First-time unemployment claims dropped sharply last week to 352,000, a drop of 50,000 from the previous week (the biggest one-week drop since September 2005). It’s important to point out that the moving four-week average, which is a lot less noisy, only dropped 3,000, to around a 379,000 weekly average. But that’s a lot better than where we’ve been, and it falls below the 400,000-job danger zone where jobs wouldn’t be created. It augurs for a decent January employment report, perhaps along the lines of December’s increase of 200,000 jobs.

Perhaps a bigger sign of economic progress comes from the news out of Michigan, where the unemployment rate stands at a three-year low, years after the auto industry rescue and a series of advanced battery technology investments successfully brought the local economy back to life.

Michigan’s unemployment rate in December declined another half-percentage point to 9.3%, the state’s lowest rate since the 8.9% rate recorded in September 2008, said the Michigan Department of Technology, Management & Budget. And data released Wednesday confirmed that 2011 marked the first year since 2000 that Michigan posted a net increase in jobs.

Other economic reports this week of strong U.S. manufacturing and also increased per capita economic output in metro Detroit could be indicating a fuller recovery ahead.

The perspective you have to have is that the country’s economy is coming out of a drastic hole, and this new recovery isn’t catching up to that for some time. But there is a recovery in the data, though not everywhere (witness the December drop in housing starts). And if people start turning in their old beaters – the cars on the road have an average age of 10.8 years, one of the highest ever – the auto industry will continue to improve, and that will be good news for Michigan.

It’s important to focus on how this got done in Michigan. The federal government intervened when health care costs and a financial industry-induced recession threatened the sustainability of the auto industry. In addition, the government made targeted investments, particularly in battery technology, helping new startups in the Detroit area. So federal dollars were used, albeit in an indirect way, to support and grow jobs. And it worked.

What isn’t working is the cutbacks in the public sector. They haven’t enabled private sector growth to take off. In fact, it’s weighing down this modest recovery. And the depression of wages among unionized auto worker jobs, for the purposes of “competitiveness,” has made Michigan slower to come back than they otherwise would have. But the statistics are pretty clear – government investment brought forward a recovery, wage stagnation and public-sector cutbacks did not. So maybe someone in Washington will take that lesson.