The best longer-term solution to the inequality problem is to reduce the fraction of Americans who dropout of high school, a theme I have continued to emphasize in various postings on our blog. This drop out fraction has been stagnant for the past several decades at about 30% for males, and a somewhat lower but still high percent for females. This is almost surely the highest fraction of high school dropouts among rich countries, and is heavily concentrated among children from African-Americans and Hispanic families. In large cities, often less than half of all the children enrolled in public schools end up graduating.
In considering the effect of wage stagnation and growing income inequality, it is important to distinguish between money income and standard of living. As long as the quality of goods and services increases (largely because of technological innovation in a broad sense that includes new business methods as well as scientific and engineering progress) faster than their cost, the standard of living will rise even if incomes do not. The quality of health care continues increasing rapidly, and part at least of the rapid rise in health insurance premiums is payment for that increased quality. The quality-adjusted cost of consumer electronics has plummeted in the same period.
Self-recommending as always. And for the best recent inequality read, see Will Wilkinson.