Strongindustry direct premiums written growth in the second quarter suggests thatrate hikes implemented starting in 2015 to counter rising frequency andseverity continue to impact private auto insurers' results.

Privateauto insurance industry direct premiums written rose 6.41% in the secondquarter, compared with 5.14% a year ago, with the increase in the growth rateeven larger among the top 30 groups. All top 10 private autoinsurers by market share saw higher direct premiums written year over year inthe second quarter, but premium growth at Allstate Corp., GEICO Corp. and Nationwide Mutual Group slowed tovarying degrees.

AForm 10-Q filed Aug.3 shows that the Allstate, Esurance and Encompass brands all experienceddecreases in auto policies in force and new issued applications in the secondquarter. Allstate Chairman and CEO Thomas Wilson II attributed the declines tothe insurer's decision to reduce new auto business as it works on improving itsprofitability, according to an earnings call .

"Wehave chosen to go for a share of profit versus share of revenue. I would like[auto policies in force] not to be down a percent in the Allstate brand thisyear, but when you raise prices and you do it early, other companies tend tofollow you, and so what happens is you lose some business early on and then youget it back," Wilson said.

Allstatesaid its auto margin held steady because it acted quickly to mitigate thepotential impact of deteriorating auto loss cost trends by implementing aprofit improvement plan across its auto businesses.

AtBerkshire HathawayInc.'s GEICO, voluntary auto policy-in-force growth againcontributed to the year-over-year increase in premiums written and premiumsearned in the second quarter, albeit at lower levels at 4.2% compared with 6.5%in the second quarter of 2015, according to Forms 10-Q filed , and . Voluntary autonew business sales increased 4.2% in the second quarter.

andProgressive Corp. sawimpressive premium growth during the second quarter. Year-over-year growthrates at Travelers and Progressive jumped to 12.91% and 12.31% from 5.31% and6.88%, respectively. They are among the insurers whose growth rate in thesecond quarter beat the industry's overall growth.

Presidentand COO Brian MacLean said during a July earnings call that Travelers' top-linegrowth benefited from double-digit growth in agency auto during the secondquarter as agent and customer receptivity to Quantum 2.0 continues to be"exceptional," according to a transcript.

AtProgressive, agency auto business and direct auto business continued to expand,with the insurer reporting year-over-year growth in agency auto and direct autopolicies in force for April, May and June.

's Integon National Group achieved the fastest growth amongthe top 30 auto insurers with a year-over-year premium increase of 21.58%during the second quarter. Its direct premiums written climbed to $434.0million in the second quarter from $357.0 million in the prior-year period.

"Personalauto saw strong organic growth, driven by continued product enhancements andimplementation of key marketing initiatives," National General CEO BarryKarfunkel said during an earnings call, according to a .

Ofthe top 30 private auto insurers by market share, only and New Jersey ManufacturersInsurance Co. saw their direct premiums written fall.

InfinityP&C's total policies in force dropped 7.8% year over year as of June 30, asthe decline in policies in force in states in which it is running off itspersonal auto business persists. The insurer reported a 39.5% decline inpolicies in force in those states, according to a filed Aug. 4. Its "focusstates" — Arizona, California, Florida and Texas — also had reducedpolicies in force at June 30.

Theindustry's direct premiums written and growth rate continued to increase in thesecond quarter at the same time direct incurred loss ratio deteriorates. Of thetop 30 private auto insurers by market share, only GEICO, Erie Insurance Group,CSAA InsuranceExchange and Auto-Owners Insurance Co. saw their direct incurred lossratios improve.

, whose direct incurred loss ratio rose year over year to 77.09%from 67.67% in the second quarter, continued to be the largest private autoinsurer by market share.