A typical U.S. family devotes about a quarter of its annual income and half or more of its net worth to housing. Both the level and volatility of house prices thus have important implications for household behavior and welfare, as well as for the aggregate U.S. economy. Recent research has emphasized the importance of housing supply in determining house prices in different U.S. markets. This dissertation comprises three chapters, each of which focuses on constraints on housing supply, house price volatility, or the link between them. In Chapter One, I use theory and empirical evidence to understand the impact of supply regulation on price dynamics. My estimates confirm that construction lags and marginal costs play critical and complementary roles in driving up costs on the margin, distorting the elasticity of housing supply and amplifying volatility. In Chapter Two, I use detailed data on zoning and records of housing transactions in the Boston metropolitan area to estimate the channels by which regulation affects the type and quantity of residential construction. I find that restrictive zoning, particularly large minimum permitted lot sizes, drastically increases the costs of new construction, which leads to fewer, larger houses being built. In Chapter Three, written jointly with Todd Sinai, we test the hypothesis that owning a home hedges a household against correlated changes in the future cost of housing. We find that the cross-sectional variation in house values subsequent to a move is substantially lower for home owners who moved between more highly covarying cities.