Tax rates, Risk-taking, and Inequality

The above graph (source) shows the top marginal tax rate under the U.S. income tax. One striking feature is the substantial decline over the past several decades.

I present this graph as background for Richard Posner's thoughts about rising income inequality:

There are now almost 800 billionaires in the United States and countless millionaires, and one out of every 500 U.S. households have an annual income of at least $1 million.

Now this is to look only at the top of the income distribution. It is not to consider the income distribution as a whole, let alone poverty. In the more conventional focus on earnings by quintiles, one sees little change in recent years. But since 1980 the percentage of total personal income going to the top 1 percent of earners has risen from 8 percent to 16 percent. It is the top of the distribution on which I’ll be focusing.

What are the causes, and what are the effects, of this trend in the income (and of course wealth) of the highest-earning segment of the distribution? Part of it is reduced marginal tax rates, because high marginal tax rates discourage risk-taking. Consider two individuals: one is a salaried worker with an annual income of $100,000 and good job security, and the other is an entrepreneur with a 10 percent chance of earning $1 million in a given year and a 90 percent chance of earning nothing that year. Their average annual incomes are the same, but a highly progressive tax will make the entrepreneur's expected after-tax income much lower than the salaried worker's. Many of the people at the top of the income distribution are risk takers who turned out to be lucky; the unlucky risk takers fell into a lower part of the distribution.

Has the fall in top marginal tax rates over the past several decades in fact encouraged people to pursue higher-risk career paths, thereby exacerbating inequality in ex post incomes? As far as I know, this hypothesis has not received much attention in the empirical literature on income inequality.