* Popular first lady boosts U.S. designers, fashion industry
* Praised for mixing high-end, low-ended pieces
* President Obama says: "She always looks good"
WASHINGTON, Jan 21 (Reuters) - It was one of the biggest questions of Monday's inaugural ceremonies: not what would President Barack Obama say, but what would his wife, Michelle Obama, wear?
The first lady wore a navy coat and dress by designer Thom Browne, inspired by the fabric of a man's silk tie.
The belt and gloves were from J.Crew, a mid-priced chain that is a fixture in U.S. shopping malls; the necklace and earrings were designed by Cathy Waterman. The boots were by Reed Krakoff, as was the short blue cardigan she wore to the celebratory lunch in the Capitol hosted by congressional leaders.
"At the end of the inaugural festivities, the outfit and accompanying accessories will go to the National Archives," the first lady's office said.
Dressing any first lady, especially Obama, a Harvard-trained lawyer known for her style, can be a huge boost for a fashion designer or retail chain.
The White House did not divulge who crafted the gown she will wear to Monday night's inaugural balls, but the designer could see a lot of new attention. Her choice of a white chiffon Jason Wu gown for the inaugural balls in 2009 helped make the young designer a household name.
Thom Browne boasts a string of design awards, most recently, a prestigious National Design Award for fashion from the Cooper-Hewitt National Design Museum in New York, which is part of the Smithsonian Institution.
"She likes well-tailored clothes, so the inspiration was doing something that looked tailored and structured and fitted through the body and somewhat A-line for the skirt and the dress," Browne told the Los Angeles Times, adding that he picked blue because he had guessed that President Obama would wear that color.
Praised for wearing high-end designers as well as pieces from mass-market stores, the first lady has established herself as an international style trend-setter during Barack Obama's first four years in the White House.
Dresses, sweaters, shoes and belts she has worn have sold out at retailers from designer showrooms to mass market chains including Gap Inc., J. Crew and Target Corp..
Style mavens credit the 49-year-old first lady with changing the way American women put together their outfits, and, by patronizing U.S. designers, bolstering a multibillion-dollar industry.
Famed for her toned arms, Obama set a trend for sleeveless tops. Her cardigans and belted dresses have prompted many working women to switch from blazers and suits in the workplace.
NEW HAIRSTYLE, A 'SIGNIFICANT' EVENT
"Icon's a big word and it sometimes gets over used, but I think if we're going to use it, we can use it now," said Steven Kolb, chief executive of the Council of Fashion Designers of America, adding, "What makes her a real icon is the work that she does and the woman that she is."
"Michelle looks good however, wherever, whatever she does. Michelle looks good in her sleeping gown," said Sharon Johnson, a therapist who came from Baltimore to watch the inauguration, and joked that she is still looking for the green leather gloves Obama wore on Inauguration Day four years ago.
"Her beauty is so far inside, and shines so far outside," Johnson said.
When Michelle Obama held the Bible for her husband during his official swearing-in on Sunday, she wore a dark blue dress by Reed Krakoff, the creative director for the Coach leather goods company, who has become a fashion designer.
On Sunday night, she wore a sleeveless black sequined dress by Michael Kors to an inaugural reception for supporters.
At that reception, President Obama weighed in on what he termed the most "significant" event of the inaugural weekend, his wife's hotly discussed new hairstyle.
"I love her bangs," Obama said. "She looks good. She always looks good."
Interest in Michelle Obama's clothing has extended to the outfits worn by her two daughters. On Monday, the White House said Malia, 14, was wearing a J.Crew ensemble and Sasha, 11, wore a Kate Spade coat and dress.
Obama is a far bigger influence on U.S. fashion than most of her predecessors. Laura Bush favored suits by Oscar de la Renta and Hillary Clinton - now the U.S. Secretary of State - is best known for wearing a range of brightly colored pants suits. Even stylish Jackie Kennedy wore mostly European designers.
Obama's fashion choices have not always been applauded. Some Americans were angry when she wore a red gown from a British label - Alexander McQueen - to a 2011 state dinner for China's president.
Kolb dismissed such concerns, noting that fashion is a global business and that U.S. designers are thrilled when, for example, Kate Middleton, the wife of Britain's Prince of Wales, wears their clothing.
"At the end of the day, we get up in the morning and we look in our closet and we have to feel good about what we put on," he said.