Federal Reserve Chairwoman Janet Yellen said Friday that she was “greatly” concerned by the extent and continuing increase in inequality in the United States. “It is no secret that the past few decades of widening inequality can be summed up as significant income and wealth gains for those at the very top and stagnant living standards for the majority,” Yellen said in a speech to a conference on inequality sponsored by the Boston Fed. “I think it is appropriate to ask whether this trend is compatible with values rooted in our nation’s history, among them the high value Americans have traditionally placed on equality of opportunity,” she added. Yellen said that some degree on inequality of income and wealth contributes to economic growth because it rewards hard work and risk taking. But the concern is that “inequality of outcomes can exacerbate inequality of opportunity, thereby perpetuating a trend of increasing inequality.” Income inequality — as measured by what’s called the Gini index — is up 4.9% since 1993, the earliest year available for measurement, according to Census Bureau data. In her speech, Yellen did not attempt to answer what she called the “difficult questions of how best to fairly and justly promote equal opportunity.” Instead, she laid out a “factual basis” for further discussion using the Fed’s recentSurvey of Consumer Finances, a survey of the income, wealth and debt for 6,000 U.S. households conducted in 2013. Two building blocks to greater income — college and owning a business — were now uncertain, she said. College costs are making it hard for young people to obtain a degree, and it is harder now to start a business, she said. She noted that economic mobility in the U.S. is lower than in most other advanced countries. Yellen said she was concerned the large and growing burden of paying for college may make it harder for many young people to take advantage of the opportunity of higher education. It is also harder for less wealthy Americans to start a new business, she noted. By GREG ROBB SENIOR ECONOMICS REPORTER