For the past five years, a fierce war of words and policies has been fought in America and other economically challenged countries around the world.

On one side were economists and politicians who wanted to increase government spending to offset weakness in the private sector. This "stimulus" spending, economists like Paul Krugman argued, would help reduce unemployment and prop up economic growth until the private sector healed itself and began to spend again.

On the other side were economists and politicians who wanted to cut spending to reduce deficits and "restore confidence." Government stimulus, these folks argued, would only increase debt loads, which were already alarmingly high. If governments did not cut spending, countries would soon cross a deadly debt-to-GDP threshold, after which growth would be permanently impaired. The countries would also be beset by hyper-inflation, as bond investors suddenly freaked out and demanded higher interest rates. Once government spending was cut, this theory went, deficits would shrink and "confidence" would return.

This debate has not just been academic.

Those in favor of economic stimulus won a brief victory in the depths of the financial crisis, with countries like the U.S. implementing stimulus packages. But the so-called "Austerians" fought back. And in the past several years, government policies in Europe and the U.S. have been shaped by the belief that governments had to cut spending or risk collapsing under the weight of staggering debts.

Over the course of this debate, evidence has gradually piled up that the "Austerians" were wrong. Japan, for example, has continued to increase its debt-to-GDP ratio well beyond the supposed collapse threshold, and its interest rates have remained stubbornly low. More notably, in Europe, countries that embraced (or were forced to adopt) austerity, like the U.K. and Greece, have endured multiple recessions (and, in the case of Greece, a depression). Moreover, because smaller economies produced less tax revenue, the countries' deficits also remained strikingly high.

So the empirical evidence increasingly favored the Nobel-prize winning Paul Krugman and the other economists and politicians arguing that governments could continue to spend aggressively until economic health was restored.

And then, last week, a startling discovery obliterated one of the key premises upon which the whole austerity movement was based.

An academic paper that found that a ratio of 90%-debt-to-GDP was a threshold above which countries experienced slow or no economic growth was found to contain an arithmetic calculation error.

Once the error was corrected, the "90% debt-to-GDP threshold" instantly disappeared. Higher government debt levels still correlated with slower economic growth, but the relationship was not nearly as pronounced. And there was no dangerous point-of-no-return that countries had to avoid exceeding at all costs.

The discovery of this simple math error eliminated one of the key "facts" upon which the austerity movement was based.

It also, in my opinion, settled the "stimulus vs. austerity" argument once and for all.

The argument is over. Paul Krugman has won. The only question now is whether the folks who have been arguing that we have no choice but to cut government spending while the economy is still weak will be big enough to admit that.

The discovery of the calculation error, after all, came only a few months after the United States voluntarily cut spending through a government "sequester." This sequester is hurting the U.S. economy, and it is also depriving American citizens of some basic services--like a fully staffed air-traffic control system--that most first-world countries regard as a given in a developed economy. And with America's government deficit already shrinking (thanks to the rollback of some tax cuts and a modest increase in taxes), it is now even clearer that the sequester did not have to be adopted.

Yes, at some point, the American government needs to come together and figure out a smart long-term plan for containing healthcare and military costs, which are the real budget-busters in our government spending. That long-term plan does not need to be adopted immediately, however.

And in the meantime, for the sake of the country, it would be nice if our government came together and agreed to restore full funding for basic services.