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In the third chapter, "Fuzzy Bunching", we introduce a new fuzzy bunching approach that is robust to noise. The existing bunching approach identifies the extent of bunching from a sharp spike in the probability density function. In many finance settings, however, the sharp spike could be diffused by data noise. The key idea behind our fuzzy bunching estimator is to identify bunching from the area of a bulge in the cumulative distribution function. The fuzzy bunching approach also avoids density estimation, which makes it easy to implement in sparse data. We provide the theoretical foundation of this approach and illustrate the advantages by using simulated and real data.

We show that distortion in the size distribution of banks around regulatory thresholds can be used to identify costs of bank regulation. We build a structural model in which banks can strategically bunch their assets below regulatory thresholds to avoid regulations. The resulting distortion in the size distribution of banks reveals the magnitude of regulatory costs. Using U.S. bank data, we estimate the regulatory costs imposed by the Dodd-Frank Act. Although the estimated regulatory costs are substantial, they are significatnly lower than those in self-reported estimates by banks.