  Public debt is one of the important economic variables that quantitatively
describes a nation's economy. Because bankruptcy is a risk faced even by
institutions as large as governments (e.g. Iceland), national debt should be
strictly controlled with respect to national wealth. Also, the problem of
eliminating extreme poverty in the world is closely connected to the study of
extremely poor debtor nations. We analyze the time evolution of national public
debt and find "convergence": initially less-indebted countries increase their
debt more quickly than initially more-indebted countries. We also analyze the
public debt-to-GDP ratio R, a proxy for default risk, and approximate the
probability density function P(R) with a Gamma distribution, which can be used
to establish thresholds for sustainable debt. We also observe "convergence" in
R: countries with initially small R increase their R more quickly than
countries with initially large R. The scaling relationships for debt and R have
practical applications, e.g. the Maastricht Treaty requires members of the
European Monetary Union to maintain R < 0.6.
