ASKED why he robbed banks, Willie Sutton, a hold-up artist of some accomplishment during America's Depression, answered simply: “Because that's where the money is.” Advanced economies that have piled up debts are eyeing their rich for similar reasons. The way to begin filling holes in the budget, many suggest, is by extracting more from those who have done best. This week Barack Obama proposed paying for new stimulus measures and deficit cuts by reforming the tax system to ensure that millionaires do not pay a lower tax rate than middle-class families.

Mr Obama's reform is based on the “Buffett rule”, so named after Warren Buffett, a folksy billionaire who publicly scorns a system that allows him to enjoy an effective tax rate that is less than his secretary's. A growing number of the rich appear to agree. Wealthy Germans and French have signed petitions in favour of higher taxes. Luca di Montezemolo, who sells Ferraris to many of them as chairman of the Italian sports-car company, told La Repubblica it was “right” for the rich to pay more. The broader public agrees. Even in tax-hating America, some two-thirds of voters support deficit-reduction plans that include higher tax rates for top earners.

New austerity plans are bowing in this direction. Italy's latest includes a special levy on those earning more than €300,000 ($410,000). France will ask for a similar “exceptional contribution” from those making over €500,000. A sense of fairness and political reality is driving the trend. The rich can shoulder a larger share of the burden of fixing government finances, it is argued, and can be asked to do so without doing much harm to growth.

A dangerous soaking

But there is an alternative view: that a soak-the-rich strategy is misguided. History suggests that low taxes on the rich encourage investment and growth. With many economies weak, now is not the time to saddle capitalists with greater taxes, particularly since the rich are among society's most mobile: the footloose wealthy will simply move, taking their taxes with them. This debate is particularly fiery in Britain, always fearful for its London financial centre, and a 50% top marginal tax rate which came into effect in 2010. A number of economists believe it is doing lasting damage to the British economy. Others dispute the charge.

With debt burdens so high, spending cuts are inevitable. But these can only do part of the job. Reduced spending can hit lower-income households hard. Political resistance to spending-only austerity is high and rising. Voters will push for tax increases on the rich. So, it is important to understand what the effects of that would be. The debate is passionate and often ideologically driven. Three questions are crucial: What share of tax do the rich actually pay? What has happened to this tax burden over recent decades? And what does the evidence suggest about how the rich respond to changes in taxation?

The rich pay a substantial share of taxes across the developed world, and this share has risen in recent decades. According to the OECD, a think-tank, the top 10% of earners contribute about a third of total tax revenues—28% in France, 31% in Germany and 42% in Italy. Rich Britons pay about 39% of total taxes while America's wealthiest households contribute a larger share to government than in any other OECD country, at 45%. Looking just at income tax, the share paid by the top 1% of earners in America rose from 28% in 1988 to 40% in 2006, in Britain it rose from 21% in 1999 to 28% this year. America's greater dependence on its rich is due in part to their good fortune. As of 2007, the total earnings of the top 1% equalled 74% of all taxes paid, up from 24% in 1976. The rich are a juicy target because their taxes could conceivably cover far more of the budget than before.

Very little of the rising share of tax payments from the rich can be traced to changes in rates. On the contrary, tax systems are far easier on top earners than was true a few decades ago. Working out the tax burden, to answer the second question, is no simple matter. Top earners often pay tax on personal and capital income, as well as social insurance and excise taxes. Corporate tax changes largely affect owners of capital, but are also borne to some extent by workers. General trends for labour and capital-income rates are clear, however. The rich face lower rates than they used to.

In the late 1970s top marginal income-tax rates of 60-90% were not uncommon across advanced economies. But with the dawn of stagnation, academic economists favoured reduced government intervention, and lower, flatter tax systems gained ground. Tax burdens on the rich have fallen (see chart 1). Across the OECD the average top marginal rate fell by nearly 11 percentage points. The trend was particularly pronounced in America and Britain. Ronald Reagan campaigned by touting tax cuts as a means to rescue the American economy from stagnation. During his administration, top marginal tax rates dropped in steps from 70% to 28%. In Britain Margaret Thatcher slashed the top marginal income tax rate from 83% to 40% between 1979 and 1988. These tax systems remain progressive, but much less so than they used to be. Marginal and average tax rates still rise with income, but overall tax structures are much flatter than they were a generation ago. Other economies followed suit, if slightly less ambitiously. In 1988 Canada reformed its tax system, flattening the rate structure and cutting top rates. Germany passed a tax reform that same year, reducing marginal rates. Norway dramatically cut top rates on both labour and capital income in 1992, from a 58% top income-tax rate to 28%. In the 1990s and 2000s many central and eastern European economies embraced tax reform, adopting simpler—and often flat—tax systems designed to reduce tax rates and evasion. Russia overhauled its progressive tax system in 2001, dropping the top rate from 45% in 1999 to a flat 13%. Rates were occasionally pushed up after the broad declines of the 1980s. In the 1990s America raised its top marginal income rate to 39.6% in an effort to rein in deficits. Over the past 30 years as a whole, however, governments have taken less of each dollar or pound pocketed by the rich. Rates on corporate and capital income followed suit. Across the OECD the average corporate-tax rate was 28% in 2007, down from over 40% in the 1980s. Declines on tax rates for capital income have been smaller than those for labour income, not least because tax rates were lower before the 1980s. Greater mobility of capital relative to labour ensured the trend towards reduced capital taxation was broadly shared. Economies reduced corporate-tax rates to stay competitive with their neighbours. Ireland's 12.5% rate continues to irk fellow euro-zone members.

Despite falling rates, advanced economies remain as dependent on top earners as ever. In most rich countries, but especially Nordic and English-speaking economies, the rich have done very well while incomes for other earners have lagged. In America the income share of the rich has grown faster than the share of taxes paid. Across the OECD, income inequality as measured by Gini coefficients (which calculate how far an economy is from perfect income equality) rose by roughly 7% from the 1980s to the 2000s.

More of the pie

In Britain the share of pre-tax income flowing to the top 1% of earners more than doubled from 1976 to 2007, from 5.9% to 14.6%, and it has risen in other countries too (see chart 2). America's rich have done better still. The top 1% of earners in America (roughly, those earning more than $400,000 a year) captured 58% of real economic growth from 1976 to 2007, and now take home roughly 18% of all pre-tax income earned, up from less than 10% in the 1970s. The share of the top 0.1% alone quadrupled over that period. The rich have done very well in recent decades and the richest have done best of all. The present debate hinges on whether these changes have been for the good, which addresses the third question about how the rich have responded. The ideal tax system strikes a balance between efficiency and equity. Voters set priorities, among them defence, infrastructure and a social safety net. Different societies make different choices, but a government cannot avoid a basic trade-off. The more it wishes to spend, the more it must extract from the economy via taxation. When governments tax more, workers react and take steps to avoid higher tax burdens. These responses distort the functioning of the economy, often reducing potential growth and the economy's ability to provide a high standard of living to all. The supply-side tax revolutions of earlier eras prompted a wave of studies looking at the effect of lower taxes. Did people behave as expected? And were tax changes good for growth? Early results were instructive. The rich do not often respond to tax increases by working less, for instance, as was widely assumed. But taxable income is very responsive to tax changes. The rich adjust by tweaking the manner and timing of their compensation. Studying America's 1986 Tax Reform Act, which lowered the top marginal rate from 50% to 28%, Martin Feldstein, a Harvard economist, found that taxable income among high earners adjusted, dollar-for-dollar, with tax rates. Mr Feldstein argued that higher tax rates on the rich, such as the 1993 tax increase that laid the groundwork for the balanced budgets of the Clinton presidency, were likely to distort economic activity without raising much money. Similar work analysing Mrs Thatcher's tax cuts in Britain found a comparably sharp response to changing rates; the taxable income of the rich swung from falling to rising in 1979.

Later studies challenged these findings. Austan Goolsbee, a Chicago University economist and recent head of President Obama's Council of Economic Advisers, said that estimates from the 1980s and 1990s overstated the effect of tax cuts. Top incomes were rising as part of a long-term economic trend, leading economists to overestimate the beneficial impact of tax cuts. Other historical episodes painted a different picture, Mr Goolsbee argued. From the 1920s to the 1970s responses were more modest. A tax increase in 1935 corresponded with an increase in the taxable incomes of the rich—at a time when William Randolph Hearst ordered his newspaper editors to christen the New Deal the “Raw Deal” and harangue Franklin Roosevelt for his attempts to “soak the successful”.

Mr Goolsbee also questioned whether the behaviour of the rich hurt growth over the long run. A tax increase might prompt a one-time shift in the timing of compensation without meaningfully altering long-term choices. A big measured fall in income after the tax rise of 1993, for instance, mainly reflected a one-off pre-reform cash-out of stock options by a relatively small group of rich taxpayers. Thereafter, the change in behaviour was smaller.

In general and across time periods and countries, tax changes affect the choices of the rich, though the big responses of the 1980s and 1990s may have been unusually large. Studies generally show that a 1% increase in the marginal tax rate reduced taxable income by 0.1-0.4%, though sometimes and in some places it may be higher. The rich, though, are more sensitive, responding two to three times more than poor households, according to a Danish study. Changes in taxes on capital income also generate bigger responses than changes on labour income.

The rich may move more than their incomes when taxes rise; they might move house. On a rough calculation for The Economist by KPMG, getting out of London would be lucrative (see chart 3). New technologies benefit highly talented workers, who market themselves globally and reap large returns. These “superstars” are more mobile than ever before. After Britain's Thatcher-era tax reforms, the share of foreigners among top earners grew much faster than did the share in the middle and bottom of the income distribution, reflecting the mobility of international talent. A similar pattern appears in studies of tax responses in New Zealand. Indeed, the threat of migration appears to be strongest within Europe and across the English-speaking world. High scorers A recent paper by Henrik Jacobsen Kleven of the London School of Economics, Camille Landais of Stanford University and Emmanuel Saez of Berkeley examined responses to tax variation among top football players. They found that after the European football market was liberalised in 1995 countries with higher tax rates attracted fewer foreign stars and their domestic leagues' performance was poorer. Spain adopted the so-called “Beckham law” in 2005 (named after Britain's David Beckham who had joined Real Madrid), which gave preferential tax status to foreigners living in Spain. Thereafter, Spain's share of top foreign players rose sharply and diverged from that in Italy, which had followed a similar trend. Footballers may be more mobile than most, but there is likely to be some effect from tax rates on where the most talented individuals locate. Neither is income the only thing governments tax. The rich commonly earn money from corporate profits and capital investments. Economists usually recommend against taxing capital, for several reasons. Corporate taxation distorts patterns of production, and although governments may wish to fiddle with the final distribution of goods and services they need production to be as efficient as possible. Since capital is an input to future growth, taxation of capital income can reduce investment and distort production over time.

Berkeley's Mr Saez and Peter Diamond, a Nobel laureate at the Massachusetts Institute of Technology, nonetheless say that taxing investment income is justifiable. It is often hard to draw a clear distinction between investment and labour income, especially for top earners. A low or zero rate of tax on corporate and capital income may simply encourage top earners to change how they take their compensation.

The case of carried interest in private equity and hedge funds provides an example. Fund managers earn a share of profits as compensation, which is treated as capital income for tax purposes. This suits managers just fine given the lower rate of capital taxation. There is a compelling argument that such compensation is simply labour income, however, and that the current pattern is basic tax-avoidance. Indeed, they suggest that a reform which closes loopholes like the carried-interest exception and reduces the difference between tax rates on capital and labour income may prove more efficient while also boosting revenues. Many economists consider this an attractive alternative to higher top marginal income-tax rates.

When the rich change their behaviour it can distort economic activity; top earners may alter their sources of income, adjust their business strategies or simply pack up and move. The impact varies, with smaller rate changes producing fewer distortions. By closing loopholes governments can reduce avoidance, and fewer loopholes also mean a broader tax base and more revenue for a given rate of tax.

A surprisingly difficult question to answer is how tax changes affect long-run economic growth. Economies are constantly buffeted by changes—booms and busts, random shocks and demographic trends among them. These complications obscure the effect of lone tax changes. The simplest of analyses might note that the high-tax years of the early post-war period were associated with rapid growth while the low-tax years following the 1970s were not. Yet it is wrong to conclude that high taxes cause rapid growth. In central and eastern Europe tax reform coincided with a period of scorching growth. It is very difficult to separate the effects of tax changes from broader economic liberalisation and closer integration with western Europe.

To overcome such complicating distractions, Christina and David Romer, two economists at Berkeley, use a narrative approach. They pore over historical documents to work out why tax shifts were made. When they find reforms adopted primarily to boost long-run growth, and not to fix a flagging or overheating economy, they add them to their sample. Studying those changes alone gives a cleaner picture of the effect of tax reform.