Oct 1 (Reuters) - Finding an apartment to rent got even harder in the third quarter, as the U.S. apartment vacancy rate fell to its lowest level in more than a decade, according to an industry report released on Tuesday.The national apartment vacancy rate fell 0.1 percentage point to 4.2 percent in the third quarter from the second quarter, according to a preliminary report by real estate research firm Reis Inc.It was the lowest vacancy rate since the third quarter of 2001 when it was 3.9 percent. Some 47 out of 79 markets that Reis tracks posted vacancy decreases.Despite the decline in the vacancy rate, a weak job market and stagnant wages have prevented a commensurate rise in rents, Reis said.While the average U.S. effective rent in the third quarter grew by 1 percent sequentially, and 3 percent year-over-year, the increase in rent was less than what would have been expected in such a tight market, Reis said.Effective rent is the rent landlords receive after months of free rent and other perks."Demand has been so strong to push vacancy rates to such a low level, yet we haven't seen rent growth of the magnitude we would normally expect," Reis Senior Economist Ryan Severino said.With such a low vacancy rate, effective rent would have been expected to grow by about 4 percent to 5 percent year-over-year but was stymied by lack of job and income growth, Severino said."If median household income is growing at somewhere about 2 percent a year, give or take, once you back out inflation how much money is left for increased spending on rent? Not a lot," he said.Net absorption, the number of apartments rented over those that are unoccupied, reached 40,392, the most so far this year and 54 percent higher than a year earlier.New construction that is expected to come on line next year may fuel a rise in the vacancy rate and could slow the increase in rental rates, Severino said.Over the past five years, the apartment sector has been the beneficiary of the U.S. housing bust, the economic recovery, high mortgage requirements, and a constrained supply of new apartments.Those factors have pushed down the vacancy rate and allowed apartment owners, such as Equity Residential, Essex Property Trust Inc and AvalonBay Communities Inc to raise rents.Rising mortgage rates in the third quarter also dampened homeownership, forcing people to rent longer.The 4.2 percent average vacancy rate in the third quarter was down from 4.3 percent in the prior quarter and from 8 percent in late 2009.At 2 percent, New Haven, Connecticut had the lowest vacancy. Memphis, Tennessee had the highest vacancy rate, at 8.2 percent.The average asking rent rose 0.9 percent in the third quarter to $1,121.16 per month. The average effective rent was $1,073.29.San Francisco and San Jose, U.S. capitals of the technology industry, saw the highest effective rent increase, both up 2.2 percent to $2,043.02 per month for San Francisco and $1,685.72 for San Jose.New York remained the most expensive place to rent in the United States with an average effective rent of $3,049.37 per month, up 0.9 percent. The cheapest was Wichita, Kansas, at $528.95 per month, up 0.8 percent.