Free Discontinuity Design: With an Application to the Economic Effects of Internet Shutdowns

Author:

Florian Gunsilius, David Van Dijcke

Keyword:

Economics, Econometrics, Econometrics (econ.EM), Computer Vision and Pattern Recognition (cs.CV), Statistics Theory (math.ST), Applications (stat.AP), Methodology (stat.ME)

journal:

date:

2023-09-25 16:00:00

Abstract

Thresholds in treatment assignments can produce discontinuities in outcomes, revealing causal insights. In many contexts, like geographic settings, these thresholds are unknown and multivariate. We propose a non-parametric method to estimate the resulting discontinuities by segmenting the regression surface into smooth and discontinuous parts. This estimator uses a convex relaxation of the Mumford-Shah functional, for which we establish identification and convergence. Using our method, we estimate that an internet shutdown in India resulted in a reduction of economic activity by over 50%, greatly surpassing previous estimates and shedding new light on the true cost of such shutdowns for digital economies globally.

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