287.5315.42–11.30
193.54–2.623.704.44–13.32
20–39.0817.034.0311.85–0.74
21–50.8314.1414.398.44–1.80
22–22.9311.699.9612.55–3.69
23–33.8514.849.8217.42–8.29
24–37.6815.727.7916.38–4.40
25–41.9311.1710.6917.63–22.80
26–44.749.0114.56–1.47–3.64
27–55.3418.158.23–2.336.06
28–55.2118.960.402.557.78
29–54.5918.79–3.626.696.03
30–24.94–0.3810.778.2511.01
31–5.951.988.6810.502.79
32–12.440.7615.616.200.40
332.420.5712.005.3310.27
34–0.850.5010.709.256.95
353.77–1.239.5011.618.35
36–4.34–2.4017.2013.448.95
37–3.70–0.4018.2610.825.14
38–13.150.1319.8116.34–0.28
39–12.12–0.3619.9115.910.12
40–14.114.8020.9714.74–4.75
41–5.582.3622.4818.221.58
42–0.11–1.2822.6521.76–5.63
434.79–5.0824.3915.363.21
44–1.181.2323.3710.7115.03
45–1.38–0.5521.5514.141.37
46–1.98–3.0315.9821.265.71
47–15.8210.8416.2119.07–0.55
485.706.7612.5826.82–1.71
494.237.3512.8223.08–12.51
504.808.439.5624.71–2.19
516.3810.7116.2119.845.63
52–3.6319.7212.2315.096.92
537.5315.5216.6515.045.62
5421.8614.5920.1115.14–3.34
5516.1611.2312.835.39
5613.3510.469.9815.33
5711.110.6624.7215.81
587.694.8320.5513.34
595.3210.2320.8316.30
6014.9310.6617.0414.23
615.4214.6920.702.58
6214.1013.8520.87–6.76
6310.5521.46–0.30
6410.6422.11–2.20
656.7925.71–12.12
6625.49–25.38
6723.40–14.70
6823.41–14.93
6922.37–28.68
7020.43–27.07
Not increased1742636838
Not decreased37202232

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Published Online: 2015-12-23
Published in Print: 2016-1-1