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The dynamics of house prices, sales, construction, and population growth in response to city-specific income shocks are characterized for 106 US cities. A dynamic model of search in the housing market in which construction, the entry of buyers, house prices, and sales are determined in equilibrium is then developed. The theory generates dynamics qualitatively consistent with the observations and a version calibrated to match key features of the US housing market offers a substantial quantitative improvement over models without search. In particular, variation in the time it takes to sell induces transaction prices to exhibit serially correlated growth. (JEL D83, R21, R23, R31)We explore the consequences of time-consuming search and matching for the dynamics of house prices, sales, and construction at the city level. First, we characterize the impact of city-specific income shocks on the short-run dynamics of average house prices, home sales, construction, and population growth for a panel of US cities. We then develop a model in which the entry of new buyers and the construction of new houses in response to such shocks are endogenously determined. Our theory generates serial correlation in the growth rates of house prices and construction, even if income is strictly mean-reverting following shocks. 1 When calibrated to data on US cities our model accounts for over 80 percent of the variance of house price movements driven by city-specific income shocks and nearly half of the observed autocorrelation of house price growth.In our empirical analysis, we estimate a structural panel vector autoregressive (VAR) model using city-level observations on the variables listed above. We focus 1 This behavior has been referred to as "price momentum" in the literature (e.g., Glaeser et al. 2011).

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Several empirical studies have documented a positive relationship between the rate of inflation and the dispersion of consumer prices. We examine this relationship and the welfare costs of inflation in a monetary economy in which ex ante identical buyers search among prices posted by identical sellers. Under certain conditions, stationary monetary equilibria of our economy necessarily exhibit dispersion of real prices. If the degree of buyers' incomplete information about posted prices is fixed exogenously, both price dispersion and the average real price are increasing in the inflation rate. Money creation lowers welfare by increasing the market power of sellers and exacerbating the effects of the inflation tax. As the rate of inflation approaches the Friedman rule, price dispersion and welfare costs both vanish. If households choose the number of prices to observe, then the Friedman rule is not optimal. Rather, up to some point increased inflation lowers the average real price and raises welfare by inducing search and eroding sellers' market power.