Journal of Productivity Analysis

, Volume 43, Issue 1, pp 85–97 | Cite as

Constrained nonparametric estimation of input distance function



This paper proposes a constrained nonparametric method of estimating an input distance function. A regression function is estimated via kernel methods without functional form assumptions. To guarantee that the estimated input distance function satisfies its properties, monotonicity constraints are imposed on the regression surface via the constraint weighted bootstrapping method borrowed from statistics literature. The first, second, and cross partial analytical derivatives of the estimated input distance function are derived, and thus the elasticities measuring input substitutability can be computed from them. The method is then applied to a cross-section of 3,249 Norwegian timber producers.


Nonparametric estimation Input distance function Constraints Elasticities 

JEL Classification

C14 D24 



The author would like to thank Gudbrand Lien for providing the data set, Daniel J. Henderson, Subal C. Kumbhakar, Christopher F. Parmeter, attendees at the 2011 Econometric Society North American Winter Meeting, and the two anonymous referees for useful comments. The author is responsible for any remaining errors.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Economics and Strategy Group, Aston Business SchoolAston UniversityBirminghamUK

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