NEW YORK, FEB. 25 -- Austin, Tex., which has a four-year record of economic expansion unmatched anywhere in the country, today was rated the fastest-growing city in the United States by Inc. magazine for the second year.

Austin was followed in the 1988 rankings by Manchester-Nashua, N.H., Orlando, Fla., Phoenix and Atlanta.

The annual listings were calculated on three factors -- business birthrate, the percentage of growth in private employment and the percentage of young companies experiencing high growth. The survey's aim was to measure the climate for entrepreneurs seeking to start new ventures, the magazine said.

The magazine said the 1988 rankings show a healthier urban economy than a year ago in the three catagories, with a median company birthrate of 2.7 percent and 2.9 percent of small young companies experiencing rapid growth. The median percentage of job growth over a four-year period was 15 percent.

Citing several outposts of heavy industry that made dramatic gains since last year, Inc. also said that the upward movement in Michigan cities such as Lansing, Flint and Saginaw Bay and Pennsylvania's Lancaster, York and Johnstown-Altoona indicates that a Rust Belt revival was under way.