WASHINGTON—When a business-school student sought out Jerome Powell several years ago for career advice, Mr. Powell, President Donald Trump’s pick to become the 16th chairman of the Federal Reserve, offered his philosophy on getting ahead.

His advice: Keep your head down and work hard, according to the student, Sean Gillispie, today a software product director in the Washington area. Mr. Powell told him he would be surprised “how many otherwise competent people self-sabotage with poor behavior,” Mr. Gillispie recalls.

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