José Ursúa and Dominic Wilson of Goldman Sachs are out with a big report examining the always controversial linkages between high public sector debt and slow growth.

Their work builds off the famous research of the famous work Carmen Reinhart and Kenneth Rogoff, who have argued that when debt-to-GDP crosses 90% in a given country, growth tends to slow, and that that alone is a reason to watch this metric.

Ursúa and Wilson have actually pushed the research even further into their note, looking at more countries, including emerging markets and developed. And the end result is that the relationship between growth and debt levels is very shakey indeed.

First, they do find that there's a relationship between debt and slower growth, but there's not much you can reveal from that. For one thing, there have been periods where developed markets saw strong growth coming off a level of high debt, most notably the US after WWII. In general, most developed markets only have seen high debt levels after wars, which makes the recent period quite unusual.

What's more, the current period of slow growth in developed markets comes after a period of financial crisis, further muddying the link between debt and growth.

Perhaps the more important conclusion from Goldman is that there's no evidence that if you trigger a certain line, that risks increase exponentially. In fact, the relationship is pretty linear across all examples.

So how does higher debt translate to slower growth?

Well, the primary result is somewhat circular:

There are several reasons why high levels of public debt may be associated with lower growth outcomes. The first is simply that at some point debt needs to be repaid. After periods of significant debt accumulation, fiscal consolidation will usually be needed to ensure that the debt path is sustainable. As we have shown elsewhere, fiscal consolidation tends, on average, to be a drag on growth. So the price for delivering sustained tighter fiscal policy may be a period where growth is weaker.

Got that? The first reason debt slows growth is that simply... when debt gets high, countries cut spending, and the cutting spending slows growth.

That much is clear, but then after that all they conclude is possible conjecture, and weak correlations.

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