It's rare for the whole economics press to dive into a single academic paper the way it did with Kenneth Rogoff and Carmen Reinhart's "Growth in a Time of Debt" this week. But lost in the debate about how consequential the two's Excel error — and the paper's causality problems — is the actual question they purported to answer: What do we actually know about the relationship between austerity and growth?

So where does Reinhart-Rogoff stand now?

Kenneth Rogoff (Reuters) and Carmen Reinhart (Bloomberg).

Reinhart-Rogoff is, for now, in question at the very least, as the changes identified by researchers at the University of Massachusetts-Amherst indicate that there's little evidence that there's a debt tipping point, even if there's a relationship between debt and growth. The researchers left out a number of countries, including Belgium and late-1940s Canada, Australia and New Zealand, that had high debt burdens and low growth, and made some strange decisions around weighting. Once those are corrected for, it's not clear the relationship they identified remains.

Moreover, it's still not clear that that paper shows that debt causes slow growth as opposed to the other way around. Arindrajit Dube, also an economist at UMass Amherst, has a great post demonstrating that high debt loads are better correlated with slow growth before the debt gets that large as opposed to after, indicating that it's the slow growth causing the debt and not the other way around:

Dube rr
Source: Arindrajit Dube

The left chart correlates debt-to-GDP ratios of a given year to the GDP growth rates of the next three years. If debt is causing slow growth, there should be a strong relationship. But except at the very low end, there isn't. Meanwhile, the right chart correlates debt-to-GDP ratios of a given year to GDP growth rates of the previous three years. There's a very strong relationship, indicating that slow growth causes high debt and not the other way around.

But is there evidence that austerity would help right now?

IMF chief economist Olivier Blanchard admitted that the fund had underestimated the size of the fiscal multiplier. (Stephen Jaffe/IMF)

Especially during economic downturns, this question quickly becomes about the size of a key economic variable, namely the fiscal multiplier. That's the amount by which GDP changes when government spending or revenue change. If the multiplier is 1, then a $1 increase in spending or decrease in revenue will increase GDP by $1. If it's negative, then the program is actually counterproductive. If it's positive but under 1, then tax cuts and spending help growth, but grow the economy less than they cost the government. If it's over 1, then we're getting more in economic output than we're spending in lost revenue or increased outlays.

For questions about whether or not economic stimulus works, the key question, then, is what's the multiplier? It's pretty clear that it has been significantly positive in the U.S. and other developed countries since the downturn. The IMF, for instance, thought the multiplier in Europe was 0.5 before the crisis hit, but has since admitted it was wrong and that the multiplier was more like 1.5. So there isn't really much doubt about whether fiscal stimulus could be used to boost growth in the economic conditions of the past few years. According to most of the literature on the American Recovery and Reinvestment Act, the fiscal stimulus approach worked.

The corollary of that finding is that in the kind of weak economy that gives you a high multiplier, budget cuts and tax increases hurt growth in the short run. What's worse, they might even add to the debt burden. Take the IMF's estimate of a multiplier of 1.5. That means that if you cut spending by 1 percent of GDP, the economy would shrink by 1.5 percent as well. And because the economy is shrinking by more than the debt burden is growing, the debt-to-GDP ratio would actually go up. Even if you think that high debt-to-GDP ratios cause slower growth, the answer may not be short-term austerity.

It's for reasons like this that economists such as Larry Summers and Brad DeLong have argued that the stimulus package will end up paying for itself. All the economic growth it generated means more tax revenue and less welfare spending, and perhaps enough to pay for the whole shebang.

What about the long run?

Berkeley economist Christina Romer, who along with her husband David has pioneered a new method of identifying fiscal contractions. (Charles Dharapak/Associated Press)

This was the question Reinhart-Rogoff sought to answer. But now we need to look for other evidence.

The other main paper arguing that low debt leads to high growth is Alberto Alesina and Silvia Ardagna's "Large Changes in Fiscal Policy: Taxes Versus Spending." They looked at 107 cases of fiscal consolidation and isolated 26 examples of "expansionary" austerity, or austerity that lead to high growth relative to the large G7 economies.

Arjun Jayadev, an economist at UMass Amherst (yep, them again), and friend-of-the-blog Mike Konczal wrote a paper critiquing Alesina and Ardagna in 2010. First, Jayadev and Konczal note that Alesina and Ardagna are looking more or less exclusively at countries that  have pursued austerity during good economic times. "The first thing to note is that the average real growth rate in the year preceding is 4.1% across all episodes," Jayadev and Konczal write. "In other words, their examples of successful consolidation were, on average, growing strongly the year before the year of adjustment."

So what effect did adopting austerity have on these countries? Well, first off, six of the 26 countries cut during economic downturns, and all but one of those had slower growth after austerity than before. That's consistent with what we know from multiplier estimates. Setting those aside, there remain 20 cases of austerity during good economic times. Among those twenty countries, growth was on average 1.8 points higher in the three years following consolidation than it was the three years before. In three of those, growth was lower after austerity than it was before.

Does that mean that austerity is a good idea during economic expansions? It's hard to say. The 1.8 point average comes from the 20 cases of expansion-era austerity that Alesina and Ardagna have already identified as "successful." It's unclear if the result would hold up if you averaged the consequences of austerity throughout their database. What's more, Alesina and Ardagna don't really have much in the way of controls for other factors which may drive austerity. That means that some of the economic success following austerity programs may not be attributable to those programs themselves.

A better method was pioneered in a 2010 paper by Berkeley's Christina and David Romer (the former of whom, you'll recall, was Obama's first Council of Economic Advisors chair). The Romers use historical data to isolate cases where policymakers have chosen to adopt austerity as a means of reducing the debt load, rather than for any other reason.

Their paper is mainly focused on tax changes, but a follow-up IMF working paper by Jaime Guajardo, Daniel Leigh and Andrea Pescatori took a broader look. They concluded that a 1 percent reduction in spending or increase in taxes reduces real GDP, on average, by 0.62 percent. That suggests that it may be possible to reduce the debt burden through austerity, but that the effect on growth is, again, negative on average. Moreover, their results held up even in countries with heavy debt burdens, suggesting that this is a pretty universal effect of austerity.

Another recent IMF paper by Nicoletta Batini, Giovanni Callegari and Giovanni Melina confirms Guajardo et al's findings. "Spending cuts initiated during recessions are contractionary over the entire simulation horizon," which is to say in both the short and long run, they write. "However, in Japan, the United States and to a lesser extent in the Euro Area, spending cuts that begin during expansions are contractionary only in the short run, becoming expansionary in the long run."

By contrast, tax increases decrease growth in the long run across their sample. Going slowly, rather than cutting all at once, helps too. "Frontloading fiscal consolidations tends to have harsher and more protracted adverse effects on output, without accelerating the drop in the debt-to-GDP ratio relative to a more evenly-distributed consolidation," they write.

To sum up: There's basically no evidence that fast austerity programs, or ones undertaken during economic downturns, are even good at reducing the debt burden. It's very clear they're bad for growth. Austerity through spending cuts may help growth in the long run, but so do a lot of things, and if those cuts are to things known to boost growth, like early childhood education or research, they could be counterproductive. But for the time being, austerity is the wrong prescription for advanced economies.