The short answer to the question is .25. That is, a plausible mid-range estimate based on the economics research literature is that raising the marginal tax rate by 10% (not 10 percentage points, but 10% above the previous rate) would lead over the long-term to a reduction in taxable income of 2.5%. The longer answer is that understanding the implications of the question is difficult. The article itself is on the technical side, but here are some of the key issues.
When marginal tax rates rise, people will seek to avoid paying at least some of the increase. But how they seek to avoid the higher taxes matters. For example, one possibility is that people react to the marginal tax rate by working fewer hours or by making less entrepreneurial effort. Another possibility is that they find ways to shift taxable income to future years, in which case a decrease in tax revenue now might be offset by an increase in tax revenue later. Yet another possibility is that they find a way to shift the form of income, perhaps by receiving more income in the form of untaxed fringe benefits or in lower-taxed capital gains. People may also react to higher marginal tax rates by taking greater advantage of tax deductions: for example, they may give more to charity.
Economic studies that consider how revenues changes in response to past tax changes tend to pick up short term effects of these changes, and the most common short-term effects are probably changes in timing of taxable income or shifting it to less taxable income. From society's overall point of view, these changes are not of central importance. In fact, if the problem with higher marginal tax rates is that people are finding ways to avoid paying those higher rates legally, then an obvious answer is to combine the higher marginal tax rates with rules and enforcement to make such legal tax avoidance more difficult. The long-term responses are potentially more worrisome, but also in the nature of things much harder to measure with confidence. Consider the difficulties, for example, of figuring out how a change in higher marginal tax rates might (or might not!) affect incentives to get an additional graduate degree or to start a company. Here's Saez, Slemrod, and Giertz:
"One might expect short-term tax responses to be larger than longer-term responses because people may be able to easily shift income between adjacent years without altering real behavior. However, adjusting to a tax change might take time (as individuals might decide to change their career or educational choices or businesses might change their long-term investment decisions) and thus the relative magnitude of the two responses is theoretically ambiguous. The long-term response is of most interest for policy making although, as we discuss below, the long-term response is more difficult to identify empirically. The empirical literature has primarily focused on short-term (one year) and medium-term (up to five year) responses, and is not able to convincingly identify very long-term responses."
It also seems likely that the economic reaction to higher marginal tax rates is not a single constant number, but may vary for different taxpayers, and under different tax regimes (like what is being taxed, and how many opportunities the tax code offers for legally minimizing one's tax burden). For example, it's plausible that higher-income taxpayers have greater incentives and resources to search for legal ways to minimize their tax burden. For example, it seems clear that after the 1986 tax return, which broadened the tax base and reduced top personal income tax rates, there was a large shift in reported income from corporations to the personal income tax, and a vast reduction in personal tax shelters.
The very top incomes were about 60 percent from dividend payments in the early 1960s, and faced top marginal tax rates of about 80%, which suggest that these investors had little control over the form in which their payments were received. But there has been a huge shift and now top incomes are much more likely to be from partnerships and wage income, which suggests much greater potential for control of the form and timing in which income is received. As they write (citations omitted):
"The difficult question to resolve is to what extent the secular growth in top wage incomes was due to the dramatic decline in top marginal tax rates since the 1960s. This question cannot be resolved solely looking at U.S. evidence. Evidence from other countries on the pattern of top incomes and top tax rates suggests that reducing top tax rates to levels below 50 percent is a necessary—but not sufficient—condition to produce a surge in top incomes. Countries such as the United States or the United Kingdom have experienced both a dramatic reduction in top tax rates and a surge in top incomes, while other countries such as Japan have also experienced significant declines in topAmong the goals that they suggest for future research are a greater effort to disentangle the different responses to higher tax rates:
tax rates, but no comparable surge in top incomes over recent decades ..."
"[F]uture research that attempts to quantify the welfare cost of higher tax rates should attempt to measure the components of behavioral responses as well as their sum. It needs to be more attentive to the extent to which the behavioral response reflects shifting to other bases and the extent to which the behavioral response comes from margins with substantial externalities. ... [R]esearchers should be sensitive to the possibility that nonstandard aspects of tax systems and the behavioral response to them—such as salience, information, popular support, and asymmetric response to increases versus decreases—might affect the size of behavioral response."
As I said at the start, the short answer from economic research to the question of how higher marginal tax rates reduce tax income is .25: a 10% rise in marginal tax rates will tend to reduce taxable income by 2.5%. But given the current state of research, that answer includes considerable uncertainty over its size and its underlying economic meaning.