A Krugman meme?

In Government Debt and Economic Growth (Economic Policy Institute, July 26, 2010) Josh Bivens and John Irons write:

The GITD threshold rests on a simple correlation of high debt levels with slower growth, but no evidence on causality is given. This is important given that contemporaneous causality is actually more likely to run in the opposite direction that what is claimed in the report. That is, causality is more likely to run from slow growth to high debt levels, and this alternative explanation is even supported in the GITD data.

In Not to Pile On, But…Correcting Reinhart and Rogoff (On the Economy, Apr 16, 2013) Jared Bernstein writes:

As I’ve written many times, riffing off of Bivens and Irons for one, if you mush everything together they way they do, you’re likely to get the causality backwards. You’ll convince yourself that higher debt leads to slower growth when it’s more often the opposite.

In Debt and Transfiguration (The Conscience of a Liberal, March 12, 2010) Paul Krugman wrote:

I’ve been going through this chartbook somewhat in tandem with rereading the recent Reinhart-Rogoff paper on debt and growth (subs. req.) — the one that’s being widely cited as evidence that bad things happen when debt goes above 90 percent of GDP...

What I think I’m seeing, although I haven’t tested this carefully, is that the causal relationship largely runs from growth to debt rather than the other way around. That is, it’s not so much that bad things happen to growth when debt is high, it’s that bad things happen to debt when growth is low.

This is definitely the case for the United States...

So, as I wrote before,

Paul Krugman argued against the view that a high level of debt causes problems in the economy. Inadequate growth, he said, makes debt appear excessive. He thinks the people who worry about the debt have cause and consequence reversed.

We see now that Josh Bivens and John Irons have the same idea, as does Jared Bernstein, and Arindrajit Dube, and probably many, many others.

I don't care. If you are evaluating the work of Reinhart and Rogoff, evaluating their analysis of Federal debt and its impact on growth, how are you going to deal with the fact that other debt has grown to be a far bigger number than Federal debt, and carries far greater cost?

Do you just assume it away with an implicit ceteris paribus?

The only way to deal with "other" debt is to consider it, in your studies of debt. If other debt is not constant -- and you know it is not -- then by ignoring it you invalidate your own study of central government debt.

In my simple view, the Reinhart and Rogoff study is completely invalid because it ignores debt other than central government debt. In everybody else's view, it seems the R&R study is great, except they got the causality wrong.

So, who has the better argument?