Inverse Probability Tilting with Spatial Data: Some Monte Carlo Evidence and an Application to Commercial Real Estate Prices

Examining the impacts of develpment on one side of a city's border or the other in a cross-sectional data set is important for real estate investments. Proximity to more densely developed urban centers can lead to higher prices per square foot because of agglomeration economies. An important consideration is the identi cation strategy in the research design. While a study focusing on sales prices data spanning a long period of time should consider an event, together with a proximity variable, as part of an identi cation strategy for estimating the Average Treatment E ect (ATE) of a development location decision, there is a di erent strand of literature focused on ATE identi cation in a cross-sectional context. One set of approaches in more general settings is propensity score approaches. Within the context of propensity score approaches, there is an extensive body of literature on Inverse Probability Weighting (IPW), as in Imbens et al (2003), and more recently Inverse Probability Tilting (IPT), as in Graham et al (2012). In particular, the attractive features of IPT that rely on a relatively straightforward method of moments approach have prompted us to explore a more general version of IPT. We consider an additional adaptation to the IPT estimator as a part of our ATE identi cation strategy speci cally, re-weighting that allows for geographic heterogeneity in a cross sectional context, in addition to a propensity score approach. We present our innovation that incorporates geographic heterogeneity in the data and the adjustments to the weights that we make to allow for more geographically distant observations to be down-weighted relative to more close observations. We call this semi-parametric approach our Inverse Probability Tilting-Locally Weighted estimator (IPT-LW). We describe the computation process of the IPT-LW ATE, then provide some Monte Carlo simulation evidence to demonstrate our estimator performs well in small samples. An application of how a cross-section of commercial property prices are impacted by being sold in 2013 in the city limits of Vancouver, BC, Canada (opposed to commercial properties that sold in the Vancouver suburbs in 2013) demonstrates the implementation of the IPTLW estimator in calculating the ATE of a decision of whether to develop real estate on one side or the ∗Corresponding author, University of Connecticut, School of Business, 2100 Hillside Road, Unit 1041-RE, Storrs, CT 06269. Je [email protected] †University of Hartford, Barney School of Business, 200 Bloom eld Ave, West Hartford, CT 06117; [email protected]