Estimating Equilibrium Models of Sorting Across Locations

Abstract

With the growing recognition of the role played by geography in all sorts of economic problems, there is strong interest in measuring the size and scope of local spillovers (i.e., simple anonymous agglomeration or congestion effects, or more complicated interactions between individuals or firms of specific types). It is well-understood, however, that such spillovers cannot be distinguished from unobservable local attributes using just the observed location decisions of individuals or firms. We propose an empirical strategy for recovering estimates of spillovers in the presence of unobserved local attributes for a broadly applicable class of equilibrium sorting models. This approach relies on an instrumental variables strategy derived from the internal logic of the sorting model itself.We show practically how the strategy is implemented, provide intuition for our instrumental variables, and discuss the role of effective choice-set variation in identifying the model, and carry-out a series of Monte Carlo experiments to demonstrate the instruments' performance in small samples.JEL Codes: H7, R0, R2, R3

Supermarkets as a Natural Oligopoly

“…The importance of unobserved heterogeneity and correlated unobservables is not unique to this setting, arising as well in the contexts of peer e¤ects, locational sorting, and entry games (e.g. Bajari et al (2010), Bayer andTimmins (2007), Ellickson and Misra (2008)). Following this literature, I proceed by identifying a suitable instrument for competitor's size.…”

Identification of Social Interactions

“…To do this, modify (68) and (69) Little econometric work has been done on multinomial choice models with social interactions; as far as we know the only contributions are Brock andDurlauf (2002,2006) and Bayer and Timmins (2007). Nevertheless these models seem important in many contexts.…”

“…As far as we are aware, there does not exist any multinomial generalizations of Manski (1988) so that the error distribution may be identified (up to scale) via intragroup variation in individual characteristics and associated behaviors. Bayer and Timmins (2007) study a variation of the multinomial choice problem which focuses on choices across locations. They thus consider a population that forms a single group.…”

Decomposing the structural identification of non-market values

“…If income were to increase, the borders of the partition would shift to the left. 6 Intuitively, the choice to live in B reveals a lower range of preferences for a wealthier household that can more easily afford to live in communities C and D, which are more expensive because they provide more public goods. .…”

“…When applied to the market for housing, these models use information on households and their location choices to estimate structural parameters which characterize heterogeneity in preferences for local public goods and environmental amenities [6,10]. The results can be used to predict the distributional welfare implications of future policy changes, while recognizing that a sufficiently large shock will induce some households to move [24,25].…”