New Yorkers are rolling out the welcome mat for one of the world’s largest industrial firms, Alcoa, as that company moves its principal office to midtown Manhattan from Pittsburgh. Or rather, New Yorkers would be rolling out the welcome mat if Alcoa were making a major move to the city instead of merely newly designating a small location as its “principal executive offices” on a filing with the Securities and Exchange Commission. Thus, the company’s decision marks both good news and a challenge to New York’s leaders.

The good news is that it’s a step in a turnaround, however modest. The number of Fortune 500 companies based in the city had been plunging for several decades, to 39 in 2002 from 140 in 1955. That number has started rebounding, reaching 65 on the 2005 list. Alcoa makes one more. The bad news is that job growth hasn’t followed suit. Between September 2001 and 2004, the city had a loss of 170,000 jobs. Wall Street, the motor for the city’s economy, is still 20,000 financial services jobs behind its 2000 peak. While firms like Citigroup may keep their formal headquarters and top executives here, they are increasingly sending their mid-level employees elsewhere.

High individual, corporate, and property taxes in the city and the state, as well as regulations driving up the cost of rents and electricity for businesses and hiking the cost of living for employees, have been forcing traditional mainstays of the city’s economy to New Jersey or Connecticut or beyond. At the city level, the New York metropolitan area continues to lag dramatically in respect of job growth in a recent study by California’s Milken Institute. The city and its environs ranked 161st in relation to other major metropolitan areas.

No doubt this has something to do with the findings of another recently released study, which casts a light on how New York fares against its neighbors on one factor that influences companies’ decisions about where to do business. At the state-to-state level, New York ranks dead last in the Tax Foundation’s most recent survey of business tax climate, as the Sun’s Jacob Gershman reported yesterday. Based on a combination of its business, individual income, and sales taxes, New York trailed New Jersey (49th), Connecticut (39th) Massachusetts (27th). Even Vermont, a state so liberal it elects America’s only self-described socialist as its lone congressman, ranked 46th. Alcoa, incidentally, will still be incorporated in Pennsylvania, which ranked 16th on the Tax Foundation survey.

Alcoa’s move, in one sense, isn’t much of a move. About five years ago, the company opened an office in the Lever Building at 390 Park Avenue. The office now employs 60 people, a spokesman for the company, Kevin Lowery, told us recently. That’s not much of an office compared to the 2,000 administrative employees who will remain based at the company’s three Pittsburgh campuses. Yet this symbolic move was motivated by the belief that a worldwide corporation should have its main address in a world-class city, Mr. Lowery told the Sun. That the city still houses many of the Wall Street investors, banks, and bankers with which Alcoa does business also helped. Mr. Lowery described the recent change on the SEC filing as a formality enshrining the company’s decision five years ago that its executives needed offices in New York in addition to Pittsburgh.

The challenge for New York’s leaders, at both the state and city levels, is to make New York not just an attractive symbolic location but a desirable practical alternative, too. Mayors Giuliani and Bloomberg have made progress in things like providing safe streets, but much work remains to be done, from property and income taxes to building codes, before companies start flocking from Pennsylvania or Delaware – or back from New Jersey or Connecticut – to incorporate in New York, or to base more employees here. Alcoa has concluded that New York is a world-class city symbolically. Now it falls to our politicians to deliver a world-class business environment.