THEORY AND APPLICATION TO THE US MILITARY

Abstract

An ever‐growing share of defence R&D expenditures is being dedicated to the development and fielding of integrative technologies that enable separate individual systems to work in a coordinated and synergistic fashion as a single system. This study explores the optimal defence budget allocation to the development and acquisition of weapon systems and to the development of integrative technologies. We develop a suitable optimization framework, and then use it to derive the optimal budget allocation and analyse its properties. Finally, we use US defence budget data to calibrate the parameters of the model and provide a quantitative measure for the apparent US military supremacy.

Keywords:

• Research and Development
• Integrative technologies
• Budget allocation

JEL Codes:

• H56
• O33

Notes

1. Parameter values for this example are: N=3, α_i /ρ=0.6, β_i /ρ=0.4, ρ=0.5, η_i =1, c_i =1, r_i =2, δ ₁=1, δ ₂=3, δ ₃=1, r_I =3.

2. See www.dtic.mil/comptroller for budget data, and www.dtic.mil/descriptivesum for descriptive summaries of the various R&D programmes. The final data set is available from the authors.

3. The specification of the model allows for simultaneous estimation of all the model parameters and the variance–covariance matrix of the relevant error terms (using maximum likelihood estimation, for example), followed by a conventional statistical analysis of the results. The small number of observations suggests that such a procedure is too ambitious and can provide a very limited amount of reliable information on the true parameters. Clearly, the calibrated parameter values in this paper should be seen as ‘ball park’ estimates.

4. In the following discussion, the subscripts A, N and AF denote Army, Navy and Air Force, respectively.

5. Other specifications yielded inferior results: constant η_i yielded highly skewed residuals. Given ρ, it is also possible to calculate η_i for each time period, as was done for the relative elasticities, but then it is impossible to identify ρ.

6. This is a reasonable assumption, as the budget shares of the Air Force and Navy are of similar magnitude. However, it is straightforward to estimate (21) when the error terms feature different variances.

7. Allowing the specification of η_Af and η_N to be quadratic in time yielded statistically insignificant estimates of the quadratic terms. Hence, this specification is omitted.

8. We use the sequential optimal budget allocation of the theoretical model as a justification for a sequential calibration procedure. Thus, the calibrated parameters in the third stage are conditional on the calibration results of the second stage. This means that the standard errors of the parameters in the third calibration stage are also conditional on the calibrated parameters in the previous stage. We feel that owing to the limited available data, this procedure, although somewhat incomplete, is sufficient for the calibration we present here.

9. Testing the null hypothesis that δ ₁=0 is therefore not interesting: it implies an infinite potential contribution, which does not make any sense.

10. Technically, the LHS of the first‐order condition given in equation (22) goes to infinity when δ ₃ approaches zero.