Sept 3 (Reuters) - Joe Perkins, head of Michigan-based auto supplier Mobex Global, marked Labor Day weekend this year as more than a holiday or a symbolic nod to U.S. workers. It now carries real-world significance as the lapse of federal unemployment benefits on Sept. 4 brings hope of a surge in job applicants to fill open positions that have kept his company 10% short of its hiring goals despite wage hikes and other incentives. "We"ve tried everything. We"ve tried wage adjustments. We"ve tried busing people from remote locations ... We are out of initiatives," Perkins said, adding he still needs to add around 100 employees to the current workforce of around 1,000. "I"m hoping that the reduction of (unemployment insurance) has a material impact on workforce availability. That"s what we are really banking on." If the U.S. economy"s behavior in 2021 holds any lessons for Perkins, though, he may be disappointed as the hiring needs of firms compete with a surge in coronavirus infections. The gap between job openings and hiring rates, with as many open positions than there are people unemployed, has been one of many puzzles posed by a U.S. recovery that proceeded faster than expected on some fronts, but still lags in terms of employment. Through July there were about 5.7 million jobs still missing from before the pandemic and 3 million additional unemployed. From top economic policymakers to human resource chiefs to small business owners with "help wanted" signs posted in shop windows, the nationwide expiration of federal unemployment benefits on Saturday has been anticipated as the day when the true state of the U.S. job market becomes apparent, cleared of whatever influence the weekly unemployment payments have had on people"s decisions about work. The emerging consensus among economists, however, is that the availability of benefits has mattered less than a host of other pandemic concerns like risks from COVID-19 itself and scarce and pricey childcare. A "THAWING" UNDER WAY? About half of U.S. states decided to end the federal benefit during June or July, arguing it kept people from returning to work. There has been little evidence that has emerged since of a surge in job growth, though various studies concluded some reshuffling of the labor market ensued. For instance, the unemployed in states that ended benefits early were slightly more likely to find jobs over the summer. At the same time, those states were less successful in attracting people from the sidelines of the labor market into either employment or a job search. That could mean the labor "supply shock," the human capital element of shortages that have confounded the global economic reopening, continues longer than expected, and the loss of benefits becomes a net drag on growth. States were told by President Joe Biden they could use other federal money to extend the benefits, but none have announced plans to do so yet. "We don’t expect the end of emergency (unemployment) benefits to lead to an immediate jump in employment and in the near-term expect it will weigh more on personal income and spending," wrote Nancy Vanden Houten, lead U.S. economist for Oxford Economics. At its peak in May 2020, the unemployment program was funneling an additional $600 a week to 25 million people, a critical $15 billion weekly infusion that kept household incomes intact amid the largest-ever jump in U.S. joblessness and allowed people to buy groceries, pay rents and mortgages, and even splurge on new cars and appliances. It was cut to $300 a week, and the number of recipients is down to around 9.2 million. Efforts to disentangle how that money influenced labor market choices have generally concluded that other factors - fear of the virus or lack of available childcare, for example - have been more top-of-mind. Still, companies hold out hope that the great worker shortage of 2021 will ease soon. David Reilly, president of plastic products maker United Solutions, said monthly job applications at his company"s Sardis, Mississippi, plant more than doubled from 40 to 90 between May, before the state axed the federal unemployment payments, and August. He said he has already detected a "thawing" at his other location in Leominster, Massachusetts, with applications picking up. "It"s a continuous cycle" of hiring and recruiting, said Reilly, and one he now hopes will let him get ahead of a curve that has left him about 50 workers short at each of his plants.