You'd think that the community with a 3.9 percent unemployment rate - the lowest in the nation - would be on cloud nine. Indeed, Stamford, Conn., a once-sleepy New York City suburb that some call ''Houston on Long Island Sound,'' has much going for it.
In the past decade, nearly 120 corporate headquarters and regional executive offices have moved out of New York. Seventy-eight relocated in Stamford and nearby Greenwich, with this city getting the lion's share. Stamford has 14 Fortune 500 company headquarters.
Over the past 15 years, nearly a half-billion dollars has been spent - mostly by the private sector - to rebuild the aging downtown area of Stamford, the state's second-largest and fastest-growing city. Last year, a $100-million downtown shopping mall opened.
Recently, Group W Satellite Communications was hiring workers for its new corporate center. One day alone, 300 people started new jobs, and company officials had to pass out color-coded T-shirts to help identify them.
''It was like college registration all over again,'' says a Group W spokesman.
''I'm thrilled with Stamford's unemployment rate,'' declares Stamford Mayor Louis A. Clapes.
Now a growing number of problems are casting a shadow over this economic growth: a lack of adequate housing for low- and middle-income groups, continuing high levels of minority unemployment, and mounting traffic congestion.
But most politicians, developers, and long-time residents agree that the city's biggest challenge is housing. A recent report by the Connecticut Housing Department noted that more than 14 percent of the families in wealthy Fairfield County, where Stamford is located, live in inadequate or substandard housing. While much of this poor housing is in industrial Bridgeport, Stamford has its share of antiquated row-house slums and ramshackle single-family dwellings.
In addition, there isn't enough housing for the hundreds of new workers arriving each month. And many among the growing population of senior citizens find that skyrocketing property values are pushing property taxes so high they can't afford to live here anymore.
Mayor Clapes and other urban experts here admit the answers to these and other problems won't come easily. A committee the mayor formed recently spent 18 months working on solutions, he explains, and ''hasn't built a single unit.''
A smattering of low- and moderate-income housing has gone up since the city launched an urban-renewel program in the early 1960s. In fact, the impressive high-rise apartment towers that vie with the new steel-and-glass corporate giants on the downtown skyline are for people of very moderate incomes.
''We've had a lot of housing built in Stamford in the past decade,'' says former Stamford Mayor Thomas Mayers. ''But it's been housing that will sell at the greatest profit - luxury housing.''
Mr. Mayers was one of the leading architects of this city's transformation from a weary post-industrial ''commuter'' town to - as David Anderson, president of the nonprofit Stamford Economic Assistance Corporation (SEAC), calls it - ''the jobs machine.''
Studies show the economic expansion in Southwestern Connecticut over the past 15 years has produced a net increase of 35,000-40,000 jobs for Stamford and the seven surrounding communties of Greenwich, Darien, New Canaan, Norwalk, Weston, Wilton, and Westport. Half of these are in Stamford proper, and the job market is still expanding. Currently, the city is seeing an influx of so-called ''support'' industries, such as advertising and public-relations firms, which are following the Fortune 500 migration.
As a result of the housing crunch, many who get jobs here have to commute. One recent study shows that more than 25,000 out-of-towners come here to work every day, as compared to 18,000 residents who commute to New York or elsewhere to work - a sharp reverse from the trends of the 1940s, '50s, and '60s. Most inbound commuters drive, adding to the already considerable rush-hour traffic.
Still, falling though the cracks of Stamford's prosperity are many in the city's black and Hispanic residents. According to Mr. Anderson, the SEAC president, the unemployment rate among blacks is nearly 12 percent. While lower than black unemployment in many cities, the rate is still too high for many community leaders here. They blame corporations for not making enough job-training programs available.
Stamford's minorities grew slightly from 1970 to 1980, and now constitute about 22 percent of the population, according to 1980 Census data. Blacks comprise more than 16 percent of this total.
SEAC and the Southwestern Area Commerce & Industry Association, an industry lobbying group, are trying to get the private sector more involved in what remains of the federal government's job-training programs, including CETA.
New Neighborhoods Inc., a nonprofit association of 44 churches and synagogues , is taking positive, though small, steps to see that more middle- and lower-income housing is built. Pitney Bowes Inc., an old Stamford company, recently sold for $1 a valuable half-acre tract to New Neighborhoods to be used for moderate-income housing.
As the price of single-family homes continues to soar - the average price for a single-family house is about $150,000 - city fathers and private developers are trying to find ways to keep Stamford from becoming a city that only the rich can afford.
''Our middle class is rapidly disappearing,'' laments Mary Jean Long, who runs the Stamford-area congressional office of Rep. Stewart B. McKinney (R). ''We could blow it (the economic prosperity) if something is not done.''