金融危機爆發後總會相應地產生各種債務——債務之多或許需要幾代人來償還。英國《金融時報》與世界貨幣基金組織（IMF）一起開發了一種關於一系列的因素是如何影響一個國家債務的交互式工具。數據以及預測是基於IMF最新的世界經濟前景及其可持續性債務分析模型。
實際GDP增長率
每年根據通貨膨脹調整後的GDP增長率。所以，如果一個國家的名義GDP是5%，但是通貨膨脹率為4%，那麼該國的實際增長率大約為1%。或者，如果一個國家正在遭受通貨緊縮，價格一年内下降了2%，但是該國的經濟仍然實現了名義上的1%增長，那麼該國的實際GDP增長率大約為3%。
有效的實際利率
根據通貨膨脹調整後，用於償還國家總債務的平均利率。如果一個國家平均每年償還4%的總債務，但是價格水平當年下降了1%，那麼有效的實際利率為5%。但是如果該國的通貨膨脹為10%，那麼有效的實際利率為-6%。
基礎平衡預算
平衡預算，扣除了淨利息，是GDP的一部分。那麼，如果政府的財政赤字增長率為3%，但是只有2%GDP用於緩解赤字，那麼基本平衡預算是-1%。
實際匯率上升
實際匯率衡量一個貨幣相對於那些主要交易貨幣對的價值，並會根據國家不同的物價水平相應的調整。匯率的上升或下降會影響其以外國貨幣計價的債務價值。
外幣債務份額
一些國家基本上只借貸本國貨幣，而另外一些國家由於自己金融市場不夠發達，則更依賴於以國外貨幣（比如美元）計價的貸款或債券。外幣所占份額越大，匯率對該國的總借貸價值影響越明顯。
扇形圖表示國債與基準線之間的可能偏差，它是基於一個國家的主要宏觀經濟變量的歷史偏差得出。這些變量包括:GDP實際增長率（g），有效的實際利率（r），基礎平衡預算（pb），實際匯率的變化（z），以及國債中的外匯份額（s）。這些變量對國債的影響可以用關系式表示：
dt = dt − 1 × (1 + rt) ÷ (1 + gt) × ((1 − st − 1) + s t − 1 ÷ (1 + zt)) − pbt
假定關鍵變量遵循基於歷史平均數、偏差以及協方差的聯合正態分佈，並從中隨機地生成可能的國債路徑，得出基準線的扇形圖。註：由於沒有得到IMF關於實際匯率以及國債的外匯市場份額的預測，因此，基準線的零變化是與IMF關於國債基準線的預測是一致的。
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.
本文翻譯由兄弟財經提供
文章來源：http://www.ft.com/ig/sites/2014/debt-to-gdp-ratio/#usa