In this post, I present a very crude analysis of the relationship between the top marginal tax rate on income and income tax revenues in the United States. I do not consider the level of income at which the top marginal tax rate applies; nor do I consider the lower income tax rates, or the levels of income at which they apply. Data are from the White House and the Tax Foundation.
The chart below depicts income tax revenues as a percentage of GDP and the top marginal tax rate since 1934--the earliest year for which I could find data. After rising from a very low level prior to 1944, income tax revenues have been remarkably stable over the 20th and early 21st centuries. Prima facie, revenues from income tax do not appear to bear much relationship to the top marginal tax rate.
The chart below shows the same information as the one above, but with income tax revenues on a separate axis. It confirms that--superficially at least--the two variables do not bear much relation to one another. For example, as the top marginal tax rate decreased from 91% in the early 1960s to 28% in the late 1980s, the medium-term trend in income tax revenues was more-or-less flat. In fact, there was a very slight upward trend from the early 1950s to the mid 1980s.
Under plausible assumptions about human behaviour, one should not expect to collect any income tax revenues (over and above those provided by lower income tax rates) when the top marginal rate is 0% and when it is 100%. At a top marginal rate of 0%, any additional tax revenue would have to come from people willing to pay income tax voluntarily. And at a top marginal rate of 100%, any additional tax revenue would come from people willing to work voluntarily. Therefore, one should expect to observe what is known as the Laffer-curve: an inverse-U-shaped relationship between income tax revenues and the top marginal rate, with two minima at top marginal rates of 0% and 100%, respectively.
The chart below shows the bivariate relationship between income tax revenues and the top marginal rate, with a quadratic (i.e., U-shaped) function fit to the data. Contrary to theoretical expectation, the peaks of the function are at the lowest and highest top marginal rates! But this is almost certainly attributable to the pre-1944 outliers: years in which very little income tax revenue was collected, despite high top marginal rates.
Incidentally, I do not understand why so little income tax revenue was collected prior to 1944. There must be a good legal or economic reason. Nevertheless, as the chart below indicates, once the pre-1944 values are excluded, the quadratic function takes the expected form.