Constrained nonparametric estimation of input distance function

Kai Sun

Research output: Contribution to journalArticle


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.
Original languageEnglish
Pages (from-to)85-97
Number of pages13
JournalJournal of Productivity Analysis
Issue number1
Early online date23 Nov 2013
Publication statusPublished - 1 Feb 2015


Bibliographical note

The final publication is available at Springer via


  • nonparametric estimation
  • input distance function
  • constraints
  • elasticities

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