Planning Problems and Redistribution of Income in Models of Urban Economics

Abstract

We study the planning problem of a standard location-choice model to discuss why a planner might optimally redistribute output across locations. In this model, ex-ante identical households value consumption and housing and choose a location in which to live, where locations vary in productivity, amenities, and the quantity of housing. Two features of this model lead the planner to redistribute output. First, the supply of housing is fixed in each location and subject to a congestion externality. Second, households randomly and unobservably vary in their attachment' to any given location, affecting both household location choice and utility. We demonstrate that researcher choice in modeling attachment critically affects the size and direction of optimal transfers of output across locations. This is a key problem as the location-choice data do not discipline this facet of the model: A plethora of frameworks may be observationally equivalent, but predicted optimal transfers can vary greatly across approaches. We propose a simple adjustment to the planning problem that removes the influence of the attachment-modeling choice on predicted optimal policy but preserves the planner's incentives to redistribute across locations in response to housing congestion and/or other externalities.