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Statistics Seminar

Detecting Changes in Production Frontier and Beyond

With Yining Chen (LSE)

Detecting Changes in Production Frontier and Beyond

In this talk, we first give a brief review of the nonparametric estimation problem of production frontier function, which concerns the maximum possible output given input levels and the efficiency of the firms. We then look at how multiple changes over time in the production frontier can be detected. By assuming that the frontier always shifts upwards over time, which is plausible thanks to the advance in technologies, we can detect changes in the frontier at the near-optimal rate under regularity conditions, irrelevant of the dimensionality of the input. This can be achieved by modifying and utilising the well-known Free Disposal Hull (FDH) or Data Envelopment Analysis (DEA) algorithm in different ways, depending on whether the shift is local or global. Finally, we discuss how the confidence intervals for both the location of the change and the frontier can be constructed. For the latter, we also illustrate how nuisance parameters in the limit distribution can be eliminated by taking advantage of the structure of the FDH , and demonstrate how this idea can be useful for other problems such as testing the shape of the frontier.

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