Until yesterday, politicians who wanted to raise taxes and cut government spending frequently cited a 2010 paper by Carmen Reinhart and Kenneth Rogoff called "Growth in a Time of Debt." The paper implied that high public indebtedness leads to slower economic growth.

Yesterday, it was revealed that the authors' methodology, choice of data and competence with the Microsoft Excel spreadsheet were all found wanting. When it comes to policymaking, this news changes very little: the Reinhart-Rogoff paper was always a flimsy justification for fiscal austerity.

Reinhart and Rogoff never explicitly said that high levels of public debt retard economic growth. Instead, the professors merely identified a weak correlation between the two variables.

Their paper also refrained from addressing some important questions: How specifically does public indebtedness affect economic growth, if at all? Are countries with their own currency, including the U.S., the U.K. and Japan, fundamentally different from those without, such as members of the euro area? How should countries near the magic threshold of 90 percent public debt to GDP behave in order to maximize long-term growth?

Politicians -- particularly those with an atavistic fear of government budget deficits -- rarely grasped these subtleties. Regrettably, the professors did not overexert themselves correcting misinterpretations of their work, so advocates of tax increases and spending cuts eagerly cited Reinhart and Rogoff for years. It turns out, though, that even someone who uncritically accepts the implications of "Growth in a Time of Debt" shouldn't support fiscal tightening when the economy is weak.

The reason is that the policies of austerity don't affect the ratio of public debt to national income in a straightforward way. That ratio has two parts: the level of income and the level of debt. Fiscal austerity affects both. When the economy is weak, the negative effect of tax hikes and spending cuts often outweighs the reduced level of borrowing. In other words, fiscal tightening actually increases, rather than decreases, the level of public indebtedness. Similarly, tax cuts and spending increases can lower the ratio of public debt to national income under certain circumstances.

This point was cleverly made by the International Monetary Fund in its October 2012 World Economic Outlook. In box 1.1, Olivier Blanchard, the IMF's chief economist, and Daniel Leigh looked at the "fiscal multiplier" that relates changes in government spending and taxation against changes in overall economic output. The IMF and national governments forecast economic activity, public debt-to-GDP ratios and budget deficits on a regular basis. Those forecasts all require assumptions about the size and direction of the fiscal multiplier. Blanchard and Leigh compared these forecasts against what actually happened and found that "the negative short-term effects of fiscal cutbacks have been larger than expected because fiscal multipliers were underestimated."

Those forecasting errors had real policy implications. Overly optimistic projections were regularly used to justify controversial -- and ultimately counterproductive -- policies in the U.K. and the euro area. Those policies failed to produce the desired results because, as Blanchard and Leigh explain, "the multipliers used in generating growth forecasts have been systematically too low since the start of the Great Recession."

That finding explains why Reinhart and Rogoff never made a strong case for austerity. The easiest way to avoid crossing some magic threshold of public debt to GDP is to avoid raising taxes and cutting spending when the economy is weak. In other words, serious believers in Reinhart and Rogoff should have been the strongest opponents of fiscal tightening.

(Matthew C. Klein is a contributor to the Ticker. Follow him on Twitter.)