Nonparametric Identification of Spatial Treatment Effect Boundaries: Evidence from Bank Branch Consolidation

Abstract

I develop a nonparametric framework for identifying spatial boundaries of treatment effects without imposing parametric functional form restrictions. The method employs local linear regression with data-driven bandwidth selection to flexibly estimate spatial decay patterns and detect treatment effect boundaries. Monte Carlo simulations demonstrate that the nonparametric approach exhibits lower bias and correctly identifies the absence of boundaries when none exist, unlike parametric methods that may impose spurious spatial patterns. I apply this framework to bank branch openings during 2015--2020, matching 5,743 new branches to 5.9 million mortgage applications across 14,209 census tracts. The analysis reveals that branch proximity significantly affects loan application volume (8.5\% decline per 10 miles) but not approval rates, consistent with branches stimulating demand through local presence while credit decisions remain centralized. Examining branch survival during the digital transformation era (2010--2023), I find a non-monotonic relationship with area income: high-income areas experience more closures despite conventional wisdom. This counterintuitive pattern reflects strategic consolidation of redundant branches in over-banked wealthy urban areas rather than discrimination against poor neighborhoods. Controlling for branch density, urbanization, and competition, the direct income effect diminishes substantially, with branch density emerging as the primary determinant of survival. These findings demonstrate the necessity of flexible nonparametric methods for detecting complex spatial patterns that parametric models would miss, and challenge simplistic narratives about banking deserts by revealing the organizational complexity underlying spatial consolidation decisions.