Detecting Changes in Production Frontiers

TL;DR

This paper introduces a nonparametric change point detection method for identifying when technological levels shift in an economy, with theoretical guarantees and practical applications demonstrated through simulations and real data.

Contribution

It develops a minimax optimal offline change point detection procedure for technological shifts in production frontiers, including confidence interval construction and local change adaptation.

Findings

Achieves near minimax localization rates for change points.

Provides a simple method for confidence intervals of change locations.

Demonstrates effectiveness through simulations and real data examples.

Abstract

We study the problem of estimating locations in time at which the level of technology in an economy changes when given a sequence of time ordered inputs and outputs. We approach the problem through the lens of nonparametric frontier analysis with frontiers that expand sharply and globally over time, and develop an offline change point detection procedure which achieves the minimax localization rates for the problem at hand up to logarithmic factors. We additionally give a simple method for constructing confidence intervals for the unobserved change point locations. Finally, we explain how the procedure can be modified to accommodate local changes in technology, meaning that efficiency gains are only realized for certain combinations of inputs. Simulation studies and real data examples are also presented to illustrate the practical value of our methods.