Debt-To-Pay-Debt Lemma: Lessons from Japan

Abstract

I propose and empirically test Debt-To-Pay-Debt Lemma, which posits that a significant portion of an entity’s current debt is allocated to servicing its previous period’s debt obligations. Japan, despite being categorized as a wealthy nation, ranks among the highest in public-debt globally. I test the lemma using autoregressive integrated moving average (ARIMA) modeling technique. I utilize World Bank quarterly time-series from 1990 to 2022. Dependent variable is Japan’s central government debt, total (% of GDP), while moving average (MA) and autoregressive (AR) components function as independent variables. Conditional least squares parameter estimate yields a statistically significant AR(1) coefficient of 0.75534, indicating that approximately 76% of Japan’s current-year debt is allocated to servicing previous-year debt obligations, thereby empirically validating Debt-To-Pay-Debt Lemma. ARIMA(1,1,1) diagnostics yield an adjusted R-squared of 0.652144, suggesting that the model explains 65.2% of public-debt variations. These findings underscore a self perpetuating nature of public-debt accumulation in Japan, challenging conventional perceptions of a looming debt crisis. I recommend re-thinking conservative fiscal policy frameworks by adopting adaptive, context-sensitive strategies that account for cyclical interplay between borrowing and debt servicing.