Will major economies be able to repay their debt? According to The Economist, lots of major economies are in debt to the extent of it consuming most of the countries' GDP. And the whole system almost seems to resemble a Ponzi scheme at a macro level. I'm sure this is a gross simplification of how things work and I'm no economist by any measure. But at some point, wouldn't the debt of these countries grow beyond the expectation that it will ever be paid off? How is it there is so much worldwide debt without the whole system ready to implode?
Whether a country's debt is sustainable is a difficult question to answer. Bohn developped a framework for answering this question and the cited paper is a summary of much of its findings.

Henning Bohn, 2005.
"The Sustainability of Fiscal Policy in the United States,"
CESifo Working Paper Series 
1446, CESifo Group Munich.

Bohn proposes to estimate a fiscal reaction function to model a country's fiscal policy. He concludes that for a country's fiscal policy to be sustainable, it is sufficient that its primary balance is a (linear) increasing function of its lagged debt-GDP .

$pb_{it}= \alpha_i + \beta_i d_{it-1} + \delta_i X_{it} \ \ \ \ \  \beta_i&gt;0$

($X_{it}$ is a vector of control variables)

There are however some problems with this framework. If for example does not exclude an ever increasing debt limit, which seems counter-intuitive. Some of these problems are resolved in Ghosh et. al. 2011 and non-linearities in a fiscal reaction function are added and they introduce the concept of fiscal space.

Atish R. Ghosh &amp; Jun I. Kim &amp; Enrique G. Mendoza &amp; Jonathan D. Ostry &amp; Mahvash S. Qureshi, 2011.
"Fiscal Fatigue, Fiscal Space and Debt Sustainability in Advanced Economies,"
NBER Working Papers 
16782, National Bureau of Economic Research, Inc.

Yet, there are still some drawbacks to this approach. Japan is a country that has almost reached its debt limit but financial markets doe no seem to response to this fact. Therefore this framework as evolved from estimating these fiscal reaction functions to stochastic debt simulation. Celasun, Debrun and Ostry wrote a seminal paper on this procedure.

Oya Celasun &amp; Xavier Debrun &amp; Jonathan David Ostry, 2006.
"Primary Surplus Behavior and Risks to Fiscal Sustainability in Emerging Market Countries: A &quot;Fan-Chart&quot; Approach,"
IMF Working Papers 
06/67, International Monetary Fund.

They for example calculate the probability that a country's debt-GDP ratio increases more than 10% in comparison to a baseline-year. But again, this does not answer some fundamental questions. If for example the indebtedness of a country does increase with 10% in 5 years, does this mean that fiscal policy was insustainable?

It should be clear now that determining the sustainability of a country's debt is difficult. In the end, it really all comes down to the fact that a country's fiscal policy is sustainable as long as institutions and individuals are willing to buy their debt instruments.

edit:
To answer your comment, I think the easiest concept to understand, it the one of fiscal space so I will try to explain that:

Assume a country's fiscal policy looks the following:

$pb_{t}= \alpha + \beta_1 d_{t-1}+ \beta_2 d_{t-1}^2 + \delta X_{it} $

In which $\beta_1&gt;0&gt;\beta_2$. This thus implies that a country's primary balance initially increases as debt increases to offset the debt accumulation but will decrease after a certain point, called fiscal fatigue. This fiscal fatigue implies a limit to the debt ratio a country could pay back. To see this, you have to look at the debt dynamics, (r-g) equals the interest rate-growth differential:
$\Delta d_t= (r-g) d_{t-1} -pb_t$

This equation explains how an increase in primary balance could counter debt accumulation. The debt limit, lets call it $d^m$ is the highest debt ratio for which the primary balance sufficies to hold the debt ratio constant. ($X_t$ is ignored):

$(r-g) d^m = pb= \alpha + \beta_1 d^m + \beta_2 d^{m2}$



After $d^m$, the primary balance will never be high enough to hold debt constant due to fiscal fatigue. Lenders to the government know this and thus will never buy debt securities after this point, causing a country to default.
 Fiscal space is now simply the difference between a country's current debt ratio and the debt limit and thus is a measure of the amount of fiscal maneouvrability a country has left before it will default.