NEW YORK ( TheStreet) -- The sharp recovery in housing amid still-high unemployment, tight credit and flat incomes has sparked concerns that prices might be rising too fast. Skeptics believe the housing recovery is investor driven and question the sustainability of home prices, given that first-time home buyers largely remain on the sidelines. Blackstone ( BX), which has pumped billions into single-family homes through its subsidiary Invitation Homes over the past year, disputes critics who argue that investors are influencing home prices. "Blackstone is not buying houses in sufficient numbers to make overall difference in house prices," the private equity company said in a blog post Monday. The firm has bought 29,000 homes over the past year, a tiny fraction of the total housing stock of 115 million units. Another report makes a similar argument, though it focuses on the housing market in Greater Phoenix where home prices have been rising at a scorching pace. Concerns that institutional investors are causing a bubble in Phoenix are overdone, according to a June 5 report by Arizona State University's W.P. Carey School of Business. Michael Orr, director at the Center for Real Estate Theory and Practice says the impact of institutional investors is dramatically overstated. "The commentators often talk ominously of a bubble bursting when these homes come back onto the market. Such talk gets a lot of attention because we are over-sensitized to bubble-talk after the disruptive events of the last bubble between 2004 and 2006," he wrote in a June 5 report. "The entire institutional inventory of 11,000 rental homes represents a tiny fraction, less than 1%, of our housing stock. If every single one were to be placed for sale on our local MLS next month we would still have less supply than in a normal balanced market. This is because our active listing count is down by about 15,000." So the problem is not so much high demand, but lack of supply. Given the balance between supply and population growth in Phoenix, home prices are unlikely to fall below today's level and "are more likely to continue to climb for a long time, though at a more gentle pace," he wrote.