This article improves and refines the joint product model so that it can better analyze nuclear war alliances. In particular, the refined models demonstrate that allies' responses to defense spillovers depend upon the consumption relationship (i.e., complementarity or substitutability) of the jointly produced defense outputs as well as the allies' income responsiveness. The stability and size of alliances are also related to the consumption relationship of the joint outputs. This article uses a generalized least-squares estimate on data for 12 NATO allies to estimate their defense expenditure functions. The statistical results conform well with our predictions.
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