This dissertation studies two wide ranging phenomena and their socio-economic impacts: urban divergence in terms of geographical skill sorting and fast rising housing prices. The first essay explores the empirical pattern as well as the driving forces behind the American cities’ diverging path over the past forty years. Compared to the rest of the U.S. cities, the top 20 largest cities have been growing faster in several aspects, such as city-average wage, housing price, and measured innovation intensity (e.g., patents, venture capital). In addition, this geographical divergence has contributed substantially to the rising inequality in America. To explore the causes of this divergence, this paper constructs a spatial sorting model where entrepreneurs with different talents can freely move across cities. The key idea is that cities with advantages in innovation attract more productive entrepreneurs and more workers, thereby driving up wages and housing prices. Two things distinguish my models from others: 1. Large cities are having endogenous innovation advantage in equilibrium; 2. I can freely explore the driving forces behind the divergence, with an emphasis on how technology changes can reinforce the spatial sorting mechanism. Specifically, three types of technological changes have increased the benefits of skill clustering in innovative cities: general productivity increases; improvements in communications technologies; and declines in trade costs.

The second essay studies how heterogeneous households respond to the fast rising housing prices through their life-cycle behaviors. Chinese housing market has been undergoing a rapid booming period since 1998, causing the house prices increasing significantly. As a result, households endured severe financial burdens to buy homes at price-to-income ratios of around six. Along with the rising house prices, household savings rate has been increasing consistently since 1998. Can the rising house prices be an important factor to explain the increase in household saving rate? This paper develops a life cycle dynastic model with endogenous choice on housing, coresidence and intergenerational transfer, then quantitatively analyze the effect of housing price on household saving. It shows that housing is an important motive for saving, and it accounts for about 35% of the increase in household savings rate. The housing situation affects households’ saving behavior through three channels. First, households are financially constrained due to the down payment requirement and they choose to limit their consumption in order to buy houses. Second, young adults live in their parents’ houses for a long time and save more intensively, since they get to pay less for the housing expenses under coresidence. Thirdly, older parents make large sum of intergeneration transfer in aid of the children’s housing purchase, indicating the housing affordability issue also has influence on old parents’ saving decisions.