(Linda Stern is a freelance writer. Any opinions in the column are solely those of Ms. Stern. You can e-mail her at lindastern@aol.com.) (Correctly identifies ZipRealty.com as a real estate brokerage in paragraph 3.)

By Linda Stern

WASHINGTON, June 17 (Reuters) - Those green shoots that optimists keep seeing may be growing in the real estate market -- there are some indicators of healthier, more stable activity in housing.

In May, new housing starts jumped 17 percent over the previous month, and there was a 4 percent increase in building permits, too, according to new reports from the Commerce Department.

Housing inventories -- the backlog of homes on the market -- now stand at close to nine months. That is still high by historical standards, but lower than the 11-month levels reached at the end of 2007, says ZipRealty.com, a real estate brokerage.

But those inventories don't include the flood of foreclosures likely to hit the market soon. And with mortgage interest rates moving up (and they are), it's premature to believe that housing is poised to bounce back in a hurry.

Nonetheless, it's a good time for would-be buyers -- first-time homebuyers in particular -- to start checking out the market. Here's how to proceed.

-- Research your local market. Those national figures are almost meaningless when it comes to real estate. Markets in some parts of the country remain in free fall; others are already seeing bidding wars from speculators moving in to snap up underpriced homes. Talk to local real estate agents to discover how many months of inventory are on the market where you want to buy. Do research on websites like Trulia (www.trulia.com) that list pricing history and sales prices for many local markets. Discover where in the cycle your market is and how much fluff remains in prices. If inventories are falling and prices are rising, that is a solid sign that your neighborhood has bottomed out.

-- Take advantage of the first-time homebuyer tax credit. The Obama Administration's recovery package includes an $8,000 fully-refundable tax credit for first-time homebuyers who complete their purchases by Dec. 1, 2009. To qualify as a first-time homebuyer, you can't have owned a home for three years, but that means some previous homeowners may qualify. For the full credit, your income must be less than $75,000 ($150,000 for couples filing jointly); it phases down for the next $20,000 of income. The Federal Housing Administration and some other local organizations are offering bridge loans to homebuyers so they can use these credits to pay for a downpayment or closing costs, and then pay back the bridge loan when they receive their annual tax refund in 2010.