UPDATE 1-Auto insurer Progressive profit rises

* First quarterly profit increase in three years

* Investments improve, claims payout ratio dips

* Competes with State Farm, Allstate, Buffett's Geico

NEW YORK, July 10 (Reuters) - Progressive Corp (PGR.N), one of the largest U.S. auto insurers, posted its first quarterly profit increase since 2006 on Friday as premiums and investment performance improved and it paid out a smaller percentage of revenue to cover claims.

Second-quarter net income for the Mayfield Village, Ohio-based company rose to $250.1 million, or 37 cents per share, from $215.5 million, or 32 cents, a year earlier.

Net premiums written grew 1 percent to $3.53 billion, and net premiums earned also increased 1 percent, to $3.44 billion. Results included $15.9 million of pre-tax investment gains, compared with a year-earlier loss of $44.6 million.

Analysts on average expected profit of 36 cents per share on revenue of $3.54 billion, according to Reuters Estimates.

Progressive has increased its advertising to better compete with rivals including the similarly-sized Geico Corp, a unit of Warren Buffett's Berkshire Hathaway Inc (BRKa.N) (BRKb.N). Larger rivals include State Farm and Allstate Corp (ALL.N).

As of June 30, Progressive's policies in force were up 4 percent from a year earlier to 7.39 million in personal lines, and up 4 percent to 3.47 million in special lines.