A continuous time simulation model of the arms expenditures and arms stockpiles of the Soviet Union (USSR) and the United States (US) from 1951 through 1978 is developed in this article. This model suggests that contemporary superpowers react primarily to comparisons between their weapons stockpiles and those of their perceived opponents, rather than to the military budgets of their perceived opponents. The parameters for this model - which is developed in a system of ordinary differen tial equations - have been estimated by coupling a nonlinear least squares minimization algorithm, NL2SOL, with the solu tion trajectories of the differential equation system. The predic tions of the model are quite close to the actual data series, with standard errors of the estimates for each individual equation being quite small. In contrast to some public opinion and con siderable scholarly research, the results provide strong confirma tion for the proposition that there is a current arms race between the US and the USSR. The US and the USSR each try to achieve or maintain a lead over the other in the stock of weapons- both the conventional and strategic - which each possesses. Stability analysis of the systems of equations suggests that the system may require approximately 3,000 years to return to the steady state, once it had been pushed off the stability trajectories.
Allan, P., and Luterbacher, U. "Analyzing Detente: Simulations and Scenarios." Unpublished manuscript (1981).
2.
Anderson, T.W.An Introduction to Multivariate Statistics. Wiley, New York, New York (1958).
3.
Azar, E.E. "The Codebook of the Conflict and Peace Data Bank (COPDAB): A Computer-Assisted Approach to Monitoring and Analyzing International and Domestic Events." University of North Carolina, Chapel Hill, North Carolina (1980a).
4.
Azar, E.E. "The Conflict and Peace Data Bank (COPDAB) Project." Journal of Conflict Resolution24:1 (1980b), 143-152.
5.
Bailey, R.W.; Hall, V.B.; and Phillips, P C. B. "A Model of Output, Employment, Capital Formation and Inflation." Cowles Foundation discussion paper no. 552. Cowles Foundation for Research in Economics, New Haven, Connecticut (1980).
6.
Bergstrom, A.R.Stastical Inference in Continuous Time Economic Models. North-Holland, Amsterdam (1976).
7.
Carter, R.A.L. and Nagar, A.L. "Coefficients of Correlation for Simultaneous Equation Systems." Journal of Econometrics6 (1977), 39-50.
8.
Cusack, T.R. and Ward, M.D. "Military Spending in the United States, Soviet Union and the People's Republic of China." Journal of Conflict Resolution25 (1981 ), 429-469.
9.
Dennis, J.E. JR.; Gay, D.M.; and Welsh, R.E. 'An Adaptive Nonlinear Least Squares Algorithm ." ACM Transactions on Mathematical Software7:3 (1981a), 348-368.
10.
Dennis, J.E. JR.; Gay, D.M.; and Welsh, R.E. "Algorithm 573-NL2SOL - An Adaptive Nonlinear Least Squares Algorithm". ACM Transactions on Mathematical Software7:3 (1981b), 369-383.
11.
Fischer, G.W. and Crecine, J.P. "Defense Budgets, Fiscal Policy, Domestic Spending and Arms Races." Presented to the Annual Meeting of the American Political Science Association. Washington, D.C. (August 1979).
12.
Gandolfo, G.Economic Dynamics: Methods and Models. North-Holland, Amsterdam (1980).
13.
Gandolfo, G.Qualitative Analysis and Econometric Estimation of Continuous Time Dynamic Models. North-Holland, Amsterdam (1981).
14.
Green, D.W. and Higgins, C.I.SOVMOD I: A Macroeconometric Model of the Soviet Union. Academic Press, New York, New York ( 1977).
15.
Gillespie, J.V.; Zinnes, D.A.; Schrodt, P.A.; Tahim, G.S.; and Rubinson , R.M. "An Optimal Control Model of Arms Races":American Political Science Review71 (1977), 226-244.
16.
Gregory, P. "Economic Growth, U.S. Defense Expenditures and the Soviet Budget:"Soviet Studies24 (1974), 72-80.
17.
Hamblin, R.L. ; Hout, M.; Miller, J.L.L.: and Pitcher , B.L. 'Arms Races: A Test of Two Models." American Sociological Review42 (1977), 338-354.
18.
Hollist, W.L. 'An Analysis of Arms Processes in the United States and the Soviet Union." International Studies Quarterly21 (1977a), 503-528.
19.
Hollist, W.L. 'Alternative Explanations of Competitive Arms Processes: Tests on Four Pairs of Nations." American Journal of Political Science21 (1977b), 313-340.
20.
Hollist, W.L. and Guetzkow, H. "Cumulative Research in International Relations: Empirical Analysis and Computer Simulation of Competitive Arms Processes." In Exploring Competitive Arms Processes: Applications of Mathematical Modeling and Computer Simulation in Arms Policy Analysis (W. L. Hollist, ed.). Dekker, New York, New York (1978), 165-195.
21.
Holzman, F.D. 'Are the Soviets Really Outspending the U.S. on Defense?" International Security4 (1980), 86-104.
22.
Holzman, F.D. "Soviet Military Spending: Assessing the Numbers Game." International Security6 (1982), 78-101.
23.
Hopple, G.W.; Rossa, P.J.; and Wilkenfeld, J. "Threat and Foreign Policy Analysis: Assessing the Overt Behavior of States in Conflict." In Sage International Yearbook of Foreign Policy Studies (P. J. McGowan and C. W. Kegley, Jr., eds.). Sage, Beverly Hills, California (1980), 19-53.
24.
Hutchings, R. "Fluctuation and Interaction in Estimates of Soviet Budget Expenditure." Osteuropa Wirtschaft18 (1973), 53-79.
25.
International Institute of Strategic StudiesThe Military Balance, 1971-72; 1972-73, 1973-74; 1974-75; 1975-76; 1976-77; 1977-78 ; 1978-79; and 1979-80. London (1971-1979).
26.
James, R. and Roos, M. Minuit.CERNLIB Documentation: Report D506 ( 1975).
27.
Korn, G.A. and Wait, J.V.Digital Continuous System Simulation. Prentice-Hall, Englewood Cliffs, New Jersey (1977).
28.
Koyck, L.M.Distributed Lags and Investment Analysis. North-Holland , Amsterdam (1954).
29.
Kugler, J. and Organski, A.F.K. , with Fox, D.J. "Deterrence and the Arms Race: The Impotence of Power." International Security1 (1980), 105-138.
30.
Lambelet, J.C. "Toward a Dynamic Two Theater Model of the East-West Arms Race." journal of Peace Science1 (1973), 1-37.
31.
Lambelet, J.C. and Luterbacher, U., with Allan, P. "Dynamics of Arms Races: Mutual Stimulation vs. Self-Stimulation." Journal of Peace Science4 (1979), 4-66.
32.
Lee, W.T.The Estimation of Soviet Defense Expenditures: 1955-1975, an Unconventional Approach. Praeger, New York, New York (1977).
33.
Luterbacher, U.Dimensions historiques de modeles dynamiques de conflit. Application aux courses armements 1900-1965. Sijthoff, Leiden (1974).
34.
Luterbacher, U. 'Arms Race Models: Where Do We Stand?" European Journal of Political Research3 (1975), 199-217.
35.
Luterbacher, U.; Allan, P.; and Imhoff, A. "SIMPEST: A Simulation Model of Political, Economic and Strategic Interactions Among Major Powers." Paper presented at the Xlth World Congress of the International Political Science Association. Moscow (12-18 August 1979), 1-38.
36.
Majeski, S. and Jones, D. 'Arms Race Modeling: Causality Analysis and Model Specification." Journal of Conflict Resolution25 (1981), 259-288.
37.
Mcguire, M.C. 'A Quantitative Study of the Strategic Arms Race in the Missile Age." Review of Economics and Statistics59 (1977), 328-349.
38.
Moll, K. and Luebbert, G. "Arms Races and Military Expenditure Models." Journal of Conflict Resolution24 (1980 ) 153-186.
39.
Nincic, M. and Cusack, T.R. "The Political Economy of U.S. Military Spending." Journal of Peace Research16 (1979 ), 101-115.
40.
Nincic, M.The Political Economy of U.S. Military Spending. Praeger , New York, New York (1982).
41.
Organski, A.K.F. and Kugler, J.The War Ledger. University of Chicago Press, Chicago, Illinois (1980).
42.
Ostrom, C. "Evaluating Alternative Foreign Policy Models: An Empirical Test between an Arms Race Model and an Organizational Politics Model." Journal of Conflict Resolution21 ( 1977), 239-265.
43.
Phillips, P.C.B. "The Estimation of Some Continuous Time Models ." Econometrica42 ( 1975), 803-832.
44.
Rattinger, H. "Econometrics and Arms Races: A Critical Review and Some Extensions." European Journal of Political Research4:4 ( 1976), 421-439.
45.
Richardson, L.F.Arms and Insecurity. Homewood, Pittsburgh, Pennsylvania (1919/1960). 46 Richelson, J.
46.
" Evaluating the Strategic Balance."American Journal of Political Science24:4 (1980), 779-801. 47 Richelson, J.
47.
" Static Indicators and the Ranking of Strategic Forces." Journal of Conflict Resolution26:2 (1982), 265-282.
48.
Saris, W. and Middendorp, C. 'Arms Races: External Security or Domestic Pressure?" British Journal of Political Science10 (1980), 121-178.
49.
Schrodt, P.A. ; Gillespie, J.V.; and Zinnes, D.A. "Parameter Estimation by Numerical Minimization Methods." International Interactions4 (1978), 279-301.
50.
Strauss, R. 'An Adaptive Expectations Model of the East West Arms Race." Peace Research Society (International) Papers19 (1972), 29-34.
51.
Strauss, R."Interdependent National Budgets: A Model of U.S.-U.S.S.R. Defense Expenditures." Exploring Competitive Arms Processes: Applications of Mathematical Modeling and Computer Simulation in Arms Policy Analysis ( W. L. Hollist, ed.). Marcel DekkerNew York, New York (1978), 89-98.
52.
Squires, M.L. "Modeling the U.S.-U.S.S.R. Strategic Arms Race ." Paper presented to the Annual Meetings of the International Studies Association. Cincinnati, Ohio (25 March 1982).
53.
Taagepera, R.; Shiffler, G.M.; Perkins, R.T.; and Wagner, D.L. "Soviet-American and Israeli-Arab Arms Races and the Richardson Model." General Systems Yearbook20 (1975), 151-158.
54.
Taagepera, R. "Stockpile-Budget and Ratio Interaction Models for Arms Races." Peace Science Society (International) Papers29 (1979-1980 ), 67-78.
55.
U.S. Department of Defense Soviet Military Power. Washington, D.C. (1981).
56.
Wagner, D.L. ; Perkins, R.T.; and Taagepera , R. "Complete Solution of Richardson's Arms Race Equations." Journal of Peace Science1 (1975), 159-172.
57.
Wait, J.V. and Clarke, D., III DAREP User's Manual. Unpublished mimeograph. Department of Electrical Engineering, College of Engineering, University of Arizona. Tucson, Arizona (1979).
58.
59.
' Arms Races and Escalation." Journal of Conflict Resolution23 (1979), 3-16. 59 Wallace, M.D.
60.
" Some Persisting Findings: A Reply to Professor Weede." Journal of Conflict Resolution24 (1980 a), 289-292. 60 Ward, M.D.
61.
" Dynamics of Cooperation and Conflict in Foreign Policy Behavior: Reaction and Memory." International Studies Quarterly26:1 (1982), 87-126. 61 Wymer, C.R.
" Estimation of Continuous Time Models with an Application to the World Sugar Market." In Quantitative Models of Commodity Markets (W. C. Labys, ed.). Praeger, New York, New York (1975), 173-191. 63 Zinnes, D.A. and Gillespie, J.V. 'Analysis of Arms Race Models." Modeling and Simulation4 (1973), 149-154.
