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Estimating alternative technology sets in nonparametric efficiency analysis: restriction tests for panel and clustered data

Nonparametric efficiency analysis has become a widely applied technique to support industrial benchmarking as well as a variety of incentive-based regulation policies. In practice such exercises are often plagued by incomplete knowledge about the correct specifications of inputs and outputs. Simar and Wilson (Commun Stat Simul Comput 30(1):159–184, 2001) and Schubert and Simar (J Prod Anal 36(1):55–69, 2011) propose restriction tests to support such specification decisions for cross-section data. However, the typical oligopolized market structure pertinent to regulation contexts often leads to low numbers of cross-section observations, rendering reliable estimation based on these tests practically unfeasible. This small-sample problem could often be avoided with the use of panel data, which would in any case require an extension of the cross-section restriction tests to handle panel data. In this paper we derive these tests. We prove the consistency of the proposed method and apply it to a sample of US natural gas transmission companies from 2003 through 2007. We find that the total quantity of natural gas delivered and natural gas delivered in peak periods measure essentially the same output. Therefore only one needs to be included. We also show that the length of mains as a measure of transportation service is non-redundant and therefore must be included.