GIDDY on debt, the aging country faces a troubling future.

By standard fiscal criteria, Japan is in worse shape than Greece. The Japanese government hasn’t balanced a budget since 1992 and runs one of the highest deficits on Earth. The stock of debt is eight times as high as annual tax revenue. The familiar ratio of debt/GDP has risen in 20 years from 80% to 243%, the highest level in the world. How did its public finances get so rotten?

**The Road to Ruin**

Debt dynamics depend on five things which, properly arranged, get you GIDDY: growth (g), inflation (i), debt (D), deficit (d), and yield (y). A short equation describes the relationship:

The formula says that this year’s debt/GDP ratio, Dt, is equal to last year’s, D_{t - 1}, multiplied by the term (*1 + y - g - i*), plus this year’s deficit (d_{t}).

The apparent causes of Japan’s debt explosion, then, are three. First, despite ground-low interest rates, economic growth plus inflation were even lower, so the term (*y - g - i*) was positive for most of the past two decades. The implicit interest rate has averaged 1.9% since 1993. Real GDP has increased a mere 0.9% a year, while the GDP deflator (a broad measure of prices) has fallen 1% per year. Deflation more than erased the gain in real output.

Second, the larger the debt balance, the harder it is to pay it off, as any credit card holder knows. That’s because debt itself, D, is multiplied by the term (*1 + y - g - i*). Even a small positive difference between the interest rate and nominal growth makes a significant impact, once debt gets as high as Japan’s.

And third is the primary fiscal deficit, d. If expenses exceed revenues the government must finance the gap by borrowing, which adds to debt. Japan has averaged a fiscal gap of 5.4% of GDP over two decades.

**Aging Weighs Down Public Finances**

At a deeper level, the debt problem has a demographic root: Japan’s population is aging and shrinking, fast.