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I understand the question may come across broad, I am new to government economics, but I am looking for a somewhat textbook answer. I hope you can make a rational guess, if the question seems odd, as to what I am asking.

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A budget surplus simply means that the government received more revenue than planned expenses for a given period, usually a year. A negative debt to GDP ratio would mean that a country has negative debt or a country has a negative GDP, which isn't really possible. Many economic reports use the term negative growth instead of shrinking/reduced and its possible you confused negative growth of GDP or debt to GDP ratio. Negative growth of GDP would generally be a bad thing as that means the economy is smaller. Negative growth of the debt to GDP ratio is generally good, as it indicates a country is more likely to be able to take on debt at more favorable terms.

A budget surplus doesn't mean that total debt was reduced, for example there was a budget surplus in the U.S. under Clinton but the total debt from the first day of the surplus to the last still increased. A budget surplus only means that more revenue was received than anticipated.

A negative debt isn't really possible with standard accounting. Generally when you are owed money it is considered an asset, though it could be called negative debt so if a country is owed more than it owes others that could be a negative debt.

A negative GDP would mean that the total value of everything a country produced was less than 0 which is impossible. A continually shrinking GDP puts a country into depression and things will either get better or there will be war and anarchy long before GDP gets to 0.

These two things are only loosely related. A continued budget surplus would reduce the debt to GDP ratio, but would be unlike to make it go negative. Budget surpluses are usually a sign that there is a larger than expected growth in GDP which will reduce the debt to GDP ratio by making the denominator bigger, but it doesn't affect the numerator at all.

  • I think a budget surplus does imply that total debt is reduced. On the other hand, it might not decrease the overall amount of debt relative to the GDP (because the GDP is changing as well) and a primary budget surplus does not imply a reduction of the debt if the government is forced to borrow money to pay interests and roll-over its pre-existing debt. Also I don't think your description of a negative GDP makes sense and a continued budget surplus does not necessarily reduce the debt to GDP ration (again, because the GDP is changing too). – Relaxed Sep 29 '15 at 12:07
  • Finally, the debt-to-GDP ratio can be reduced with moderate deficit, without ever having a balanced budget or a surplus (there is a name for this strategy that I can't recall at the moment). – Relaxed Sep 29 '15 at 12:10
  • @Relaxed a budget surplus has no real bearing on the total debt see this question with US specific examples. The debt to GDP ratio can be increased or decreased in many ways so long as the gdp grows faster than the debt, which is possible with a deficit or a surplus, but a surplus is more likely to indicate GDP increaseing faster than debt. – Ryathal Sep 29 '15 at 13:21
  • My point wasn't at all related to all this, I was only speaking of the nominal debt. I obviously agree with all the points Lennart makes but if you want to highlight the role of inflation or the size of the debt relative to GDP, then you ought to be more careful with the terminology. – Relaxed Sep 29 '15 at 13:36
  • But actually you are right, while a deficit does imply issuing new debt, a surplus has no direct bearing on the total debt, even in nominal terms, which does also contradict your statement about the effect of a continued budget surplus. You still need to correct the other inaccuracies I pointed out too. – Relaxed Sep 29 '15 at 13:40

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