If you want to appear authoritative it really does make sense to dress smart. Various studies have shown that people in more formal attire get served more quickly in shops, have more luck in interviews and are usually judged to be more intelligent and academic. A study that looked specifically at female applicants for a managerial job found those who dressed in a smart masculine style were perceived as more forceful and aggressive and were more likely to get hired.
Image credit: Cad & the Dandy