Yes, the direction was created by ignoring swathes of contrary data and arbitrarily weighting the data that was included. The paper was unworthy of publication in a credible journal. Just correcting the latter eliminates their result, while the former would probably suggest the reverse effect.
I'm not sure where you're getting this, but that's absolutely untrue.
As luck would have it, their coding errors mostly cancelled each other out; fixing them changed their conclusion from growth of -0.1% in high-debt countries to 0.2%; an insignificant change.
As for the weighting chosen, Reinhart and Rogoff chose a fairly standard weighting which - as it turns out - has some flaws. In particular it makes their conclusion highly sensitive to the experience of NZ (which had terrible growth during the brief period it had high debt), which is - admittedly - problematic. But their chief critic suggests an unusual weighting which is subject to the precise same flaws except in reverse. By weighting each year equally, Herndon's conclusions are dominated by the results of Greece (which ran debts for year after year will little result). Than sensitivity is also problematic, and the inherent correlation of debt loads in sequential years raises questions about the meaningfulness of their results.
Professional economists are now debating the question of the best weighting, but if anything Reinhart and Rogoff seem to have the better argument so far.
In short: Their errors did not eliminate their result. Even changing weighting did not eliminate the result (much less reverse it - that would mean more debt leads to higher growth; a simply absurd result!). And in any case, the method they chose has strong arguments in its favour.
Negative growth to positive is a change in direction, no?
How is treating nineteen years of British data as having the same weight as one year of NZ data a "fairly standard weighting"? Britain is far larger in population on top of everything else.
"So what do Herndon-Ash-Pollin conclude? They find "the average real GDP growth rate for countries carrying a public debt-to-GDP ratio of over 90 percent is actually 2.2 percent, not -0.1 percent as [Reinhart-Rogoff claim]." [UPDATE: To clarify, they find 2.2 percent if they include all the years, weigh by number of years, and avoid the Excel error.] Going further into the data, they are unable to find a breakpoint where growth falls quickly and significantly."
2.2 vs -0.1 — you're only out by an order of magnitude.
As you say, weighting by number of years is also a problem. If you weighted the values by population or size of economy ("fairly standard weighting") I suspect the results would shift again but be biased in favor of more recent figures (economies and populations are bigger over time).
The figure was negative 0.1 percent (contraction) vs 2.2 percent (growth). Furthermore, Reinhart and Rogoff were careful to not link correlation with causation. Neither should we.
"Impact" implies causation. Low growth, for any reason, would lead to a higher ratio of debt to GDP. The original (erroneous) results of this study suggested that there was a point at which the relationship between the two changed.
