Nonparametric frontier estimation via local exponential regression: an application to bank agencies in the United States Carlos Martins-Filho,1 Hudson Torrent2 and Flavio Ziegelmann3 March, 2010
Abstract. In this paper we consider the estimation of a nonparametric frontier model first proposed in Martins-Filho and Yao (2007). We improve their estimation procedure by adopting a variant of the local exponential smoothing introduced in Ziegelmann (2002). Our estimator is shown to be consistent and asymptotically normal under mild regularity conditions. In addition, due to local exponential smoothing, potential negativity of conditional variance functions that may hinder the use of Martins-Filho and Yao’s estimator is avoided. A Monte Carlo study is performed to shed light on the finite sample properties of the estimator and to contrast its performance with that of the estimator proposed in Martins-Filho and Yao (2007). We also perform an empirical data analysis, estimating the frontier curves and efficiencies for United States bank agencies. Overall we find that there can be significant improvements in finite sample performance when using exponential smoothing in this context. Keywords and phrases. exponential regression.
nonparametric frontier models; local exponential smoothing; local
JEL Classifications. C14, C21 AMS-MS Classification. 62G05, 62G08, 62G20.
1 Department of Economics, University of Colorado, Boulder, CO 80309-0256, USA, email:
[email protected] and IFPRI, 2033 K Street NW, Washington, DC 20006-1002, USA, email:
[email protected] 2 Department of Economics, Federal University of Rio Grande do Sul, Porto Alegre, RS 90040-000, Brazil, email:
[email protected] 3 Department of Statistics, Federal University of Rio Grande do Sul, Porto Alegre, RS 90040-000, Brazil, email:
[email protected] and Department of Statistics, London School of Economics, London, WC2A 2AE UK.
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Introduction
There exists a large and growing literature on the specification and estimation of production frontiers in economics. Simar and Wilson (2006) provide a an extensive review of recent developments. The main objective in this literature can be stated simply. Let Ψ = {(x, y) ∈
