Urban development under uncertainty: A real options approach
Kostov, Krassimir Iliev
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The main objective of the dissertation is to provide an insight about urban development under uncertainty. The dissertation consists of two distinctive models that study the effect of household income volatility on urban growth. The first is a stochastic model of urban development, with risk neutral landowners, who invest either in agricultural land or in urban housing. Agricultural rent is known, while housing rent is stochastic, due to household income uncertainty. Investors can switch between land uses by paying fixed investment costs. They choose the time of development or demolition of housing, which has a fixed lot size. The uncertainty and the fixed costs create option values of each land use and make the developers reluctant to change their status quo investment. This investment inertia results in discontinuous urban development spurts, as a result of which short-term changes in the economic conditions lead to persistent, long-term consequences. If demolition is prohibitively expensive, cities with similar income growth rates, but different volatilities, expand at the same rate of growth. This may explain similarities in growth patterns of cities in the Western or Eastern United States, whose housing markets are more volatile, with cities in the Mid-West. The second model analyzes the possibility of urban leapfrog development. In it, landowners decide when to develop and at what lot size, but cannot demolish housing to use the land for agriculture. Income evolves stochastically, which generates an option value of agricultural land. Households derive utility from the consumption of housing and the numeraire, and disutility from commuting. The model is solved numerically using Monte Carlo simulations. The solution to a perfect foresight benchmark model shows that leapfrog development can take place under some conditions. Higher uncertainty (a) decreases leapfrogging; (b) raises housing bid-rents; (c) increases the urban population density; (d) delays urban development; and (e) smoothes out the housing lot size distribution.