Since even before Arthur Laffer drew his curve on a napkin, Republicans and Democrats have been having the same fight about taxes and growth. Republican politicians insist that tax cuts “pay for themselves,” increasing receipts by goosing economic growth. Democrats and virtually all economists say they’re wrong. Today, this very dispute animates the showdown between Republicans and Democrats over whether to include any tax increases in the long-term plan to reduce the deficit. But there are a few cases where tax cuts have arguably raised receipts. These cases are instructive, as they are so specific and so rare.

Let’s look at three. First, back in the 1920s, Treasury Secretary Andrew Mellon pushed Congress to enact a series of tax cuts. The U.S. dropped the top marginal income-tax rate from 73 percent to 25 percent. Tax receipts from the wealthiest Americans rose. According to Treasury data, income taxes paid by Americans making more than $100,000 per year increased from $302 million to $714 million between 1922 and 1928, with the rich’s share of income taxes paid rising from 35 to 61 percent.

Second, Kennedy-era income tax cuts brought the top marginal rate from an eye-watering 91 percent down to a still-eye-watering 70 percent in 1964. The wealthiest earners paid more tax after the tax cut, some say, even though the rate dropped 21 percentage points. An analysis by Laffer showed, for instance, that in 1965 people making more than $100,000 a year paid $3.76 billion in taxes, versus the $2.1 billion forecast under the higher rate. A few economists say that Ronald Reagan’s income-tax cuts, which dropped the top bracket’s rate to 50 percent, had a similar effect. Berkeley economist Brad DeLong, for instance, writes, “Arthur Laffer is probably right at the top end: reducing the top tax rate from 70 percent to 50 percent is probably a revenue gainer and surely not much of a loser.”

Third, we look abroad. In the 1990s, Ireland’s parliament enacted legislation that took certain corporate income tax rates down to 12.5 percent, one of the lowest rates on earth. Receipts climbed. The country, in its “Celtic Tiger” boom period, rapidly became richer. Corporate tax revenues jumped from less than 2 percent of GDP to more than 3 percent of GDP.

In all three cases, the tax cuts likely helped to increase tax receipts. How do lower taxes raise the amount the government takes in? Three answers are commonly given. First, tax cuts encourage businesses and individuals to be more honest about their earnings. Rather than hiding income, taxpayers just fess up and pay their share. Second, lower taxes encourage businesses and individuals to move money from lower-productivity, tax-free investments and shelters to more productive, taxable investments. Third, most importantly, perhaps, tax cuts goose growth. The government might be taking a smaller piece of the pie, but the tax cuts make the pie bigger. (In Ireland’s case, of course, there’s a fourth: The country became a kind of tax haven.)

The problem, according to most economists, is that Republicans now apply that dogma to all taxes, in all situations, even though there are few times when tax cuts actually pay for themselves. And even the case studies that do argue for supply-side economics are more ambiguous than they seem at first blush.

Both the Kennedy and Mellon tax-cut packages actually lowered overall revenue, relative to a baseline where the tax cuts did not happen. They just increased some receipts from richer families. Take a Congressional Budget Office analysis of the Kennedy-era cuts. No studies “showed that the increased economic activity generated by the tax cut raised revenues and lowered countercyclical transfer payments enough to make the tax-rate reductions self-financing,” it wrote in 1978. “Instead, the models showed a net increase in the federal deficit, after three years, of $5 billion to $13 billion,” versus models where the tax cuts never took effect. Shorthand: The tax cuts did pay for themselves a little bit by inducing growth, but not nearly enough to pay for themselves entirely.

Moreover, economists stress that tax cuts (and increases, for that matter) hardly work in a vacuum to bring about changes in receipts. Income-tax payments tend to naturally increase year-on-year because of population growth, GDP growth, and inflation. Monetary policy, government spending, and the business cycle also have a major impact. Thus, showing causation becomes a tricky exercise when it comes to taxes. Receipts often climb after tax cuts, but not necessarily because of them.

The Irish case also offers little support for the idea that tax cuts always pay for themselves by goosing growth. The cut in the corporate tax rate did not aid Irish companies’ bottom lines so much as it attracted extraordinary amounts of foreign capital. International firms like Pfizer relocated their European headquarters to the country to take advantage of the low tax rates. All those new companies contributed to an expanded corporate tax base. (Now, Ireland, suffering from crippling debts, is scared to raise the tax rate, which might encourage the companies to leave.)

In short, those who say that every tax cut pays for itself are simply wrong. President Bush, for instance, insisted, “You cut taxes, and the tax revenues increase.” GOP presidential hopeful Tim Pawlenty thinks the same (but adds a wan caveat): “As people look back to the historical examples, there’s been other chapters where tax cuts have been enacted, and almost always they raise revenues if you just isolate the effect of the tax cuts.” Sorry, governor. A few examples hardly prove the rule.