Eduardo Porter has an interesting discussion of inequality, based in large part on the views of M.I.T. Professor Robert Solow. Solow views it as unlikely that it will be possible politically any time soon to have tax and transfer policies that do much to lesson inequality. However he does hold out the hope that changes in corporate practices could lessen before tax inequality.
This is an extremely important point. There is considerable research showing that CEOs and other top management essentially ripoff shareholders, taking advantage of their insider power to give themselves pay that has little to do with their productivity, measured as the return they give to shareholders. (Lucian Bebchuk has a good summary of the issues.) If shareholders can better gain control of their companies, they might cut pay by 50 percent or more, bringing CEO pay in the United States in line with pay in other wealthy countries.
Since CEOs are among the very top earners in the US economy, reductions in their pay will have a substantial impact on wage inequality. In addition, there is likely to be a spillover effect. If the CEOs of major companies earned $3-4 million, instead of $10-$20 million, then the pay of top management in places like universities, non-profit hospitals, and private charities might be similarly reduced. The lower pay of top executives in these institutions would also free up money for higher pay for those at the middle and bottom of the wage ladder.
The key to reducing CEO pay is to create a well-working system of corporate governance where shareholders can actually impose a check on top management. This is a soluble problem, as demonstrated by the fact that other countries have been able to rein in CEO pay.