公共债务增长的规模不变性质
Scale invariant properties of public debt growth
摘要：
公共债务是定量描述一国经济的重要经济变量之一。由于即使是像政府这样大的机构（如冰岛）也面临破产风险，因此应严格控制国家债务相对于国家财富的比例。此外，消除世界极端贫困的问题与对极端贫困债务国的研究密切相关。我们分析了国家公共债务的时间演变，发现“收敛”：最初负债较少的国家增加债务的速度比最初负债较多的国家更快。我们还分析了公共债务与GDP的比率R，这是违约风险的代理，并用伽马分布近似概率密度函数P（R），这可以用来建立可持续债务的阈值。我们还观察到R的“收敛”：最初R较小的国家比最初R较大的国家更快地增加R。债务和R的比例关系有实际应用，例如《马斯特里赫特条约》要求欧洲货币联盟成员国保持R < 0.6。
英文摘要：
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.
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