Fiscal Aggregation and the Limits of IS--LM--BP: Derivations, Aggregation Bias and Reproducible Adversarial Simulations

Original Abstract

This paper develops a formal critique of scalar fiscal aggregation in the IS LM BP/Mundell Fleming framework. It shows that when fiscal policy is composed of heterogeneous instruments current purchases, public investment and transfers to different households the aggregate variable G is sufficient for output analysis only under a restrictive gradient condition: all instruments must have identical marginal effects on output. The paper proves this condition, derives composition weighted multipliers, identifies aggregation bias and extends the open economy IS LM BP model to incorporate fiscal composition, public capital, debt dynamics and risk-premium effects. A reproducible computational exercise with symbolic checks, derivative tests, accounting identities, adversarial counterexamples, sensitivity sweeps, Monte Carlo simulations and stress tests confirms the internal consistency of the argument. The contribution is methodological: IS LM BP remains useful as a compact equilibrium framework, but fiscal policy analysis requires vector-valued instruments and state-contingent multipliers rather than a single homogeneous spending variable.