ARMS
RACE MODELING
BREWT D. MAST
BALL STATE UNIVERSITY
THESIS ADVISOR: STANLEY KEIL
DEPARTMENT OF ECONOMICS
IN rARTIA_
FULF1_LM~NT
Oc
RE0UI~EMENTS
FOR ID 499-HONORS THESIS
THERE HAS BEEN MUCH WRITTEN IN THE ECONOMIC AND POLITICAL
THE UNITED STATES AND THE SDVIET UNION. THE PURPOSE OF THIS
THE S 1 5 W1~ L. UE T HREE -~ F 0 L Dill)
T D DEVE LOP ,e, \£j 0 Rt'{ 1 NG DEFIN I TID N 0 F
AN ARMS RACE WITH WHICH TO WORK WITH. 2) TO SURVEY THE LITERATURE
ARMS RACE 40DELING AND WHETHER OR NOT THERE IS AN ARMS
CONC:RNI~G
R,c,CE BETWEEN THE \),S,
EXIST, TO
,6.ND U,S.S,P.
:n
IF SUCH
~N
P.,PMS P,A,CE DOES
THE CAUSALITY THROUGH ECONOMETRIC MEANS AND
DErERMI~E
TO POINT OUT THE DIFFICULTv IN DOING SUCH :CONOMETRIC WORK.
DEFORE CONSIDERING AN ARMS RACE IT W1LL BE USEFUL TO
DEFINE IT. ,A,_BERT WOHlSTETTER (1974a: 4·) DEFINES AN .ARMS F:ACE !'l.S
;.:,
l!
~'1P,Y
COM PET 1 TlJ r~ TH~. T TAr; ESON p. N EX F-' LOS I \i E LI FED FITS 0 WNTH AT
FRUS.TRfI.T': THE OBJECTl\IES OF BOTH ':ONTESTP-,NTS,
TWO SENSES:
(1)
TO "f..CCE.LERATING
IT LEADS
II
" UNCC; NH: DLlED" 0 F: ;. L.II"H.. I 1'1 IT E: D" 0 F "U NBF: I DLED
EXPLOSIVE IN
(OR "EXPONENT1Al" OR
II
0 F: "r NFl NIT E") I N-
WAR, OR AT ANY RATE MAKES WAR MUCH MORE LIKELY."
THE MOST WIDELY USED ARMS RACE MODEL IS THE RICHARDSON
Dr
FFE~:ENTl
P...
EQU,c\T ION !'lDDEL.. 1 N THE CONTEXT OF ;'.RMS F:ACE BETI,..jEEN
TWO OPPONENTS, THE
RICHA~DSON
MODEL
CAN BE EXPRESSED BY A SYSTEM
OF TWO LINEAR DIFFERENTIAL EQUATIONS:
I
\
1 !\
(
L
~.
)
(h ! d t..
-
~',
dy/dt
-
1x
y
WHERE . , ,C..NO y A.RE,
'
•. a !~
.+-
9 0, a.
by
.;-
~1
~
(
.
1 b
RESPECTIVELY,
>0)
:> 0)
THE L.EVEL. 01= ,C.,Rf'lA:'lErHS >=OF:
-
CHA~GE
TIME RATE OF
AR~S
OF
EXPENDITJRES (AS A PROXY OF THE LEVEL
OF ARMAMENT BUILD-UP) IN EACH NATION IS DETERMINED BY THREE
THE 'FATIGUE'
CAPTURED BY THE PARAMETERS a AND t.
TER~.
INDICATING THE ECONOMIC
BURD~N
OF EACH NATION MA1NTAINING ITS OWN
ARMAMENT LEVEL: AND (C) THE 'GRIEVANCE' TERM, CAPTURED BY THE
CONSTANT TERMS 9
h, INDICATING THE LEVEL
~ND
O~
HOST!LITY OF ONE
NATION TOWARD3 ITS OpPONENT NATION, IN TYIS MODEL RICHARDSON
ASSUMED THAT THE CAUSES OF ARMS EXPENDITURES ARE LINEARLY
,\DDITlVE."
REVI EW OF U
·iEF:~,TUF:E
BEFORE TRYING TO CONSIDER AN ARMS RACE AND
ONE EXISTS ONE
THIN~
TO
'.1989:
~,NDERTON
~N
~RMS
347)
EMPIRICAL FIT. THE TEST
AND
THAT,
DR NOT
TRY TO DETERMINE AN APPROPRIATE MODEL. WE CAN
MUST
ASK WHAT WE
W~ETHER
OF COARSE,
R~CE
THE
~F
~ODEL
SHOULD ACCOMPLISH. ACCORDING
"WORTH DF ,6,N
AN
DEF'Ef~DS
ARMS
ON
t.,RMS Rl\CE MCiDEL
Dc!E~3
NOT
RACE MODEL IS ITS USEFULNESS
THE
USE
TO
WHICH
IT
IS PUT.
II
ARMS RACE MODELING MAY BE USEFUL IN THREE MAJOR WAYS,
,c.,CC~;RDING
-.
rr.::
~,NDERTC!n
(1939: 347}. FIRST THEY CAN "DESCRIBE AND
SUMMARIZE
THE
USEFUL. TO
BEnER "UNDERSTAND AND PREDICT" THE COMPLEXITY OF .ARMS
RACES.
T~lRD,
CO"lPi...EX
AR~S
REAL ITV
RACE
OF
AF:MS
RACES."
SECOND,
THEY
MODELING CAN BE USEFUL IF THEY HELP
C.AN
EE
.-
"PRESCRIBE A TREATMENT THAT WILL ACHIEVE A DESIRED END."
TO THE
(198t:;J: 347) t'1.A.NY MODELS OF AF:M3 Rp.CES POINT
AND:::'RTDi·'~
P.(CORDING TO
THAT
:C~CLUSIO~
EF~EC;TE:,
HiE NEGATIVE
N~TIONS
3HOULC PURSUE EFFORTS TO SUBSIDE
DF /l,RMS PACES.
"BEYOND
THIS, HOWEVEF;, MDST
ARMS RACE MODELS ARE NOT USED TO SHED INSIGHT INTO SPECIFIC
POLICIES FOR REDUCING THE COST
~ND
DANGER
D~
ARMS RACES. THE ARMS
RACE MODELERS THAl USE THEIR MODELS TO MAKE SPECIFIC POLICY
PRESCRIPTIONS
WORK,
RARE~Y
°RESJM~BL~
RELY
ON
RICHARDSON-TYPE MODELS IN THEIR
BECAUSE THEY ARE NOT USEFUL
INSTEAD, ANALVSTS USE ARMS RACE MODELS THAT FOCUS ON
GROS& BEHAVIOR AND STRATEGIES OF PARTIES
INVOLVED
IN ARMS RACES.
SPECIFIC ARM3 CONTROL POLICY RECOMMENDATIONS BASED ON THEIR
RICHARDSON MODELS
.\NDEPTON (1989: 348)
~1AKES
NDTE TH,Ll,T "DESCRIPTION.
SUMMARIZATION. UNDERSTANDING. PREDICTION, t..ND PRESCRIPTION" ARE
W~AT
AN ARMS
R~CE
ANALYST WOULD LlwE TO BE ABLE TO DO WHEN
STUDYING AN ARMS RASE. THERE ARE VARIOUS TYPES OF ARMS RACE
MODELING APPROACHES AVAILABLE TO THE ANALYST. RICHARDSON MODELS
HAVE A
COMPARtTIVE
~DVANTAGE
RACES. "THEY ARE A TOOL
PREDICTION,
IN DESCRIBING AND SUMMARIZING ARMS
OF FIRST CUT ",ACCORDING TO ANDERTON
R!CHA~DSON-TYPE
MODELS ARE
O~TEN
AT A COMPARATIvE
DISADVANTAGE RELATIVE TO MODELS THAT PERTAIN TO STRATEGIC
CONSIDERATIONS AND GROSS BEHAVIOR.
QUESTIONED THE APPLICABILITY OF RICHARDSON-TYPE iDIFFEHENTIAL
EQUATION) MDDELS IN ANALvZING ARMS RACES WHEN ARMS RACE MODELING
WAS IN ITS EARLY STAGES. THEIR ARGUMENT WAS THAT CLASSICAL
MATHEMATICS LACKED NECESSARY CONCEPTS FOR THE STUDY OF ARMS
F:ACES.
"IT IS NO riOl'.JDER TH~,T MUCi-i ~::[tNTEMF'DR!;RY PESEP,,R(:H IN
!NTERNIHJONp< CD~~FUCT HAS PEEi\j DIRECTED TDWARD EXF-'L.AnHNG THE
DYNAMICS OF ~RMS ~ACES. AN EXHAUSTING COMP1LATION OF ARMS RACE
RESEARCH 13 ~ROVI&ED BY (IOFeI-REVILLA (1979).MUCH OF THIS
RESEARC~ CAN BE TRACED TO LEWIS F. RICHARDSON'S PIONEERING WORK
ON MATHEMATICAL ~ODELS OF COMPETITIVE ARM~MENT5 PROCESSES.
"' ..
!~iNFDRTUN~,TE.L'{,:::MPIRICp,:_
po,PPlICC"T1DNS [iF THIE MODEL OFTEN HP,VE
E:EEN DISt\PF~DINTIM;. p~ F't.,RTICULAr.;, ESTIM,c.,TES OF THE ~~:ICH,c.,RDSON
MODEL IN SITUATIONS WHICH ARE INTUITIVELY CONVINCING
tiS
~,RMS
M,c.,JEShI
F~~,CE3
~I,ND
f\Ft:l':,
r,lDNET,·!E'...ESS, GENERALL\I I.jNSATISFACTDRy';'
JDNES (1981: :itd).
f~,CCORDINc.:
"TO
A~mERTJr~
"THE MATHEMATICE
(1989:348),
RICHARDSON'S EQUATIONS AND
(EVEN THOSE WITH STOCHASTIC
ELEMENTS! IS OF THE SAME NATURE AS THE MATHEMATICS THAT DESCRIBES
THE MOTION Of PL~NETS. THE PROBLEM WITH CLASSICAL M~lHEMATICS IS
1HAT IT CANNOT ADEGUATELY DESCRIBE CONCEPTS SUCH AS BLU~FING,
COOPERATION, PLOTTING OF ONE NP,TION p,G~,INST p.,NOTHEF-:, TAKING
ACCOUNT OF STRATEGIC INTERACTION,AND SO ON. PLANETS DO NOT DO
THESE THINGS, BUT NATIONS DO."
O~
RICHARDSON-PRDCESS MODELS IN GENERAL
THIS
1~;
F'C:RHAPS THE f<EASON
TH~,T
BDULDING (1962: 24)
CONCLUDES THAT "THE CLASSICAL APPARATUS OF PHYSICAL MECHANICAL
SYSTEMS ••. HAS ONLY A VERY LIMITED APPLICABILITY TO SOCIAL
S Y S T E. N S".
o~
::;; A F' DF' 0 P T (1 957: .2 9 5)
C [I N CU F: S B Y S T p., TIN G T H ;., T
II
NO p, M0 UN T
THE DEVELJPMENT OF THE TECHNIQUES QF CLASSICAL ANALYSIS WILL
BREAK THC BARRIER WHICH SEPARATES ITS RANGE OF APPLICABILITY FROM
THAT OF HU 1'1 Af,; [:EHP,',.iI OR)).
E:OULDING
Ft-,ILdRE OF
(1962:
M~.CHpJllCP.,L.
23)
STATED THAT
DYN,<\MI~:S
.~NSWER
"ONE
TO
THE
IN SDCI,I!L SYSTEMS" !tlO!)LD BE TO
"LOOh G"OR rnC;GER AND BETTEF DIFFERENTI,c,L EQUATIONS." THIS WAS
WHAT HAoPENED IN
THE
POPULARIZATION OF
HUNDRED
LITERATURE
ARMS RACE MODELING
RICHARSON-TYPE
FOLLOWING
THE
MODELS. THERE ARE OVER ONE
RICHARDSON-PROCESS ARMS RACE MODELS IN THE LITERATURE.
ONE MIGHT ARGUE THAT THIS IS A REFLECTION OF THE POPULARITY
AND
SUCCESS OF RICHARDSON-lYPE MODELING. "I BELIEVE, HOWEVER,
THAT THE SEARCH
~OR
DIGGER AND BETTER DIFFERENTIAL EQUATIONS IS A
REFLECTION DF FRUSTRATION OVER THE LIMITED APPLICABILITY OF
RICHARDSON-TiPE MODELS.
F:ESEAR(H PRO(;!;AM,
T~IS
BUT OF
A
IS A SIGN.
NOT
O~
DEGENERAT iNG ONEil,
A SUCCESSFUL
(ANDERTON, 1989:
349) •
ANDE~TON
PROBLEMS
LATER
WIT~
IN THE
WHILE
r.~t.,CE
!VIDDELS,
GOES ON TO DISCUSS SOME OF THE EMPIRICAL
ARMS RACE MODELING. THIS TOPIC WILL BE DISCUSSED
TEXT OF THIS PAPER.
ANDERTON
COMMENTED ON THE BROAD SUBJECT OF ARMS
p,ND JONES
!'If.,)EShI
FOCUS ON
\ 1981)
PAIRS OF ARMS EXPENDITURES THAT ARE
TWELVE p.CTUp.,L
COMMONLY PROPOSED AS ARMS
RACES. MAJESKI AND JONES FIND THAT THE RICHARDSON
DI~FERENT!AL
EQUATION MODEL 16 UNSATISFACTORY AT EXPLAINING ANYTHING
STAT!STICALLY
SIGNI~lCANT
ARMS EXPENDITURES
~DR
AS
~AR
THE lWELVE
AS
CORRELATION BETWEEN PAIRS OF
, p.F:MS R '..c..t:- F- C:- '
:
~AJESKI
AND JONES
CONSIDER TWO POTENTIAL SOURCES FOR THE FAILURE OF THE RICHARDSON
f·lODEL. "::::IF;ST, T;"';EY
~OR
THOS~
i'1.AY I'JOT CONSTITUTE
A;:;:MS RACES, SECOND,
WHICH DO. THE RICHARDSON MODEL
SPEC!FIC~TION
MAY NOT BE
A D E Q U~. T E •
M 1l.,J E S r\ rAN D JON E S
1\
THE
FURTHE~
METH:DDL~GY
~X~LORE
:2 5 9) •
(1 9 B 1:
WHICH ENABLED MAJESKI AND JONES TO
THE TWELVE SUPFOSED ARMS RACES IS
"STATISTICA:'" (:;AUS~.LITY AN;'.LYSIS, AS RECENTLY F'HOI'1ULGATED IN TIME
SERIES RE5EA~CH. USING THIS METHODOLJGY1 WE FIND THAT ARMS
EXPENDITURES ARE I~DEPENDENT IN A MAJORITY OF THE TWELVE CASES
EXAMINED. ~OR THOSE CASES WHERE INTERDEPENDENCE IS FOUND, THOSE
WHICH EXHIDI- ARMS COMPETITION. THE TRADIT1DNAL RICHARDSON MODEL
SPECIFIC~TrON IS NOT EMPIRICALLY SUPPORTED. FINALLY,
WE PROVIDE
A SPECIFIC METHODOLOGy FOR IMPROVED MODEL SPECIFICATION DERIVED
f.:POM
~,
MAJESK I
GENE::;;!I,L D1STRIBUTED LAG MODEL
I~ND
JDNES
,; 1981:
:::-or;~
ANY
!~,FMS
PRClF'CtSED
F:J.\CL
11
259).
U.S.-U.S.S.R.
] WILL NOw ATTEMPT TO SURVEY THE LITERATURE CONCERNING A
PAl<TICULf.E '.;1,RMS fUI.CE',
THfH BETWEEN THE
UNI TED
ST,~·.TES
AND THE
U.S.S.R .. AS ONE MIGHT GUESS, THERE IS NO CONCLUSIVE EVIDENCE
FOR OR
AGAIN3T
THE EXISTENCE OF
A COMPETITIVE ARMS RACE
BETWEEN
THE U.S. AND U.S.S.R. BUT BY A CAREFUL SURVEY OF THE LITERATURE,
I HOPE TO
SH~D
AT LEAST A LITTLE LIGHT ON THE SUBJECT.
SURVE~
1N
PROB~EM
SECTIDN 1
OF U.S.-U.S.S.R.
OF ,c.,Yfo.NIlld'oj'S
OF MEASURING A NUCLEAR
AYANIAN ALSO PRESENTS
LITERATURE
(1'186)
Pp.PER HE DISCUSSES THE
STOCKPILE VIA
THE DATA AND
~ORCE
A
SINGLE NUMBER.
MEASURES
EMoLOYED IN HIS
PAPER. IN THE SECOND SECTION OF AYANIAN'S PAPER A FORMAL MODEL OF
THE NUCLEAR ARMS RACE IS PRESENTED IN THE SPIRIT OF LEWIS
F~ICHp,r;:DSDN.
"THE P,PMS RACE i-lYPOTHESL3 15 FDUND TO 1::E
INCONSISTan
WITH THE OBSERVED NUCLEAR STOCKPILING ACTIVITIES OF THE UNITED
ST,c\TES p,ND TrE SDVIET UNIOH." p.,YANIAN (1986: 202). It,j SECTION
·TH~:EE
" .••
AN
ASyj~iMETRICAL
NUCLEiI,i;
STClCr(PlLlNG MODEL IS PF:ESENTED
1M WHICH U.S. ACTIVITY IS EXOGENOUS, DETERMINED AS A BY-PRODUCT
OF DOMESTIC lNTEREST GROUP POLITICS. WITH LITTLE REFERENCE TO
SOVIET ACTIVlTV. WHILE SOVIET STOCKPILING DISPLAYS
THIS
TO OBSERVED CHANGES IN U.S./SOVIET
MODEL
r.::ATICS IE STrdhlNG.", AY,t.,NIAN (1986:
SALT I AND SALT ;1. IN SECTION
~IV~
R~TIDNALITY
NUClEA~
FORCE
202). SECTION FOUR DISCUSSES
AYANIAN DISCUSSES NUCLEAR
OPPORTUNISM AND THE PROSPECTIVE FOR 7HE U.S. TO SURVIVE. SECTION
SIX ]S A SUMMARY.
"THERE IS NO EVIDENCE OF A NUCLEAR ARMS RACE BETWEEN THE UNITED
STATES AND THE SOVIET UNION. ON THE CONTRARY. THERE IS CLEAR
EVIDENCE OF 3CVIET 'NUCLEAR OPPORTUNISM' AND AMERICAN 'NUCLEAR
DF:ll="
[i\/EF: THIS :'[R10D. DtiP1NC THESE DECADES THE U.S. WELFARE
SYSTEM HAS EX~ANnED IN TWO DIRECTIONS: INTO THE FEDERAL nUDGET,
CROWDING-OUT DE;ENSE. AND I~TO THE PRIVATE SECTOR. REDUCING THE
UNTAXED TAXABLE CAPACITY OF THE NATION. THIS PROCESS HAS RENDERED
1HE U.S. NUC~EAR FORCE LEVeLS UNRESPONSIVE TO CHANGES IN SOVIET
NUCL~AR FORCE, WrlILE ALLOWING THE SOVIETS TO PURSUE POLITICAL
DDl"lI;"JAr~CE~
TH'~:OUG,·j
Nl!'::LEAF: SUPEF:IORIT',;
F,S
~,!'1ERICp,N
'LP,TENT
HilS- DECLINED" ,IT IS DIFFICULT TC) SE.E HOW DEMOCRt.,CYt,ND
THE WEST ARE TO SURvIVE WITHOUT A REALLOCATION OF RESOURCES
TOWARD DEFENSE."
STF;E\\lGTH"
FOR OTHER AUTHORS 5JGGESTING THERE IS NO STRATECIC ARMS
RACE BETWEEN THE UNITED STATES AND SOVIET UNION. SEE TULLOCK
(1974),
l~,ND
~JDHLSTETTER
(i974a)
IN HIS 1984 PAPER
TITLED
A,ND
!1974b),
"THE
POLITICAL ECONOMY OF ARMS
"DEVE;.. OPED, MEP-,SURED AND TESTED ,t:., CONTINUOUS TIME MODEL WHICH
EXISTS BETWEEN THE U.S. AND U.S.S.R. AN ARMS RACE IS EHOWN TO
EXIST, ALBEIT A RACE CONCERNED MOST DIRECTLY WITH WEAPONS
ACQUTSITIONS, NOT WITH BUDGETS. THE SENSITIVITIES OF THIS SYSTEM
WERE EXPLORED, AND THEY SUGGESTED THAT THE SYSTEM IS HIGHLY
SENSITIVE BOTH TO THE WAVS IN WHICH COMPARISONS OF WEAPONS GET
TRANSLATED INTO 2XPENDITURES BY THE SQVIET UNION AND THE U.S.,
p, ND "1 D 1 HE U, 'v' ELen: 3 i} P E F: 1=' D~J E~: TEN SID r,~ ,J HIe HIS F' ERCEI i) EDT [!
E X1ST I NTH E 1 NT ERrJ p, T I or~ p, ~. ;:, 0 LITE AL ': L Hi ATE .. • THE Me., J 0 R GOA LIS
TO ILLUSTRATE IN A RIGOROUS AND AND VERI~IABLE FASHION THAT THE
ARMS RACE BE1WEEN THE U.S. AND SOVIET UNION DOES EXIST AND IS NOT
A NEW PHENOMENON."
Wp"RD
?li.
~1984:
IT IS INTERESTING TO NOTE THAT AYANIAN
USED
AN INDEX OF
NUCLEAR FORCE IN HIS PAPER, WHILE WARD USED AN INDEX OF NUCLEAR
C!~,SE"-:QF;;
"WHILE THE
INCLUS10N CF SCtME MEp.SURE OF
W[p,F'ONS
STOCKS
IN ARMS RACE STUDIES IS PERSUASIVE, THERE IS NO CLEAR CONSENSUS
AMONG ARMS RACE MODELERS AS TO WHAT TVPE(S)
O~
MEA5URE!SI SHOULD
E:E EMPLOYED."
THE
EXPLICITLY
ON
~URP:3E
T~ST
OF THE TANG AND YANG (1988) PAPER WAS
rYE CAUSALITY !MPLICATION
AND
GLOBA~
RELATIONSHIP
,A,S
p,
PLAYER IN THE INTERNATIONAL SECURITY SYSTEM", TANG
(1988: 197)
YM~G
THE RICHARDSON MODEL
"P-,RMS R,A.CE". THEY RECOGNIZE CHI Nt>,
THE U .. S,-J.S.fLR.
hMAJDR
O~
TO
,ANDc',TTEMP'T
TO INVESTIGATE THE
C!~\VSf>,L
OF THE UNITED STATES AND RUSSIA IN THE PRESENCE OF
CHINA. THE ECDNOMETRIC TECHNIGUE EMPLOYED WAS THE HASIO TEST.
TANG AND YANG ALSO EMPLOVED A DUMMY VARIABLE FOR THE POST 1972
PERIOD TO TEST THE SIGNIFICANCE OF SALT I UPON ARMS EXPENDITURES
OF THE TWO SJPER POWERS.
IN
TP.,NG
P.,ND
YP.,NS'S
PM'EF:,
THE SENSE OF GRANGER CAUSALITY.
~ACT
SEE
ZELLNEP
(1979)
,l
IS
REFERF:ED
TO
IN
(GRANGER CAUSALITY REFERS TO THE
THAT ONE VARIABLE ADDS TO THE
\i,6,RI,c.,BLE,
'CP.,USALITY'
ABILITY
TO FORECAST ANOTHER
THE pr..,F'ER EXP.,MINED THE EMF'I;:;:ICAL
EVIDENCE
CJNCERN:~G
EXPENDITURES
I~
TH~
THE U.S. AND U.S.S.R. THAT WAS
RICHARDSO~
f: Y G h; ,.; N GEF:
T.A~,:G
(,.,)H1Ci·:
D~
~rRST;
THE RELATIONSHIP BETWEEN THE GROWTH OF ARMS
(:, 9 69)
~DDEL.
T~EY
AND H p, SID
p,;'m Yr"·NG
r~:E,c.,CHED
APP~IED
(1 97 9).
EXPLICI~LV
IMPLIED
THE METHODDLCGY DEVELOPED
THE R EWE RET ifJ 0 CON (: L US 1 (I NS
FRDM THE F:ESUL.TS OF
THEIF: STUDY,
THEY FOUND THAT THERE APPEARS TO HAVE BEEN UNIDIRECTIONAL
CAUSALITY RUNNING FROM THE GROWTH IN THE U.S.S.R. ARMS
EXPENDITURES TO THE U.S. ARMS EXPENDITURES IN THE PRESENCE OF
C!...!lN~"FRDM
1'15:2 TO 19B1, "SECOND; THE INSIGNIF!CPKE JF THE DUi"lMY
VARIABLE FJR THE POST 1972 PERIOD INDICATES THAT SALT I HAD
LITTLE IMPACT UPON THE DYNAMICS OF THE
ARMS RACE BETWEEN THE TWO
COMMENTS
MY FIRST COMMENT WILL RELATE TO THE RICHARDSON MODEL
ITSEL~,
AND TrlUS TO MANY OTHER FAPERS IN THE ARMS MODELING
LITER~,TUf;'E.c,.CCD~DIN(;
TO
GDRDOr,~
TULLOGi,';;
~1974),
"THE MOTIVc,T!NC
FORCES IN TH: RICWARDSON MODEL ARE ESSENTIALLY EMOTIONAL. RATHER
THAN RAT I [I ~J A;_. EF F DRT S TOO DT p., I N
TO SQME RATHER
DP~STIC
I':; to,
I N 0 F:
or D LOS 3 ,"
~, V
T HIS LE po, DS
DIFFERENCES BETWEEN THE RESULTS OF
TULLOCK'S REASONING AND THE RESULTS OF RICHARDSON'S.
"IN
PARTICULAR, IT IS ALWAYS RATIONAL TO START A WAR IF YOUR ENEMY IS
BOTH
F:ICH
ENDU(':;Htl,I'~D
WEp,!,>;
::?NOUGH," TULLDCf>:
(1974:
92). THIS POINT
OF VIEW WAS EXPANDED UPON BY MR. TULLOCK IN PRIVATE CONVERSATION.
-.
THIS MIGHT GIvE
~
VALID REASON WHY THE RICHARDSON MODEL FAILED TO
CI\JE Sp,TISt:''o,(:TDF;V RESULTS IN Il,NY OF THE THEUlE.
"P.,~:MS
Rp.,CES"
SrUDJED
T
D MR.
IN THE Mp,)EShI
T UL L D CK,
IT
AND )ONES
I S P, F A UL Ty
(1981)
MOD EL..
F'P.,PER.
T H lj S THE
P.,(:CORDING
Fn:: S iJ L T S
DF T~, ~"i G
':1931: 261) E;:P.TE THt-,T "ESTIMATES OF THE RiCHARDSON MODEL IN
THAT ARE INTUIT1VELY CONVINCING AS ARMS RACES ARE,
SITU~TIONS
r'WNETHELESS,
C;ILLEsr-'IE
!}NSf-o,TISFI\CTDRY.
(1973),
OSTF:OM
RECENT STUDIES BY ZINNES p.ND
(1977)
AND
HOLLIST(1977)
ARE
INDICATIVE.
THESE STUDIES VARIOUSLY REPORTED STATISTICALLY INSIGNIFICANT
POOR MEASURES OF FIT, OR UNEXPECTED
CDEF~ICIENT
~5T!~ATE5,
CO EF FIe I an
'3 r GN .3 - - SF' Eel FIe ALL y,
NEG AT I VEl NT E R,~ l::; T I 0 r~ T E RMS.
THE HEXT COMMENT REFERS NOT
~liJST
re!
Tp,NG p,ND Y,c.NG
il
~198B),
BUT TO V1RTUALLY EVERY ARMS RACE STUDY IN THE LITERATURE. THIS
COMMENT REFERS TO MEASUREMENT ERROR.
" THE T ~j [I ~1F.YJ P S J U F~ r: E S DF ME,:>, SUR EM EN T E R F: 0 FIN fl, RM5 FA CEST U DIE S
ARE INACCURACIES IN THE COLLECTION AND PUBLICATION OF DATA AND
THAT AV~ILAB~E DATA DO NOT REFER TO THE VARIABLE AS SPECIFIED.
WHILE THESE PROBLEMS CAN AFFECT ALL ARMS RACE DATA AND
VARIABLES. T~E MOST FREQJENTLY CITED EXAMPLES IN THE LITERATURE
"'HE :'DDR OUc.,LlTY OF ~,~:MS AND MILJTi\RY EXPENDITI.,.IF:E DA'Tp.,
H t I) iFF Ie UL "r Y I r~ ::: HDD'3 I NG p., MEA SuR E Di=' Ii E F E ~4 SE. • • FA CTOR 5
REDUCE DATA RELIABILITY INCLUDE INFLATION AND EXCHANGE RATE
C.,c:E:l"
D
p~
i
:;:)
--
THAT
CORRECTIONS, DIF=ERENT MODES OF DATA PREPARATION BY INSTITUTIONS,
AND UIFFERENT INSTITUTIONAL PJ?P03ES ~OR PRODUCING
IN::'OPM~T ION •• , HE)AF:I AJ::LES IN AF:MS Rp.,CE MODELS ARE PEF:CEI <jED
',i ,C, R1 to E: LE:3 • I 1=' F' 0 ',_ I CI "1 po, r': E r:: SIN THE
( V, S ,) USE CH·, EST I MAT ES DF
seVIET MILITARY EXPENDITURES WHE~ FORMULATING THEIR PDLICY, THEN
CIA DATA ARE THE BEST MEASURE OF U.S. POLICYMAKERS' PERCEPTIONS
[I); SOyIET 1'llLlTp..F:'{ E,'XF'ENDIT:)RES. ,.1F;ONIC;'.L.LY, UP[1il,TED (MORE
ACCURATEI ESTIMATES OF SOVIET MILITARY SPENDING ~OR PREVIOUS
YEAr;;s ARE: INj:EFI~3~: MEASURES. ".OF U,S" F'OLICYl"lAKEr.;'S f:'ERCEPTIONS
OF SOVIET MILITARY EXPENDITURES IN THOSE YEARS.
!~RMS F;p.,CE: Mc![;ELE:~:S STUDYING ·~HE BE Hp.'.JI OF: DF ?DL.lCYM'c.hEi:';:S
MuST IDENTIFY THE DATA THAT THE PDLICYMAKERS USED. NOT THE DATA
THE'( \THE pf~:MS ;:;:t<r: ~CtDELERS) 1 HP4f'~ IS MOS' PO,CCURp,TE,,, IF V ,3,
PERC:P1IONS
PERC~PTIONS
O~
O~
SOVIET MILITARY S~ENDING ARE DIF~ERENT FROM SOVIET
MILITARY SPENDING, TWO MEASURES DF SOVIET MILITARY
SPENDING MIGHT BE
~EEDED,
~JMILAR
REASONING MAY IMPLv THE NEED
FOR '; ',oj 0 j'1 E,,\ 5 URE: S DF U. S . M1L IT ARY SPEN DI i'J G. IF WE H.c, 'Ii E ,6, THF~ EE
NATION ARMS RACE (OR AN N-NATION RACE), THE COMPLICATIONS COULD
BE 01.)1 'IE SEVEF:E.
THERE IS A MILD CONSENSUS THAT MILITARY EXPENDITURES ARE
t-; GOD D Mr:: ,6, 3 \.i!~' E 0 :- DE FEN S E ,OR IH L E ~, S T THE: B EST .A V c" I LAB L E. , • •
HOWEVER, SOME ANALVSTS ARGUE THAT MILITARY EXPENDITURES CAN BE A
MISLEADING MEASURE 0; DEFENSE THAT SHOULD B~ REPLACED OR
SUPPLE!"1E!\iH:D BY CAF';"E:ILITY
D~,TA.
McCUE:BJt.1S
(1983)
jl,RGUE(::
THAT
THE
OF TWO NATIONS INVOLVED IN AN ARMS RACE
COULD BE UNCHANGED wHILE INTENSE ARMS COMPETITION IS OCCURRING
f:ETwEEN ONE DR TWD (OR MORE) wEAF'Or~S TYPES."
M!LIT~RY
EXPENDIT0~ES
f\NDERTON
(19B9: :352).
ECONOMETRIC ANALYSIS
1 HAVE CONSIDERED TWO MODELS OF ARMS RACE BEHAVIOR
E:ETWEEN THE 'iN1TED
STinES AND THE SO\llET UNION.
I~~
BOTH MDDELS
HAVE USED STATISTICS ON LEVELS OF RUSSIAN AND AMERICAN
FOR YEARS 1963-1985.
~ARHEADS
(BOMBER WARHEADS WERE EXCLUDED BECAUSE OF
AMBIGUIT!ES.) THE STATISTICS WERE OBTAINED WITH PERMISSION FROM
HiE
ri1,..iDSDN I \lST! TUTE. IN BOTH I'1DDELS I
U!:,~D
OLS (DPD IN,c.,RY LEp,ST
SQUAF:ES) "
F~ICHP.,RDSON
MODEL
THE RICHARDSON MODEL 1 TESTED IS A SYSTEM OF TWO LINEAR
DIFFERENTIAL E0UATIONS:
(THIS IS THE RICHARDSON MODEL IN ITS MOST
BASI C F01:;:M.)
(1)
FDRW ::: K(AWH) - A(RWH)
+
(2)
FDAW = L. (F:WH;
+ H
- [: (P.,WH)
G
FDRW (FIRST DIFFERENCE RUSSIAN WARHEADS)
FDAW
(~IHST
DIFFERENCE AMERICAN WARHEADS)
RWH
(RUSSIAN WARHEADS)
AWH
IAME~ICAN
WARHEADS)
G AND H (CONSTANTS)
I'll
c.
,~,
>=" ,-. 1;' '- c; .=; T
',-
n \t
.. ,.:~'.---"-'.,;.:....'-:
>=.c, T I
...
>="
n
T
-:...:.....~ •.
~
!_'
PROVIDE ANY SIGNIFICANT
t _. S TAl 1ST I CS. THE 3ECOND (:::) , HOWEVEF:, DID AS FOLLOWS:
(:2.9119)
(-3.3270)
R-S0jARE=.373~
WHERE THE
SGVARE=.3078
~-BAR
~J~BERS
~CCD~DING
I~
~ICHARD30N
DURBIN-H=1.6493028
PAREN1 U ESES ARE t-STATISTICS.
TO THESE RESULTS.
WITH RWH AND PDS!l!VELY
WHAT
(,21869)
WI~H
~DAW
CORRELATES NEGATIVELY
AWH. lHIS IS THE EXACT OPPOSITE OF
ORI;lNALLY PRDPOSED IN HIS MODEL. MY RESULTS
INTERACTION TERMS IN THEIR RESEARCH.
DISTRIBUTED LAG MODEL
THE
D!ST~:lBUTE:O
LA,:~
!'10DEL
1 PURPDSE IS A
SYS1E1'l
LINEAR EQUATIONS:
.-,
-
\1)
!~WH
{.2 )
AWH .- Ai
Ri
" i =1
"
i =1
=1
1., c.
n)
+ /l.
1
(
i
t
n)
+ Ri
(
1 =1 to rn
I',
to rn
,
!
+ C
)
+ C
OF Tt-JO
RWH <RUSSIAN WARHEADS)
AWH !AMERICAN WARHEADS)
R~
!RUSSIAN WARHEADS LAGGED
A~
iAMERICAN WARHE~DS
C
'. CON STAN T )
~
YEARS)
LAGGED' YEARS)
THE METHOD FOR OBTAINING nAND m WAS PROVIDED FROM TANG
f.\ N D 'I M~ G (1 9 g~. ).
(I N B R I EF,
LAG S
Po
REA DDE Ii T 0 'T HEM 0 DEL S Urn I
SIGNIFICf\NT i.-ST,a.TlSTICS WERE OBTAINED FOR /l,LL f;:1
THE
P.ND p..i).
SECOr,iD L2) EQUATION FAILED TD PF:[lVIDE fl.rnl SICNIFICANT
t - ST PO. TIS TIC S.
i~:WH
L
::::
TH :
.5B84B(Rl)
(4
I'
.~777
~HUS
f;~ S T
(1),
HOW EVE R,
+
.98040 (P·.3)
(-:2.7472)
>:::.9362)
F-BAR SQJARE
LEV~LS
DID AS F 0 L L. 0 ~J S : ( n:: 1 , m:: 3 i
+ -1.3695U.2)
.8585f.:dAl)
+
17 1S0 )
=
R-SQUARE
FI
=
.9718
(3.0704)
DURBIN-H
=
+
79.717
(.29744)
-1.5590
0= RUSSIAN WARHEADS CORRELATE WELL WITH
RUSSIAN WARHEAD LEVELS LAGGED ONE YEAR AND AMERICAN WARHEAD
LEVELS LAGGED ONE, TWO, AND THREE YEARS. AMERICAN WARHEAD LEVELS
DID NOT CORRELATE SIGNIFICANTLY WITH ANY LAGGED VALUES OF RUSSIAN
WARHEADS.
IMPLYING THAT CHANGES IN YEARLY LEVELS OF RUSSIAN
WARHEADS HAVE LITTLE TO DO WITH YEARLY CHANGES IN AMERICAN
WARHE~D
LEVELS. THE RESULTS OF THIS MODEL IMPLY THAT AMERICAN
WARHEAD 3UILn-Up PRECEDED RUSSIAN WARHEAD BUILD-UP IN A
STATISTICALLY SIGNIFICANTLY MANOR; IT TOOK THE U.S.S.R. ONE TO
T~~~~EE
YEo.RS TO C,c,TCH UP
~nTH
THE UNITED STP>,TES,
(FROM 1963-1985),
.[IF THE. T!"jD MDDELS I HAVE PF:ESENTED, I PREFCF: THE
DISTRIBUTED
~AG
~OD~LI
FOR
~EASONS
STATED EARLIER IN THIS PAPER
CONCERNING RICHARD30N MODELS. AND FOR REASONS STATED BY TULLOCK
(19741. IT WOULD BE INTERESTING TO SEE HOW BOTH MODELS HOLD UP
WHEN MILITARv
EX~ENDITURES
ARE USED INSTEAD
O~
WARHEAD LEVELS,
BUT DATA WERE NOT READILY AVAILABLE.
CONCLUSIONS
THERE IS
ARMS RACES
A~D
A~
OVERWHELMING AMOUNT OF LITERATURE CONCERNING
ARMS RACE MODELING. I REVIEWED A FEW ARTICLES
WHICH I CONSIDER TO BE IMPORTANT TO ANYONE INTERESTED IN ARMS
RACE MODELS. THERE
STATES AND
THE
O~
T~E
~RE
NO DECISIVE ANSWERS AS TO HOW THE UNITED
SOVIET UNION RESPOND TO EACH OTHER MILITARILY IN
INTERNATIDNA~
ARENA. DIFFERENT ANSWERS DEPEND ON WHICH TYPE
MODEL IS USED AND HOW STATISTICS ARE GATHERED. IT IS CERTAIN
THAT THE MAJOR ARMS RACE MODEL, THE RICHARDSON MODEL. DOES HAVE
PROBLEMS. IT IS ALSO CERTAIN THAT THERE ARE MANY PROBLEMS
ASSOCIATED WITH MEASUREMENT ERROR AND THE CHOICE OF USING
EXPENDITURES OR FORCE LEVELS (OR A COMBINATION OF BOTH).
HAVE
PRESENTED TWO MODELS OF MY OWN THAT DID A REASONABLE JOB OF
EXPLAINING THE REACTION BETWEEN THE U.S. AND U.S.S.R. AS FAR AS
WARH~AD
LEVE~9
ARMS RP.,(;:::
ARE CONCERNED. FOR SUGGESTIONS AS TO THE FUTURE OF
MODELING;, SEE ANDERTON
(1989~
357-363).
REFERENCES
(, H. (1 "~. 9 ) "p., R ~i S RAe E MOD E L Hi G" .j DUR~~ ,0, L 0 FeD NFL leT
RESOLUTION, VOL. 33 NO.2, JUNE 1989 346-367.
f\ NDE P1 0 N,
t.,YANlP,N,
R.
Hr~UCLEAR
:1986)
CONSEQUE~KES
Dr- THE
WELF~RE
5Tft-,TE.';
PUBLIC CHOICE 49: 201-222.
GDULDING, H.E. \1962)
ROW.
CONFL.ICT fIND
DEFEf~SE.
NEW
YOR~~:
Hp.,RPEF' AND
CA. (i979) "THEORIES OF ARMS RACES p,ND
MATHEMATICAL STRUCTURES IN INTERNATIONAL RELATIONS."
PRESE~TED AT THE JOINT MEETING OF THE MIDWESTERN
POLITICAL SCIENCE ASSOCIATION AND THE MIDWESTERN SECTION
OF THE PEACE SCIENCE SOCIETY(INT'L),CHICAGO, APRIL 19-21.
CIOFFI-REVILl.P."
GRp,NGEF:,
C.W,J .. {1969) ;11NVESTIG,t.,TING Cp.,USAL RELATIONS BY
ECONDMETRIC MODELS AND CF~DSS-SPECIAL METHODS H
ECONOMETRICA 37: 424-438.
HASIG,
C.
':1';'79)
DYNA~lCS
t)CAUSr~L!r,t' TESTS IN ECONOMETRICS",). ECON.
AND CONTROL 1 321-346.
(1977) "p,N p\N,tLYSIS OF t.,RMS PF:OCESSES IN THE UNITED
ST/qES P.,!\jD THE. SOVIET lJNION." INT'L SHJDIES 0. 21=
HOLLJST,~LL.
503-528.
p~
T RILl G!~, T DF-:
II, \\1 D
I~RMS
B r~: ITO (1 9 2. 5:; " ~.\ 0 N- p., F: Mp., GEDDDN SOL UTI [I N5 TOT HE
ARMS CONTROL 6: 41-57.
R~,CE"
11A)ESf\I AND )QNES (1'':;'81)
RE'30LUTION, \)OL.
"ARMS
RACE i'1ODELING"J. CONFLICT
JUt,lE 1981259-283.
25 NO.2,
r1.D. ':1983) "THE PDLlCY COMPONENTS OF AF:MS
(OMF'ETllION.1I AMERICAN J. OF' POL.. SCI. 27: 485-514.
McCUBr~IN~3,
McGIJ1F:E
DSTROM
·:1765)
UN1\}.
3::CREC,!'c.,ND
T"'tEe;RMS
~:ACE.
CP,MBRIDGE:
H,6,F:Vp.,RD
PRESS.
"E\}ALU,t,TINC; p,L..TERNP.TI\jE r70[.~EIGN POLICY DECISION
MAKING MODELS: AN EMPIRICAL TEST BETWEEN AN ARMS RACE
MODEL AND AN ORGANIZATIONAL POLITICS MODEL." J. CONFLICT
!~:ESOLUTI ON
21: 235-266.,
(1977)
it
F:p,P,c"PDF:T,t,. (1957) "LE(.-lIS F. F:ICi·-j,c,RDSOWS Mt.,THEMATlCp.,L THEORY DF
WAF:. if J. CDNFLICT F:ESDLUTION 1: :::49-304.
~.'':'PAPORT,~"
q9bl)
OF MICHIGAN
FIGHTS,
~RESS.
C;p.MES,
,c,ND DEBt-,TES.
,t"NN p"RBDF::
UNll./.
H,NG
~,ND
~'~,NG
(1ge 2)"
ARMS RACE
~OD
EST! NC FOF: CAUSII,LI TY
I N THE Fd CHp.,RDSON
Ln. MATHEMATICAL SOCIAL SCIENCES 15:
i97-203.
'iULLCJCh,
(197·~),
C:,
F'U[~L 1C~,T
Lo)!lRD,
M.D,
THE SOCIAL DILEMM,c."
(1q84~
\/a,:
UNIV.
"THE F'O:...1TlCp,L. ECONDl"1Y 01= po,RMS Rp,CES· t-,ND
INTERNATIDNA~
SCIENCE,
BL,~U~;SBVF:G,
1 DNS.
TENSION" CONFLICT MANAGEMENT AND PEACE
S~~F:ING
192,4.
48 -8 :..
:z ~ LU,j E F:, A.
rm
: 1 9 7:i ), H CA\..i ::'i p, LI T Y A
E CD N0 i'i ET RIC: 5 ii, I N ~
p, ND ,;.. H. MEL T Z E R, ED S. ' THR E E A '3 F' E CT S 0 F P DLI C'{
i<.
E: ~'\.J i'~ NER
AND POL 1 C Y
\,<tP,YI:uC=<}j(J\.-.;LEDGE, Di!,Tf\ AND Hl'31ITUTIONS,
C:c.,RNEGIE '-::;:C!c:HESTEF: CONFEF-:ENCE SERIES VOL • .to
( rW R T H - H ::J L L. AND, A, MS T E R 0 AM, 1 97 9 ) P P. 9 - 5 4 •
,.; rm GIL L ESP I E . j • i.) , (1 9 '7 3) " ,c\ ~'{ p., L Y':; I S [! F A~: MS ~: ACE
MOD E !_ S ~ i) S po, 'y' 5. US S RAN D N p, 1 0 V 5" ~n (I." p p. 1 4 ::. - i 4 BIN
~J.C ,VOG; AND M.H.
MIU;LE \t'ds.> MODEL!Ne ,';ND SIMULATION:
Z IfJ NE S , Ii. A.
VDLU1E 4. PITTSBURGH: UNIV. OF PITTSBURGH PRESS.