It’s harder than you’d think to measure the value of a boss. But some enterprising economists have done just that — and the news is good.

The Stanford economist Edward Lazear, with his co-authors Kathryn Shaw and Christopher Stanton, analyzed data from a company that has 23,000 employees and 2,000 bosses. From this data, they were able to track individual bosses and see how much a good boss can improve productivity. Their answer: about 10 percent.

Lazear also talks about one of his old bosses — President George W. Bush — and we hear from another boss who tells us that humility and a sense of humor are among the most valuable things a boss can offer.