* First quarterly profit increase in three years

* Investments improve, claims payout ratio dips

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

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.

Progressive's combined ratio, which reflects how much of premiums it pays out to cover claims, fell to 92.6 percent from 93.6 percent a year earlier.

Shares of Progressive closed Thursday at $14.43 on the New York Stock Exchange. (Reporting by Jonathan Stempel; editing by John Wallace)

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