It has been widely assumed that there was a bubble in the U.S. housing market after 1999. This paper analyzes the extent to which that was true. We define a bubble as: (1) a regime shift that is characterized by a change in the properties of deviations from the fundamentals of house price growth, and (2) where a shock to the fundamental equation is more self sustaining and volatile than in other periods. We model the fundamentals of price growth as a lagged adjustment of prices to the expected present value of future rent. We then study the autoregressive behavior of the residuals thus generated. We look at changes in momentum (the extent to which a shock to house price growth leads to further increases in house price growth) of the residuals. Our results from 44 Metropolitan Statistical Areas for the period of 1980-2005 (quarterly data) are mixed. There is evidence of momentum in house price growth throughout the period, and momentum did increase after 1999, indicating a regime shift; but by a modest amount, and while momentum was sometimes strong it was not explosive. The regime shift was less apparent in the likely bubble candidate cities along the coasts, which had shown high growth in the past. The evidence on volatility is strong. In general, volatility did not increase in the nonbubble MSAs, and it decreased in the faster-growing bubble MSAs.