金融危机爆发后总会相应地产生各种债务——债务之多或许需要几代人来偿还。英国《金融时报》与世界货币基金组织（IMF）一起开发了一种关于一系列的因素是如何影响一个国家债务的交互式工具。数据以及预测是基于IMF最新的世界经济前景及其可持续性债务分析模型。
实际GDP增长率
每年根据通货膨胀调整后的GDP增长率。所以，如果一个国家的名义GDP是5%，但是通货膨胀率为4%，那么该国的实际增长率大约为1%。或者，如果一个国家正在遭受通货紧缩，价格一年内下降了2%，但是该国的经济仍然实现了名义上的1%增长，那么该国的实际GDP增长率大约为3%。
有效的实际利率
根据通货膨胀调整后，用于偿还国家总债务的平均利率。如果一个国家平均每年偿还4%的总债务，但是价格水平当年下降了1%，那么有效的实际利率为5%。但是如果该国的通货膨胀为10%，那么有效的实际利率为-6%。
基础平衡预算
平衡预算，扣除了净利息，是GDP的一部分。那么，如果政府的财政赤字增长率为3%，但是只有2%GDP用于缓解赤字，那么基本平衡预算是-1%。
实际汇率上升
实际汇率衡量一个货币相对于那些主要交易货币对的价值，并会根据国家不同的物价水平相应的调整。汇率的上升或下降会影响其以外国货币计价的债务价值。
外币债务份额
一些国家基本上只借贷本国货币，而另外一些国家由于自己金融市场不够发达，则更依赖于以国外货币（比如美元）计价的贷款或债券。外币所占份额越大，汇率对该国的总借贷价值影响越明显。
扇形图表示国债与基准线之间的可能偏差，它是基于一个国家的主要宏观经济变量的历史偏差得出。这些变量包括:GDP实际增长率（g），有效的实际利率（r），基础平衡预算（pb），实际汇率的变化（z），以及国债中的外汇份额（s）。这些变量对国债的影响可以用关系式表示：
dt = dt − 1 × (1 + rt) ÷ (1 + gt) × ((1 − st − 1) + s t − 1 ÷ (1 + zt)) − pbt
假定关键变量遵循基于历史平均数、偏差以及协方差的联合正态分布，并从中随机地生成可能的国债路径，得出基准线的扇形图。注：由于没有得到IMF关于实际汇率以及国债的外汇市场份额的预测，因此，基准线的零变化是与IMF关于国债基准线的预测是一致的。
A world of debt
Financial crises frequently leave a wreckage of debt in their wake — debts that can take generations to pay off. The last one was no different.
Together with the International Monetary Fund, the Financial Times has developed an interactive tool that shows how a country’s debts rise and fall depending on a variety of factors. The data and projections are based on the IMF’s latest World Economic Outlook, and the model on the fund’s own debt sustainability analysis tool.
Real GDP growth rate (%)
Change in gross domestic product year on year, adjusted for inflation. So if a country’s nominal GDP is growing at 5%, but inflation is running at 4%, the real growth rate is approximately 1%. Or if a country is suffering from deflation and prices are falling 2% a year while the economy still manages to expand 1% in nominal terms, the real growth rate is approximately 3%.
Effective real interest rate (%)
The average interest rates paid on a country’s total debts, adjusted for inflation. If a country pays an average of 4% on its total borrowings, but price levels are falling by 1% a year, the effective real interest rate is 5%. But if the same country’s inflation is running at 10%, the effective real interest rate is minus 6%.
Primary budget balance (%)
The budget balance as a percentage of gross domestic product, excluding net interest payments. So if a government is running a budget deficit of 3% of GDP, but 2 percentage points of that goes only to service its debts, then the primary balance is minus 1%.
Real exchange rate appreciation (%)
The real exchange rate measures the value of a currency against those of its major trading partners, and adjusts for the different price levels in countries. Currency slumps or appreciations will have an impact on the value of debts denominated in foreign currencies.
Foreign currency debt share (%)
Some countries borrow almost exclusively in their own currencies, while others are more dependent on loans and bonds denominated in foreign currencies like the dollar, due to under-developed local financial markets. The bigger the share of debt denominated in foreign currency, the greater the impact of exchange rate changes on total debt valued in local currency. NB. For real exchange rate and foreign exchange share of public debt, IMF projection is not available and therefore baseline zero change refers to no change with respect to path implicit in IMF baseline debt projection.
The fan chart shows possible deviations of public debt from the baseline projection, based on historical variations in the country’s key macroeconomic variables (real GDP growth (g), effective real interest rate (r), primary balance (pb), the change in real exchange rate (z)), as well as the share of public debt in foreign currency (s). These variables influence the evolution of public debt as expressed by the following equation:
dt = dt − 1 × (1 + rt) ÷ (1 + gt) × ((1 − st − 1) + s t − 1 ÷ (1 + zt)) − pbt
The key variables are assumed to follow a joint normal distribution generated from their historical means, variances, and covariances. Random draws from the joint normal distribution generate alternate debt paths whose deviations from the baseline constitute the ‘fan’ in the chart.
本文翻译由兄弟财经提供
文章来源：http://www.ft.com/ig/sites/2014/debt-to-gdp-ratio/#usa