"Is high public debt harmful for economic growth?"

 VOX:

It ain’t what you don’t know that gets you into trouble. It’s what you know for sure that just ain’t so.
-- Mark Twain

Do high levels of public debt reduce economic growth? This is an important policy question. A positive answer would imply that, even if effective in the short-run, expansionary fiscal policies that increase the debt-to-GDP ratio may reduce long-run growth, and thus partly (or fully) negate the positive effects of the fiscal stimulus.

Most policymakers do seem to think that debt reduces growth. This view is in line with the results of a growing empirical literature which shows that there is a negative correlation between public debt and economic growth, and finds that this correlation becomes particularly strong when public debt approaches 100% of GDP (Reinhart and Rogoff 2010a, 2010b; Kumar and Woo 2010; Cecchetti et al. 2011).

Debt and Growth - What Causes What?

Correlation, however, does not imply causation. The link between debt and growth could be driven by the fact that it is low economic growth that leads to high levels of public debt (Krugman 2010).¹ Establishing the presence of a causal link going from debt to growth requires finding what economists call an ‘instrumental variable’.²
 
In a new paper (Panizza and Presbitero 2012), we propose a novel instrument variable that allows us to reject the notion that debt causes slower growth in OECD countries. We do confirm the oft-noted negative correlation between debt and growth, but show that debt does not have a causal effect on growth...

To answer the question "Do high levels of public debt reduce economic growth?" we follow the econometric procedure of trying to reject the proposition that “debt has no growth effects”. Our research shows that this proposition cannot be rejected, so it may well be that it is true. We cannot, however, be sure. Think of a murder trial where the jury finds the man has not been proven guilty “beyond a reasonable doubt”. This certainly suggests that he is innocent, but establishing innocence is not what the trial was about, so technically, we cannot claim that the jury declared him innocent.
Indeed, none of the papers in the literature on debt-growth links can make a strong claim the debt has a causal effect on economic growth.

In this light, we refer readers back to Mark Twain’s wisdom. There is a value in assessing the degree of our economic ignorance.