In surveys by Gallup and the McKinsey Global Institute, corporate CEOs and small business owners report difficulties finding workers with the right skills. Silicon Valley companies fight over software engineers; Union Health Service and the Harvard hospital system complain it’s hard to find nurses and technicians; manufacturers like Caterpillar and Westinghouse can’t hire enough welders and machinists to keep their state-of-the-art lathes running. Estimates of the size of the mismatch vary widely, but a May International Monetary Fund paper put it at a quarter of the 9.1 percent unemployment rate. Narayana Kocherlakota, president of the Federal Reserve Bank of Minneapolis, has suggested it accounts for a full third of the unemployment rate.