Inflation statistics are based on a mix of prices - including housing. Housing prices have been going down in the UAE, but for most of us who are locked into long term contracts, this doesn't actually affect our spending power. Look at this quote from a March 11, 2011 Reuters article:
"The dip in UAE inflation ... shows that price pressures remain benign despite prominent increases in certain costs, chiefly food and transportation," said Tim Fox, chief economist at Emirates NBD.
But for most of us, food and transportation are the main expenses - so despite what the statistics say, the average household is losing spending power.