Rethinking the guns vs. butter tradeoff: a non-linear and regime-conditioned approach in the military and health spending

Does increased military spending always reduce government health expenditure? Is the guns vs. butter tradeoff truly linear? Conventional arguments suggest a linear trade-off with inconsistency. While some studies suggest that an increase in defense spending corresponds to a proportional decline in health spending, claiming that this effect is linear and universal, others posit no tradeoff. We argue that there exists a tradeoff, but this relationship is nonlinear. Using a quadratic model, we show that military spending does not crowd out health expenditures initially. Instead, health spending remains stable or may even increase at lower levels of military expenditure. However, once a fiscal threshold is surpassed, further increases in military spending lead to sharp reductions in health budgets. Furthermore, this tradeoff differs and is influenced by regime type. Democracies sustain health spending longer, delaying the tradeoff; hybrid regimes lack a consistent threshold for shifting resources between defense and health; and autocracies experience the tradeoff earliest, prioritizing military expenditure at the expense of health spending.