Joint Implementation of Fiscal Stimulus and NPL Resolution: A Formal Proof of Complementarity with International Evidence

This paper examines the complementarity between fiscal stimulus and non-performing loan (NPL) resolution in macroeconomic crisis management. Using a reduced-form IS relation and credit supply dynamics, the paper formally proves that the output gap is supermodular in fiscal stimulus and NPL resolution. This implies that joint implementation of both policies is superior to single-instrument strategies under standard conditions. Welfare analysis confirms that complementarity improves not only output stabilization but also social welfare. International evidence from OECD and IMF data shows that countries combining fiscal expansion with credit clean-up recovered faster, while those relying on only one instrument experienced prolonged stagnation. The study provides a diagnostic framework for policymakers, offering allocation rules, timing guidance under the Domar condition, and an empirical strategy to test the interaction effect. It highlights the risks of policy bias toward only NPL resolution, as in Japan’s post-bubble era, and supports integrated interventions as the normative benchmark in crisis management. Although the complementarity of fiscal stimulus and NPL resolution may appear “obvious” in hindsight, history shows that policymakers and media often failed to treat it as such in real time. Japan’s post-bubble stagnation illustrates how the absence of a formal proof allowed debates to devolve into false dichotomies—whether to prioritize fiscal expansion or financial clean-up—rather than recognizing their joint necessity. This paper therefore exists not merely to restate what seems self-evident, but to provide a rigorous theoretical and empirical shield against political hesitation and double standards. By formalizing the “obvious” and confronting it with historical evidence, the study ensures that future crises will not repeat the mistake of treating complementarity as optional or secondary. Even when a policy relationship appears “obvious,” history demonstrates that without a formal theoretical and empirical foundation it can be disregarded or distorted in practice. The Japanese post-bubble era showed how the absence of a rigorous proof allowed policymakers and media to frame the debate as a false choice, leading to prolonged stagnation. This paper therefore underscores that discussing what is taken for granted in a formal academic framework is not redundant but essential: only by codifying the “obvious” in theory and evidence can we prevent it from being altered or ignored in moments of crisis. In this sense, the study functions as a safeguard, ensuring that complementarity remains a binding principle rather than a fragile assumption. This demonstrates that even what is considered obvious must be debated and codified in academic form, because only then can it withstand the pressures of real-world policymaking. In this way, the paper affirms that formalizing the “obvious” is not optional but indispensable for preventing policy drift and ensuring intellectual integrity.