The first couple of times Alfred J. Carpenter was turned down for a job, he didn’t know what to think.

He been laid off early in the recession and then had the bad fortune of tearing tendons in his knee just when he didn’t have health insurance. The job market was terrible and he had been out of work for more than a year. But the managers at the first two shoe stores to which he applied in the summer of 2010 seemed to be taken by his résumé. He had sold shoes for six years at Salvatore Ferragamo on Fifth Avenue and later at J. M. Weston, where a pair of men’s dress shoes can cost $2,000. The manager at one shop was already discussing salary. The other, he said, invited him to fill out the paperwork normally done on the first day on a job.

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