On Distinguishing Defence Inputs in an Alliance – The Case of NORAD

ABSTRACT

Our model extends the joint-products models to allow for two types of defence inputs used to produce both an alliance-wide public defence output and a country-specific private output. Distinguishing different defence inputs is particularly appropriate in the case of the North American Aerospace Defense Command (NORAD), as the alliance-wide defence output is produced with two inputs – military technology in the form of sensors and radars and land. These two inputs are complements in the production of the alliance-wide public output. At the same time, the military technology has country-specific private benefits as this can be used by the civilian economy. Our analysis shows that distinguishing between defence inputs may change the predictions of the joint-products model. We derive conditions under which an ally responds to an increase in the defence input by other allies by increasing or decreasing its own contribution of both or only one of the defence inputs.

KEYWORDS:

• NORAD
• public goods
• joint product model of alliances
• free riding

JEL CLASSIFICATION:

• D74
• H41
• H56

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1. The empirical literature on burden-sharing in the NATO alliance before 1967 uses defence expenditure as a percentage of GDP as a measure of burden sharing and finds evidence for the ‘exploitation’ of the large and rich allies by small and poor allies (Khanna and Sandler 1996). However, Bogers and Beeres (2013) use indicators such as deployability ands sustainability and find that the ranking of the burden-sharing in NATO depends critically on the specific measure of burden sharing. Beeres and Bollen (2017), Beeres and Bogers (2012), and Kollias (2008) study the burden-sharing problem at the level of the European Union and provide further evidence that the burden-sharing ranking changes depending on the specific measure employed.

2. Sandler and Hartley (2001) is an excellent review of the joint-products model literature.

3. NATO member states to spend 2% of their GDPs in defence and 20% of that on equipment.

4. Canadian land contribution allows resiliency as, instead of relying solely on LEO-orbit satellites, drones and fixed-wing patrol aircraft, by permitting over-the horizon radar stations on land (with Modernized NORAD reaching up to 2,000 km further north) and underwater sensors, effectiveness increases through redundancy and diversification.

5. For a discussion of the Northwest Passage sovereignty dispute see (Elliott-Meisel 2009), and (Lajeunesse and Huebert 2019).

6. In section 2.3 we present the case when defence inputs are imperfect substitutes. Our model is, however, general enough to allow for the case of a weakest-link input aggregation technology. If either ally withdraws its contribution of land (or technology), the alliance-wide defence is produced with the minimum contribution of land and technology. Thus, the model allows either of both weakest link and weaker link technologies. ‘In contrast to the weakest-link technology, if one agent is not contributing it is still possible to attain positive levels of the public good.’ (Arce 2001). So it was weaker link but that does not change this paper’s results, it just requires a recalibration of payoffs to the alliance production function by lifting the public good from zero to some positive threshold.

7. As for the land prices up North, whereas the land use is at a excess supply equilibrium even at zero price for local and civilian uses in those remote areas where NORAD radar stations are installed, there is an imputed price which derives from the benefits generated by NORAD.

8. Our model, as well as the related standard joint-products model, can be contrasted with the alternative under which the members of the military alliance would be sharing the total cost of providing the efficient level of defence for the alliance.

9. Note that, if both inputs contribute to the production of both the country-specific output and the alliance-wide output, the model collapses to the standard joint-products model and the distinction between the two inputs becomes irrelevant.

10. If $\frac{\mathrm{\partial }{n}_i}{\mathrm{\partial }{n}_j}\le 0$, the condition in (27), becomes $\left|\frac{\mathrm{\partial }{n}_i}{\mathrm{\partial }{n}_j}\right|\le \frac{{\mathit{g}{\mathit{ }}^{\mathrm{\prime }}}_{\mathit{j}}}{g_i^{\prime }}$.

11. Differentiating the aggregation technology for land, $\mathit{M}={\gamma }_i{m}_i+{\gamma }_j{m}_j$ with respect to $m_j$, gives.

$\frac{\mathrm{\partial M}}{\mathrm{\partial }{m}_j}={\gamma }_i\frac{\mathrm{\partial }{m}_i}{\mathrm{\partial }{m}_j}+{\gamma }_j.$

Substituting in $\frac{\mathrm{\partial }{m}_i}{\mathrm{\partial }{m}_j}=-\frac{{\gamma }_j}{{\gamma }_i}$ from (34) or (35) for $h_{\mathit{ij}}^{{ }^{\prime \prime }}=0$, gives $\frac{\mathrm{\partial }\mathit{M}}{\mathrm{\partial }{m}_j}=0.$