In case you missed this:
Kevin O'Rourke at the Irish Economy Blog has a succinct explanation of the findings:
The boom, not the slump, is the right time for austerity, by Kevin O’Rourke: Alan Taylor has a piece on Vox today that is a nice contribution to the debate on the output effects of austerity. That debate has largely been about the endogeneity of fiscal policy: the more you take this into account, the more contractionary austerity becomes. He and Oscar Jorda show that if you give less weight to episodes where the austerity/no austerity policy choice was more predictable (i.e. more endogenous) and more weight to episodes where the policy choice was less predictable (i.e. more exogenous) then you find that austerity was extremely contractionary in slumps. This does not mean that fiscal consolidation is never necessary, but that the time for consolidation is when times are good, not when times are bad. It would be nice if Austerians could display a similar recognition that context matters.