Working Papers
Estimation of distribution functions, their jumps and interval probabilities under measurement error
with Kairat Mynbaev and Carlos Martins-Filho
Submitted
We consider the classical additive measurement-error model 𝑋 = 𝑌 + 𝑍, where the latent random variable 𝑌 has unknown distribution 𝐹ᵧ and the error 𝑍 has a known distribution. We develop direct estimators for three functionals of 𝐹ᵧ: (i) 𝐹ᵧ(𝑥) at continuity points; (ii) interval probabilities 𝐹ᵧ(𝑦) − 𝐹ᵧ(𝑥) when 𝑥 < 𝑦 are continuity points; and (iii) the size of a jump at a prespecified discontinuity. We derive non-asymptotic bias and variance bounds, and establish asymptotic unbiasedness and consistency. Unlike previous work, we do not require 𝐹ᵧ to admit a density, have a mixture representation, or satisfy global Sobolev smoothness assumptions. The framework accommodates arbitrary latent distributions, including those with both discrete and continuous components, and distributions with multiple jumps. These results rely on a link between Fourier inversion theorems and the algebraic structure of a class of estimators proposed in Mynbaev, Martins-Filho and Henderson (2022). A simulation study evaluates feasible tuning procedures and, where available, compares the finite-sample performance of the proposed estimators with existing methods.
Under Review
This paper develops theory for deep neural network (DNN) estimators under dependent data. To provide theory applicable to a variety of DNN-based estimators, I first establish nonasymptotic probability bounds on the theoretical and empirical L2 -errors of nonparametric sieve estimators for a general class of estimation problems under possibly nonstationary β-mixing data taking values in unbounded sets. I then apply the theory to fully connected and convolutional DNN estimators without bounds or sparsity restrictions on the DNN weights. For both DNN classes, I derive general results when the function to be estimated is Hölder smooth and the data are nonstationary, subgaussian, and β-mixing with either exponential or polynomial decay. I then specialize these to nonparametric regression, logistic regression, and quantile regression settings. Under exponential β-mixing, the resulting estimators attain the nonparametric minimax rate of Stone (1982) up to logarithmic factors.
Previous version: https://arxiv.org/abs/2410.11113v3
Publications
with Jeronimo Carballo and Alessandro Peri
Journal of Law and Economics, 2024
Focusing on Chapter 11 bankruptcy reorganizations of publicly listed firms during the court competition era (1991–96), we document local legal employment effects of forum shopping, a stipulation of the law that allows firms to file for bankruptcy far from their headquarters. Bankruptcy shocks increase legal-sector employment in the bankrupt firm’s locale, but forum shopping nullifies this effect. Employment gains of received forum-shopped cases are concentrated in Delaware, with no effect in other receiving forums. Quantification shows that Delaware handled these forum-shopped bankruptcies with just one-fifth of the additional legal workforce that would have been needed if the cases were handled in the firms’ locales. This increase in productivity also coincides with substantial missed potential employment gains in communities where bankruptcies were diverted through forum shopping. The analysis uncovers meaningful effects of forum shopping on local legal labor markets, so far overlooked in the policy debate.
Previously circulated as: "Bankruptcy Shocks and Legal Labor Markets: Evidence from the Court Competition Era".
Works in Progess
Inference after Machine Learning under Dependent Data with Kyle Butts and Lucas Ladenburger
Value Function Convergence and Deep Learning with Alessandro Peri
Uniform Convergence of Deep Neural Network Sieve Estimators
Resting Papers
I consider inference in a partially linear regression model under stationary β-mixing data after first stage deep neural network (DNN) estimation. Using the DNN results of Brown (2024), I show that the estimator for the finite dimensional parameter, constructed using DNN-estimated nuisance components, achieves √n-consistency and asymptotic normality. By avoiding sample splitting, I address one of the key challenges in applying machine learning techniques to econometric models with dependent data. In a future version of this work, I plan to extend these results to obtain general conditions for semiparametric inference after DNN estimation of nuisance components, which will allow for considerations such as more efficient estimation procedures, and instrumental variable settings.