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

Kikuchi, Tatsuru (2025): 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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Spatial econometrics, nonparametric methods, treatment effects, bank branches, financial access, digital transformation
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C21 - Cross-Sectional Models ; Spatial Models ; Treatment Effect Models ; Quantile Regressions; G - Financial Economics > G2 - Financial Institutions and Services > G21 - Banks ; Depository Institutions ; Micro Finance Institutions ; Mortgages; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics > R12 - Size and Spatial Distributions of Regional Economic Activity

References

\begin{thebibliography}{99}

\bibitem[Agarwal et al.(2012)]{agarwal2012distance} Agarwal, S., Benmelech, E., Bergman, N., \& Seru, A. (2012). Did the Community Reinvestment Act (CRA) lead to risky lending? \textit{NBER Working Paper No. 18609}.

\bibitem[Banzhaf and Walsh(2019)]{banzhaf2019difference} Banzhaf, H.~S., \& Walsh, R.~P. (2019). Segregation and Tiebout sorting: The link between place-based investments and neighborhood tipping. \textit{Journal of Urban Economics}, 74, 83--98.

\bibitem[Bhutta and Ringo(2015)]{bhutta2015residential} Bhutta, N., \& Ringo, D.~R. (2015). The 2013 Home Mortgage Disclosure Act data. \textit{Federal Reserve Bulletin}, 101(4), 1--26.

\bibitem[Buchak et al.(2018)]{buchak2018fintech} Buchak, G., Matvos, G., Piskorski, T., \& Seru, A. (2018). Fintech, regulatory arbitrage, and the rise of shadow banks. \textit{Journal of Financial Economics}, 130(3), 453--483.

\bibitem[Butts(2023)]{butts2023machine} Butts, K. (2023). Machine learning methods for spatial treatment effects. \textit{Journal of Business \& Economic Statistics}, 41(4), 1124--1137.

\bibitem[Conley(1999)]{conley1999gmm} Conley, T.~G. (1999). GMM estimation with cross sectional dependence. \textit{Journal of Econometrics}, 92(1), 1--45.

\bibitem[Della Vigna and Gentzkow(2022)]{dellavigna2022predicting} DellaVigna, S., \& Gentzkow, M. (2022). Uniform pricing in U.S. retail chains. \textit{Quarterly Journal of Economics}, 134(4), 2011--2084.

\bibitem[Ergungor(2010)]{ergungor2010bank} Ergungor, O.~E. (2010). Bank branch presence and access to credit in low- to moderate-income neighborhoods. \textit{Journal of Money, Credit and Banking}, 42(7), 1321--1349.

\bibitem[Fan and Gijbels(1996)]{fan1996local} Fan, J., \& Gijbels, I. (1996). \textit{Local Polynomial Modelling and Its Applications}. Chapman \& Hall/CRC.

\bibitem[Fuster et al.(2019)]{fuster2019predictably} Fuster, A., Plosser, M., Schnabl, P., \& Vickery, J. (2019). The role of technology in mortgage lending. \textit{Review of Financial Studies}, 32(5), 1854--1899.

\bibitem[Gibbons et al.(2015)]{gibbons2015mostly} Gibbons, S., Overman, H.~G., \& Patacchini, E. (2015). Spatial methods. In G.~Duranton, J.~V.~Henderson, \& W.~C.~Strange (Eds.), \textit{Handbook of Regional and Urban Economics} (Vol.~5, pp.~115--168). Elsevier.

\bibitem[Hall and Marron(1991)]{hall1991cross} Hall, P., \& Marron, J.~S. (1991). Local minima in cross-validation functions. \textit{Journal of the Royal Statistical Society Series B}, 53(1), 245--252.

\bibitem[Hallin et al.(2004)]{hallin2004local} Hallin, M., Lu, Z., \& Tran, L.~T. (2004). Local linear spatial regression. \textit{The Annals of Statistics}, 32(6), 2469--2500.

\bibitem[Hart(1997)]{hart1997kernel} Hart, J.~D. (1997). \textit{Nonparametric Smoothing and Lack-of-Fit Tests}. Springer.

\bibitem[Jaffe et al.(1993)]{jaffe1993geographic} Jaffe, A.~B., Trajtenberg, M., \& Henderson, R. (1993). Geographic localization of knowledge spillovers as evidenced by patent citations. \textit{Quarterly Journal of Economics}, 108(3), 577--598.

\bibitem[Kikuchi(2024a)]{kikuchi2024unified} Kikuchi, T. (2024a). \newblock A unified framework for spatial and temporal treatment effect boundaries: Theory and identification. \newblock arXiv preprint arXiv:2510.00754.

\bibitem[Kikuchi(2024b)]{kikuchi2024stochastic} Kikuchi, T. (2024b). \newblock Stochastic boundaries in spatial general equilibrium: A diffusion-based approach to causal inference with spillover effects. \newblock arXiv preprint arXiv:2508.06594.

\bibitem[Kikuchi(2024c)]{kikuchi2024navier} Kikuchi, T. (2024c). \newblock Spatial and temporal boundaries in difference-in-differences: A framework from Navier-Stokes equation. \newblock arXiv preprint arXiv:2510.11013.

\bibitem[Kikuchi(2024d)]{kikuchi2024nonparametric} Kikuchi, T. (2024d). \newblock Nonparametric Identification and Estimation of Spatial Treatment Effect Boundaries: Evidence from 42 Million Pollution Observations. \newblock arXiv preprint arXiv:2510.12289.

\bibitem[Li and Racine(2007)]{li2007nonparametric} Li, Q., \& Racine, J.~S. (2007). \textit{Nonparametric Econometrics: Theory and Practice}. Princeton University Press.

\bibitem[March(1976)]{march1976ambiguity} March, J.~G. (1976). The technology of foolishness. In J.~G.~March \& J.~P.~Olsen (Eds.), \textit{Ambiguity and Choice in Organizations} (pp.~69--81). Universitetsforlaget.

\bibitem[Muller(1989)]{muller1989kernel} Muller, H.-G. (1989). Adaptive nonparametric peak estimation. \textit{The Annals of Statistics}, 17(3), 1053--1069.

\bibitem[Muller and Machado(2011)]{muller2011machado} Muller, N.~Z., \& Machado, R.~M. (2011). External costs of power plants from the U.S.: Air pollution, human health, and land disturbance. \textit{American Economic Review}, 101(5), 2264--2294.

\bibitem[M\"uller and Mendelsohn(2011)]{muller2011mendelsohn} M\"uller, N.~Z., \& Mendelsohn, R. (2011). Efficient pollution regulation: Getting the prices right. \textit{American Economic Review}, 101(5), 1714--1739.

\bibitem[M\"uller et al.(2016)]{muller2016measuring} M\"uller, N.~Z., Mendelsohn, R., \& Nordhaus, W. (2016). Environmental accounting for pollution in the United States economy. \textit{American Economic Review}, 106(8), 2180--2222.

\bibitem[Nguyen(2019)]{nguyen2019bank} Nguyen, H.-L.~Q. (2019). Are credit markets still local? Evidence from bank branch closings. \textit{American Economic Journal: Applied Economics}, 11(1), 1--32.

\bibitem[Petersen and Rajan(2002)]{petersen2002does} Petersen, M.~A., \& Rajan, R.~G. (2002). Does distance still matter? The information revolution in small business lending. \textit{Journal of Finance}, 57(6), 2533--2570.

\bibitem[Robinson(2011)]{robinson2011asymptotic} Robinson, P.~M. (2011). Asymptotic theory for nonparametric regression with spatial data. \textit{Journal of Econometrics}, 165(1), 5--19.

\bibitem[Rossi-Hansberg et al.(2019)]{rossi2019air} Rossi-Hansberg, E., Sarte, P.-D., \& Owens III, R. (2019). Housing externalities. \textit{Journal of Political Economy}, 118(3), 485--535.

\bibitem[Ruppert and Wand(1994)]{ruppert1994multivariate} Ruppert, D., \& Wand, M.~P. (1994). Multivariate locally weighted least squares regression. \textit{The Annals of Statistics}, 22(3), 1346--1370.

\end{thebibliography}